Multilevel modelling with R

An introduction with applications on wearable & mobile-based
intensive longitudinal data

Luca Menghini, Ph.D.

University of Padova, Italy

***
Post-conference workshop

17th conference Eu Academy of Occupational Health Psychology
Helsinki, 15-17 June, 2026

Powered by PSICOSTAT

2026-06-18

Course material

Course material is available on GitHub:

https://luca-menghini.github.io/Multilevel-modelling-with-R/

About myself

Luca Menghini

W/O Psychologist,
Assistant Professor
University of Padova, Italy

2016: Msc in Work Psychology
2016:
2017: Consultance internship
Biofeedback training in professional drivers
2018-19:
2020: Visiting @SRI International (USA)
Wearable sleep trackers performance
2021: Ph.D. @PsyPhyLab @uniPadova
EMA of workplace stress
2021: Post-doc @uniBologna
The daily costs of workaholism
2022: Post-doc @uniTrento
Youth transition pathways
2023: Assistant Prof. @HTLab @uniPadova
Digitalization, work-life balance, & lifestyles

About yourselfs

ESM study on burnout & resilience (5/d × 10d): pre-ESM-post
ESM study on playful work & flow (1/d × 5d) by POS (cross-level)

Workshop outline

ILD × OHP
Investigating within-person relationships of stressors & strain
R basics
Warm up & loading data
LMER intro
From linear models to multilevel modelling
HandZone
From data pre-processing to cross-level interactions
LMER advanced
3-level models, growth curve and cross-lagged models, mediation, GLMER

Intensive Longitudinal Designs
in Occupational Health Psychology

Intensive Longitudinal Designs (ILD)

Umbrella term for data sampling techniques involving numerous data points (e.g., 10-to-50 observations per participant) and short time lags (e.g., minutes, days, weeks) to capture temporal dynamics that cannot be unravelled with lower sampling rates
Bolger and Laurenceau (2013); Revelle and Wilt (2019)

Goal: “to study people’s thoughts, feelings, physiology, and behaviors in situ with enough repeated measurements to model change processes for each individual” (Laurenceau et al 2026)
Continuous, momentary, daily, weekly, monthly

ILD landscape

Ambulatory Assessment
Ecological methods to assess ongoing behaviors and physiology in natural environments
Society for Ambulatory Assessment
Experience Sampling Methods
Repeated sampling of ongoing psychology, experiences, and activities to study their intensity, frequency, and temporal patterns
Csikszentmihalyi (1987)
Ecological Momentary Assessment
Repeated sampling of subjects’ behaviors and experiences
in real time, in participants’ natural environments
Shiffman et al (2008)

Which designs?

Signal-contingent sampling: Recording at fixed (e.g., hourly, daily, weekly),
random (whatever time), or semi-random intervals (e.g., each 90 ± 30 min)
Event-contingent sampling: Recording conditional to events
(e.g., bedtime, activity, physiological trigger)
Continuous sampling: Passive monitoring (e.g., pedometer)

Advanced designs

Experimental designs:
RCT, Ecological Momentary Interventions, and Just-in-time adaptive interventions (JITAI)
Measurement Burst Designs:
ILD 1 $\rightarrow$ time lag/intervention $\rightarrow$ ILD 2
Dyadic ILDs:
leader-employee, employee-spouse, etc.
Methodological triangulation:
e.g., other-report, physiological, behavioral

Sonnentag et al (2026)

Wearable technology

de Zambotti, M., Cellini, N., Menghini, L., Sarlo, M., & Baker, F. C. (2020). Sensors capabilities, performance, and use
of consumer sleep technology. Sleep medicine clinics, 15(1), 1-30. https://doi.org/10.1016/j.jsmc.2019.11.003

Laboratory vs. Ambulatory assessment

Real-time recording
High internal validity
Low ecological validity
Gold-standard recording

Real-time recording
Low internal validity
High external validity
Ambulatory recording

Measurement reactivity (e.g., white coat effect)
Lab-to-real world generalizability: Lab stressors
are not representative of ‘natural’ stressors in terms of
duration, number, nature, and intensity

Laboratory vs. Ambulatory assessment

Wilhelm & Grossman (2010)

From ILD to Multilevel modelling

When a random variable is measured repeatedly, multilevel models partition the variance into within-subject (lv1) and between-subject (lv2).
The same when individuals (e.g., workers) are nested within groups (e.g., teams)

Between (lv2): Stable individual traits (time-invariant component)
Do individuals with higher trait rumination sleep less hours than individuals with lower trait rumination?
Within (lv1): Variable transient states (time-varying component)
Does individuals sleep less hours than usual in those days where they ruminate more than usual?

Short introduction to R

Why ?

R is an open source programming language and environment
for statistical computing and graphics.

Open source (not a black box)
Reproducible & fully controllable
User friendly (optimized default functions)
High-quality outputs
Integrated with LateX, Markdown, Quarto, etc.
Documented: try ?mean + thousands of tutorials
Still don’t know how to do it? Ask LLM ;)
Free software (GNU GP, usable anywhere worldwide)
Community-based:
R Core Team periodically updating base R
+ thousands of researchers developing
new packages exponentially

RStudio

= Development environment for using an optimized graphical interface
to make it simpler.

Console: Just write a command and execute it with Enter
Source: R Scripts (.R), docs & presentations (.Rmd/qmd), GUIs (.app), etc.
To run a command, select it and tap Ctrl + Enter or click on the Run button on the top-right
Environment: R objects included in the workspace

Some basic commands

Comments (#)
```
# this is a comment
```

Simple mathematical operations

2 + 2 # sum

[1] 4

2 * 2 # multiplication

[1] 4

log(3) # natural logarithm

[1] 1.098612

exp(1) # exponential function

[1] 2.718282

Longer expressions

sqrt(5) * ( (4 - 1/2)^2 - pi/2^(1/3) )

[1] 21.81623

Assigning values to objects (<-)

x <- 3 # creates the 'x' object with value 3
x # pint the value of x

[1] 3

Objects’ names can include letters, numbers, underscores, and, dots (e.g. tony, tony.1_)

tony_32 <- x / 3 # assign a value to the object
tony_32 # print the object's value

[1] 1

Key-sensitive but not sensitive to spaces

Tony_32

3+tony_32; 3     +  tony_32

[1] 4

[1] 4

Assign $log(\sqrt{5.5^2})$ to object a and $(3 \times 2.2)^2/4$ to object b;
then sum the two objects (should be 13.45)

Relational & logical operators

Relational operators

3 == 3 # equal to

[1] TRUE

3 != 3 # different from

[1] FALSE

x >= 3 # higher than or equal to

[1] TRUE

5 %in% c(3, 5, 8) # included in

[1] TRUE

Logical operators

x <- TRUE
y <- !x # negation of y
x & (5 < 2) # joined condition

[1] FALSE

x | (5 < 2) # inclusive disjoint

[1] TRUE

Write a command to test whether object a is equal to object b
or higher than the sum of a + b (should be FALSE)

Types of R objects (classes)

Logical

x <- TRUE
x <- T # "TRUE" or "T" is the same
class(x)

[1] "logical"

Numeric
```
x <- 1.4
class(x)
```
```
[1] "numeric"
```
Integer
```
as.integer(x)
```
```
[1] 1
```

Character

x <- "I    like R"
x # within "" the space matters!

[1] "I    like R"

Vector: series of values with the same class (e.g., all numeric) combined with the function c() (combine)

x <- c(1, 10.5, 3, 2)
x + 1

[1]  2.0 11.5  4.0  3.0

sqrt(x)

[1] 1.000000 3.240370 1.732051 1.414214

y <- c("I","like", "R")

Matrix: table with nrow * ncol

x <- matrix(1:12, nrow = 3, ncol = 4)
rownames(x) <- y # row names
x

     [,1] [,2] [,3] [,4]
I       1    4    7   10
like    2    5    8   11
R       3    6    9   12

Types of R objects: `data.frame`

Bidimensional structure of vectors with different classes (e.g., numeric, character, factor): data.frame(name_var1 = c(...), name_var2 = ...)

str(df_name) returns the df structure

x <- data.frame( # create df
   Num = 1:4,
   Char = c("a","b","c","d"),
   Logi = c(T,F,F,T))
x # print df

  Num Char  Logi
1   1    a  TRUE
2   2    b FALSE
3   3    c FALSE
4   4    d  TRUE

str(x) # df structure

'data.frame': 4 obs. of  3 variables:
 $ Num : int  1 2 3 4
 $ Char: chr  "a" "b" "c" "d"
 $ Logi: logi  TRUE FALSE FALSE TRUE

To select a column (vector) from a dataframe, we can use the $ symbol with the syntax df_name$column_name

x$Char # selecting the Char column

[1] "a" "b" "c" "d"

x$Char[2] # second value from the Char column

[1] "b"

x$Char[2] == x[2,2] # equivalent commands

[1] TRUE

x[x$Num < 3,] # selecting cases with Num < 3

  Num Char  Logi
1   1    a  TRUE
2   2    b FALSE

Create a data.frame with a column for students names (i.e., Jon, Jin, Jun)
and a column for grades (i.e., 10, 6, 8); then select the row corresponding to Jin.

How to load your data: set the work directory

To read a file from a specific folder, you should first get or set the working directory (WD), that is the folder where input files are searched and where output files are saved.

# prints the current WD
getwd() 

# changes WD to the 'data' subfolder
setwd("data") 

# set a new WD
setwd("C:/Users/mengh/OneDrive/Desktop") # set new WD

Trick with RStudio: when you start a new project (e.g., data analysis for the thesis, report), create a new R project (.Rproj) from the menu File > New R Project by selecting an existing folder or by creating a new one, which will be the default WD for any file related to that project

Get your WD; create a folder on your desktop and set it as your new WD

How to load your data: data reading

The first step in any data analysis with R is to read a dataset To do so, we need to use a specific function depending on the data format (e.g., CSV, xlsx, txt, sav).

The default R data format is RData.

load(file = "data/S2_data.RData") # import
save(qs, file = "data/S2_data.RData") # export

But it can read and export further data formats,
some of which require to install additional packages.

# Comma separated values (csv)
qs <- read.csv(file = "data/S2_data.csv") # import
write.csv(x = qs,"data/S2_data.csv") # export

# SAV (SPSS)
library(foreign)
qs <- read.spss("data/studqs.sav",to.data.frame=T)

Download the S2_data file from osf.io/awbxj/files/nv7ux
Save it in your WD; read it in R calling it “dat”
Inspect the dataset with the command View(dat)

Which dataset is it?

…we developed and evaluated parsimonious measures of momentary stressors (Task Demand and Task Control) and the Italian adaptation of the Multidimensional Mood Questionnaire as an indicator of momentary strain (Negative Valence, Tense Arousal, and Fatigue). Data from 139 full-time office workers that received seven experience sampling questionnaires per day over 3 workdays suggested satisfactory validity…

…Using an intensive longitudinal design over 10 workdays with 114 workers from various occupations (2,534 measurement occasions), we found higher systolic and diastolic blood pressure, emotional exhaustion, and sleep disturbances in workdays characterized by higher-than-usual workaholism symptoms … Finally,we found evidence of a buffering effect of evening psychological detachment…

The dataset

ID: participant’s code
day: participation day (1-10)
SBP_aft, DBP_aft: blood pressure in the afternoon (mmHg)
WHLSM1 … WHLSM6: state workaholism (1-7)
SBP_eve, DBP_eve: blood pressure in the evening (mmHg)
EE1 … EE4: emotional exhaustion at bedtime (1-7)
R.det1 … R.det3: psych detachment in the evening (1-7)
SQ1 … SQ4: morning ratings of sleep disturbances (1-7)
gender: “F” or “M”
age: years of age
BMI: body mass index ($kg/m^2$)
IN.resp: response rate inclusion criteria (TRUE/FALSE)
IN.bp: blood pressure inclusion criteria (TRUE/FALSE)

str(dat) # data structure

'data.frame':   1084 obs. of  28 variables:
 $ X      : int  1 2 3 4 5 6 7 8 9 10 ...
 $ ID     : chr  "S001" "S001" "S001" "S001" ...
 $ day    : int  1 2 3 4 5 7 8 9 10 11 ...
 $ SBP_aft: num  130 114 114 120 112 ...
 $ WHLSM1 : int  3 6 5 3 3 3 2 3 2 3 ...
 $ WHLSM2 : int  2 6 6 3 2 3 2 3 2 4 ...
 $ WHLSM3 : int  1 6 1 2 1 1 1 1 3 1 ...
 $ WHLSM4 : int  2 4 2 1 3 3 2 3 2 3 ...
 $ WHLSM5 : int  1 2 1 1 1 1 1 1 2 1 ...
 $ WHLSM6 : int  1 3 5 2 3 4 2 5 2 5 ...
 $ SBP_eve: num  122 108 106 113 112 ...
 $ DBP_eve: num  77 76 66.5 75 74 75.5 80 76 86.5 84 ...
 $ EE1    : int  5 6 7 4 3 5 5 5 5 5 ...
 $ EE2    : int  5 4 5 3 2 5 4 5 5 4 ...
 $ EE3    : int  4 1 2 2 2 5 3 1 3 1 ...
 $ EE4    : int  2 1 1 2 2 5 1 1 4 1 ...
 $ R.det1 : int  3 2 2 1 1 2 2 4 3 4 ...
 $ R.det2 : int  2 1 3 1 1 2 3 4 3 3 ...
 $ R.det3 : int  6 4 5 1 1 2 4 5 5 6 ...
 $ SQ1    : int  2 1 1 3 2 2 2 1 2 2 ...
 $ SQ2    : int  3 1 1 3 1 1 2 1 2 1 ...
 $ SQ3    : int  1 1 1 3 1 1 1 1 2 2 ...
 $ SQ4    : int  1 1 1 2 1 1 1 1 2 1 ...
 $ gender : chr  "F" "F" "F" "F" ...
 $ age    : int  59 59 59 59 59 59 59 59 59 59 ...
 $ BMI    : num  18.8 18.8 18.8 18.8 18.8 ...
 $ IN.resp: logi  TRUE TRUE TRUE TRUE TRUE TRUE ...
 $ IN.bp  : logi  TRUE TRUE TRUE TRUE TRUE TRUE ...

Workspace: Functions & packages

Many things in R can be done by using functions, which always include the function name and arguments (arg_name = arg_value or without name, based on the default position)
```
mean(x = c(1,2,3))
```
```
[1] 2
```
```
mean(c(1,2,3))
```
```
[1] 2
```
R Help system: To know the details of any function (arguments, value, etc.), just add the ? symbol before the function name
```
?mean
```

R packages: To get additional functions than those included in the base R packages, you need to install and open the related package
```
install.packages("pkg_name") # install
library(pkg_name) # open package
```

Compute the mean of the variable SBP_aft for each participant ID using the function aggregate with the following syntax:

aggregate(variable ~ participant, 
          data = mydataset, FUN = function, 
          na.rm = TRUE)

Install the package psych and use the describe function to compute the descriptive statistics of the variables SBP_aft and WHLSM1

Time for a (micro) break!

But before it write this code on your console and run

install.packages("multilevelTools") # reliability
install.packages("plyr") # data merging
install.packages("lme4") # multilevel
install.packages("sjPlot") # visuals

LMER intro:
From linear models
to multilevel modelling

Linear models (LM)

LM allow to determine the link between two variables
as expressed by a linear function: $y_i = \beta_0 + \beta_1 x_i + \epsilon_i$
which can be graphically represented as a straight line, where:

$\beta_0$ is the intercept (value assumed by $y$ when $x = 0$)
$\beta_1$ is the slope (predicted change in $y$ when $x$ increases by 1 unit)
$\epsilon_i$ are the errors (distance between observation $i$ and the regression line)

$x_i$ and $y_i$ are the values of observation $i$
for the casual variables $x$ and $y$
$\beta_0$, $\beta_1$, and $\epsilon_i$ are called “parameters”, or “coefficients”. They are estimated from the sampled data and generalized to the whole population.

LM core assumptions

Linearity: $x_i$ and $y_i$ are linearly associated
$\rightarrow$ the expected (mean) value of $\epsilon_i$ is zero
Normality: Residuals $\epsilon_i$ are normally distributed with $\epsilon_i \sim \mathcal{N}(0,\,\sigma^{2})$
Homoscedasticity: $\epsilon_i$ variance is constant over the levels of $x_i$ (homogeneity of variance)
Independence of predictors & errors: Predictors $x_i$
are unrelated to residuals $\epsilon_i$
Independence of observations
For any two observations $i$ and $j$ with $i \neq j$, the residual terms $\epsilon_i$ and $\epsilon_j$ are independent (no common disturbance factors)

Linear models in

Basic syntax:

# null model
m0 <- lm( y ~ 1, data = mydataset)

# simple regression
m1 <- lm( y ~ x1, data = mydataset)

# multiple regression
m2 <- lm( y ~ x1 + x2 + x3 + ..., 
          data = mydataset)

For instance:

# fit model
m <- lm( SBP_aft ~ WHLSM1, data = dat )

# results
summary(m)$coefficients

              Estimate Std. Error   t value     Pr(>|t|)
(Intercept) 115.200802  1.3641239 84.450398 0.000000e+00
WHLSM1        1.783148  0.3159729  5.643356 2.230611e-08

# fit and assumptions
par(mfrow=c(2,2),mai=rep(0.3,4)); plot(m)

Nested data & Local dependencies

   Person Time   Y
1    Lumi    1 3.0
2    Lumi    2 2.5
3    Lumi    3 2.2
4    Lumi    4 2.8
5    Lumi    5 2.0
6   Toivo    1 0.0
7   Toivo    2 0.5
8   Toivo    3 0.2
9   Toivo    4 1.0
10  Toivo    5 0.8

Repeated-measure designs always result in nested data structures where level-1 individual observations
(i.e., statistical units) are nested within level-2 cluster variables (e.g., participants)
Nested data structures are incompatible with the LM assumption of independence of observations
Local dependencies = correlations that exist among observations within a specific cluster
(but the software doesn’t know!)
- Biased standard errors (++ false positives)
- Neglected cluster-level variables potentially affecting
  level-1 relationships (e.g., cross-level interactions)

Linear mixed-effects regression models (LMER)

Multilevel models are part of the largest LMER family that include
additional variance terms for handling local dependencies.

Why ‘mixed-effects’?
Because such additional terms come from the distinction between:
- Fixed effects: effects that remain constant across clusters whose levels are exhaustively considered by the researcher (e.g., gender, steps of Likert scales, experimental conditions)
- Random effects: effects that vary from cluster to cluster whose levels are randomly sampled from a population (e.g., organizations, people)

Let the visuals talk!
http://mfviz.com/hierarchical-models/
Michael Freeman (2017)

From LM to LMER

LM formula: $y_i = \beta_0 + \beta_1 x_i + \epsilon_i$

Intercept and slope are constant across all individual observations $i$ within the population
$x$, $y$, and the error term $\epsilon$ only variate across individual observations $i$

LMER formula: $y_{i{\color{purple}j}} = \beta_{0{\color{purple}j}} + \beta_{1{\color{purple}j}} x_{i{\color{purple}j}} + \epsilon_{i{\color{purple}j}}$

Intercept and slope have both a fixed ($_{0/1}$) and a random component ( $_j$)
$y$, $x$, and $\epsilon$ vary across individual observations $i$ as well as across clusters $\color{purple}j$

\[ y_{ij} = \color{blue}{\beta_{0j}} + \color{red}{\beta_{1j}}x_{ij} + \epsilon_{ij} = \color{blue}{(\beta_{00} + \lambda_{0j})} + \color{red}{(\beta_{10} + \lambda_{1j})}x + \epsilon_{ij} \]

LMER are an extension of LM where the intercept and the slope are decomposed into:
- the fixed components $\color{blue}{\beta_{00}}$ and $\color{red}{\beta_{10}}$, referred to the whole sample
- the random components $\color{blue}{\lambda_{0j}}$ and $\color{red}{\lambda_{1j}}$, randomly varying across clusters

Random intercept

Let’s start with a null model (intercept-only) where Burnout ($y_{ij}$)
is only predicted by the intercept $\beta_{00}$ and the residuals $\epsilon_{ij}$

LM: $y_{i} = \beta_0 + \epsilon_i$
The intercept value $\beta_0$ is common to all observations
LMER: $y_{i{\color{blue}j}} = \beta_{0{\color{blue}j}} + \epsilon_{i{\color{blue}j}} = (\beta_{00} + \color{blue}{\lambda_{0j}}) + \epsilon_{ij}$
- $\beta_{00}$ is the fixed intercept that applies to all observations = sample’s grand average
- $\lambda_{0j}$ is the random intercept = cluster-specific deviation from the fixed intercept
  = person’s average burnout - sample’s grand average

Random slope

Let’s now add a predictor: Workload levels $x_{ij}$

Random intercept model

$y_{ij} = \color{blue}{\beta_{0j}} + \beta_1x_{ij} + \epsilon_{ij}$
$=\color{blue}{(\beta_{00} + \lambda_{0j})} + \beta_1x_{ij} + \epsilon_{ij}$

$y_{ij}$ is predicted by the overall mean Burnout $\beta_{00}$, its average relationship with Workload $\beta_{10}$, the random variation among clusters $\lambda_{0j}$ (random intercept), and the random variation within clusters $\epsilon_{ij}$ (residuals)

Random intercept & random slope model

$y_{ij} = \color{blue}{\beta_{0j}} + \color{red}{\beta_{1j}}x_{ij} + \epsilon_{ij}$
$=({\beta_{00} + \color{blue}{\lambda_{0j}}}) + ({\beta_{10} + \color{red}{\lambda_{1j}}}) x_{ij} + \epsilon_{ij}$

Since the effect of Workload might not be the same across all persons, we partition $\beta_{1}$ into the overall average relationship between calmness and physiological activity $\beta_{10}$ (fixed slope) and the cluster-specific variation in the relationship $\lambda_{1j}$ (random slope) - basically an interaction

From LMER to multilevel modelling

LMER is often called ‘multilevel modelling’ due to the underlying
variance decomposition of the $y_{ij}$ variable into the within-cluster and the between-cluster levels.

Indeed the LMER formula can be splitted in two separate levels:

\[ \begin{aligned} \text{Level 1 (within): } y_{ij} &= \beta_{0j} + \beta_{1j}x_{ij} + \epsilon_{ij} \\ \text{Level 2 (between): } \beta_{0j} &= \beta_{00} + \lambda_{0j} \\ \beta_{1j} &= \beta_{10} + \lambda_{1j} \end{aligned} \]

HandZone:
From data pre-processing
to cross-level interactions

The dataset

ID: participant’s code
day: participation day (1-10)
SBP_aft, DBP_aft: blood pressure in the afternoon (mmHg)
WHLSM1 … WHLSM6: state workaholism (1-7)
SBP_eve, DBP_eve: blood pressure in the evening (mmHg)
EE1 … EE4: emotional exhaustion at bedtime (1-7)
R.det1 … R.det3: psych detachment in the evening (1-7)
SQ1 … SQ4: morning ratings of sleep disturbances (1-7)
gender: “F” or “M”
age: years of age
BMI: body mass index ($kg/m^2$)
IN.resp: response rate inclusion criteria (TRUE/FALSE)
IN.bp: blood pressure inclusion criteria (TRUE/FALSE)

str(dat) # data structure

'data.frame':   1084 obs. of  28 variables:
 $ X      : int  1 2 3 4 5 6 7 8 9 10 ...
 $ ID     : chr  "S001" "S001" "S001" "S001" ...
 $ day    : int  1 2 3 4 5 7 8 9 10 11 ...
 $ SBP_aft: num  130 114 114 120 112 ...
 $ WHLSM1 : int  3 6 5 3 3 3 2 3 2 3 ...
 $ WHLSM2 : int  2 6 6 3 2 3 2 3 2 4 ...
 $ WHLSM3 : int  1 6 1 2 1 1 1 1 3 1 ...
 $ WHLSM4 : int  2 4 2 1 3 3 2 3 2 3 ...
 $ WHLSM5 : int  1 2 1 1 1 1 1 1 2 1 ...
 $ WHLSM6 : int  1 3 5 2 3 4 2 5 2 5 ...
 $ SBP_eve: num  122 108 106 113 112 ...
 $ DBP_eve: num  77 76 66.5 75 74 75.5 80 76 86.5 84 ...
 $ EE1    : int  5 6 7 4 3 5 5 5 5 5 ...
 $ EE2    : int  5 4 5 3 2 5 4 5 5 4 ...
 $ EE3    : int  4 1 2 2 2 5 3 1 3 1 ...
 $ EE4    : int  2 1 1 2 2 5 1 1 4 1 ...
 $ R.det1 : int  3 2 2 1 1 2 2 4 3 4 ...
 $ R.det2 : int  2 1 3 1 1 2 3 4 3 3 ...
 $ R.det3 : int  6 4 5 1 1 2 4 5 5 6 ...
 $ SQ1    : int  2 1 1 3 2 2 2 1 2 2 ...
 $ SQ2    : int  3 1 1 3 1 1 2 1 2 1 ...
 $ SQ3    : int  1 1 1 3 1 1 1 1 2 2 ...
 $ SQ4    : int  1 1 1 2 1 1 1 1 2 1 ...
 $ gender : chr  "F" "F" "F" "F" ...
 $ age    : int  59 59 59 59 59 59 59 59 59 59 ...
 $ BMI    : num  18.8 18.8 18.8 18.8 18.8 ...
 $ IN.resp: logi  TRUE TRUE TRUE TRUE TRUE TRUE ...
 $ IN.bp  : logi  TRUE TRUE TRUE TRUE TRUE TRUE ...

From data pre-processing to cross-level interactions

Data pre-processing
Cleaning, aggregating, and centering
Level-specific correlations
Are State Workaholism (SW) and Blood Pressure (BP) more strongly correlated at lv1 or lv2?
Null model & ICC
Does SBP vary more at lv1 or at lv2?
Main effects
Is BP higher than usual when SW is higher than usual?
Is it lower in females than in males?
Random slope & cross-level interactions
Is the within-subject relationship between SW and BP
moderated by participants’ gender?

1. Data pre-processing (1/3)

First, we need to prepare the dataset for the analysis:

1.1. Data cleaning: Removing noise from the data

Let’s turn multiverse!

Group 1 (left line):
No filtering

Group 2 (right line):
Exclude participants with CVD
or under CV meds

dat <- dat[dat$IN.bp == TRUE,]

1. Data pre-processing (2/3)

First, we need to prepare the dataset for the analysis:

1.2. Reliability & composite scores

Level-specific McDonald’s $\omega$s
Internal consistency at within-cluster and between-cluster level (i.e., not assuming equal factor loadings like $\alpha$)
Geldhof et al. (2014)

# a) selecting items
items <- c("x1","x2","x3","x4")

# b) estimating omegas from ML-CFA
library(multilevelTools)
omegaSEM(items, id = "participant", 
         data = mydataset)$Results

You should get something like this:

           label  est ci.lower ci.upper
43  omega_within 0.80    0.778    0.821
46 omega_between 0.92    0.895    0.945

# c) computing composite score
mydataset$X <- 
  apply(mydataset[,items], 1, mean)

    ID day WHLSM1 WHLSM2 ...       SW
1 S001   1      3      2 ... 1.666667
2 S001   2      6      6 ... 4.500000
3 S001   3      5      6 ... 3.333333
4 S001   4      3      3 ... 2.000000
5 S001   5      3      2 ... 2.166667
6 S001   7      3      3 ... 2.500000

1. Data pre-processing (3/3)

First, we need to prepare the dataset for the analysis:

1.3. Data centering = subtracting the mean of a variable from each variable value

# a) computing X and Y person mean (pm) for each participant
wide <- aggregate(cbind(X, Y) ~ participant, 
                  data = mydataset, FUN = mean, 
                  na.rm = TRUE)
colnames(wide) <- c("ID", "X_pm", "Y_pm") # renaming variables to avoid duplicated colnames
View(wide) # look at your results (wide-form dataset)

# b) joining cluster means to long-form dataset
library(plyr)
mydataset <- join(mydataset, wide, by="participant")

# c) person mean centering (pmc)
mydataset$X_pmc <- mydataset$X - mydataset$X_mean
mydataset$Y_pmc <- mydataset$Y - mydataset$Y_mean

You should get something like this:

   ID       SW SW_pm     SW_pmc SBP_aft SBP_aft_pm SBP_aft_pmc
 S001 1.666667  2.55 -0.8833333   129.5     117.75       11.75
 S001 4.500000  2.55  1.9500000   113.5     117.75       -4.25
 S001 3.333333  2.55  0.7833333   114.5     117.75       -3.25
 S001 2.000000  2.55 -0.5500000   120.0     117.75        2.25
 S001 2.166667  2.55 -0.3833333   111.5     117.75       -6.25
 S001 2.500000  2.55 -0.0500000   124.0     117.75        6.25

2. Level-specific correlations

Second, let’s see if the two variables correlate similarly across levels:

Level 1: Within-person correlation
= correlation between person-mean-centered scores
($n_1$ = number of observations)

cor(mydataset[,c("x_pmc","y_pmc")])

Within:

               SW_pmc SBP_aft_pmc
SW_pmc      1.0000000   0.1224328
SBP_aft_pmc 0.1224328   1.0000000

Level 2: Between-person correlation = correlation between person means
($n_2$ = number of participants)

cor(wide[,c("x_pm","y_pm")])

Between:

                SW_pm SBP_aft_pm
SW_pm      1.00000000 0.06014405
SBP_aft_pm 0.06014405 1.00000000

3. Null model & ICC

Third, let’s fit a null model (intercept-only) and compute the intraclass correlation coefficient (ICC) = Estimated proportion of between-cluster variance over the total variance
(0 = all within; 0.5 = half within, half between; 1 = all between)

# fitting a null LMER model
library(lme4)
m0 <- lmer(y ~ ( 1 | participant), data = mydataset)

# extracting variance components 
rinV <- summary(m0)$varcor$participant[[1]] # random intercept var (lv2)
resV <- summary(m0)$sigma^2 # residual var (lv1)
totV <- rinV + resV # total variance (lv1 + lv2)

# computing ICC = lv-2 variance / tot variance
rinV / totV

Here, the ICC is 0.68

4. Main effects (random intercept model)

Fourth, let’s include the 2 main effects of interest:

Level 1: SBP is predicted by cluster-mean-centered SW
Level 2: SBP is predicted by participants’ gender

# fitting additive model
m1 <- lmer(Y ~ X1 + X2 + (1|participant), data = mydataset)
summary(m1) # to inspect the model results

# visualize the results!
library(sjPlot)
plot_model(mymodel, type = "pred", terms = "X1")
plot_model(mymodel, type = "pred", terms = "X2")

Why centering level-1 predictors?

Because otherwise the estimated relationship is a mix of the within- and between-level relationships

A LMER model automatically decompose the $y_{ij}$ variance into the two components,
but the software doesn’t know about the predictors!
If a predictor $x_{ij}$ varies at both levels, then the resulting parameter is a mix
The person-mean-centered predictor only varies at the within-person level (i.e., all participants have mean = 0), focusing the estimated parameter at that level

The same result can be obtained by including both the uncentered predictor
and the corresponding person mean scores in the same model:

summary(lmer(SBP_aft ~ SW + SW_pm + (1 | ID), data = dat))$coefficients[2:3,]

        Estimate Std. Error   t value
SW     1.3164157  0.3840757  3.427490
SW_pm -0.2199844  1.1267617 -0.195236

summary(lmer(SBP_aft ~ SW_pmc + (1 | ID), data = dat))$coefficients[2,]

  Estimate Std. Error    t value 
 1.3164157  0.3840612  3.4276199

5. Random slope model

Fifth, let’s include the random slope for SW by participant:

# fitting main-effect model
m2 <- lmer(Y ~ X1 + X2 + (X1 | participant), data = mydataset)
summary(m2) # to inspect the main results

6. Cross-level interaction

Finally, let’s include the interaction between participant’s gender and SW in predicting BP

# fitting interactive model
m3 <- lmer(Y ~ X1 + X2 + X1:X2 + (X1 | participant), data = mydataset)
summary(m3) # to inspect the main results
plot_model(m3,type="pred",terms=c("SW_pmc","gender")) # to plot the interaction

Ok, but where the hell are my p-values!?

lme4 doesn’t output p-values because
calculating exact degrees of freedom in
LMER is controversial
Bates (2010)
As a rule of thumb, people consider t-values
> 1.96 as “significant” since this value
corresponds to p < 0.05 in the standardized normal distribution

Not really satisfactory to draw statistical inference: we need an inference criterion

library(lmerTest)
m1 <- lmer(SBP_aft ~ SW_pmc + (1|ID), data=dat)
s <- summary(m1)$coefficients
s <- as.data.frame(s)
s[,2:4] <- round(s[,2:4],2)
s

              Estimate Std. Error     df t value      Pr(>|t|)
(Intercept) 121.584372       1.40 135.49   86.72 1.391480e-120
SW_pmc        1.316416       0.38 773.13    3.43  6.411022e-04

A more rigorous way to get p-values:
Model comparison with likelihood ratio test:

m0 <- lmer(SBP_aft ~ 1 + ( 1 | ID), data = dat)
m1 <- lmer(SBP_aft ~ SW_pmc + ( 1 | ID), data = dat)
m2 <- lmer(SBP_aft ~ SW_pmc + gender + ( 1 | ID), data = dat)
round( anova(m0,m1,m2), 3)

Data: dat
Models:
m0: SBP_aft ~ 1 + (1 | ID)
m1: SBP_aft ~ SW_pmc + (1 | ID)
m2: SBP_aft ~ SW_pmc + gender + (1 | ID)
   npar    AIC    BIC  logLik -2*log(L)  Chisq Df Pr(>Chisq)    
m0    3 7227.9 7242.4 -3611.0    7221.9                         
m1    4 7218.3 7237.5 -3605.1    7210.3 11.675  1      0.001 ***
m2    5 7217.0 7241.0 -3603.5    7207.0  3.267  1      0.071 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

and with information criteria

AIC(m0,m1,m2)

   df      AIC
m0  3 7225.421
m1  4 7215.823
m2  5 7210.702

One (fundamental) step back: Model assumptions

plot_model(m3, type="diag")

Cluster-level influential cases

Influential case = Observation (or entire cluster) that has a disproportionately large impact on your model. If you exclude this case, your parameter estimates (such as fixed slopes, standard errors, or p-values) change significantly.

library(influence.ME)
infl <- influence(m2, group = "ID")
plot(infl, "cook")

From data pre-processing to cross-level interactions

Data pre-processing
Cleaning, aggregating, and centering
Level-specific correlations
Are State Workaholism (SW) and Systolic Blood Pressure (SBP)
more strongly correlated at lv1 or lv2?
Null model & ICC
Does SBP vary more at lv1 or at lv2?
Main effects
Is BP higher than usual when SW is higher than usual?
Is it lower in females than in males?
Random slope & cross-level interactions
Is the within-subject relationship between SW and BP
moderated by participants’ gender?

LMER advanced
3-level models, growth curve and cross-lagged models, mediation, GLMER

3-level models

In some cases, we have multiple clustering values nested within each other
(e.g., time within day within participant; day within participant within team)

        ID night time_from_so     rmssd TASW
1        2     1    2.7992536  54.00617 3.50
2        2     1    8.7653994  53.10374 3.50
3        2     1   13.7653994  46.29045 3.50
4        2     1   18.7653994  40.93889 3.50
5        2     1   23.7653994  38.19453 3.50
6        2     1   28.7653994  37.64720 3.50
7        2     1   33.7653994  38.13251 3.50
8        2     1   38.7653994  38.34409 3.50
9        2     1   43.7653994  46.28378 3.50
10       2     1   47.5766070  38.01781 3.50
11       2     1   51.1823458        NA 3.50
12       2     1   55.6753145        NA 3.50
13       2     1   60.1128145  45.31099 3.50
14       2     1   64.1001843  45.74549 3.50
15       2     1   66.7701062        NA 3.50
16       2     1   68.4581270  47.99512 3.50
17       2     1   71.5260889  40.55882 3.50
18       2     1   76.2128008  58.74436 3.50
19       2     1   81.2128008  55.50705 3.50
20       2     1   86.2128008  53.53481 3.50
21       2     1   91.2128008  50.34942 3.50
22       2     1   95.9742592  50.12215 3.50
23       2     1  100.9698321        NA 3.50
24       2     1  105.9698321  47.69289 3.50
25       2     1  110.9698321  43.14594 3.50
26       2     1  115.9698321  42.51798 3.50
27       2     1  120.9698321  48.41389 3.50
28       2     1  124.3615059  54.66733 3.50
29       2     1  126.2529192        NA 3.50
30       2     1  128.5859921  61.64679 3.50
31       2     1  132.6082478  67.00114 3.50
32       2     1  136.6685244  75.69257 3.50
33       2     1  139.0122744  70.43812 3.50
34       2     1  141.6923525  60.34546 3.50
35       2     1  146.1862327  52.90437 3.50
36       2     1  151.1862327  32.39172 3.50
37       2     1  154.7014671  38.56214 3.50
38       2     1  156.8509463        NA 3.50
39       2     1  160.5548523  40.25337 3.50
40       2     1  163.2577166  58.33023 3.50
41       2     1  165.5278989  54.08805 3.50
42       2     1  169.4943051  62.69128 3.50
43       2     1  172.7989926  63.89964 3.50
44       2     1  176.3812843  56.97066 3.50
45       2     1  181.3812843  52.77340 3.50
46       2     1  186.3812843  44.83207 3.50
47       2     1  191.3812843  42.38070 3.50
48       2     1  196.3812843  41.32735 3.50
49       2     1  201.3812843  43.79272 3.50
50       2     1  205.2009491        NA 3.50
51       2     1  209.2961347  46.31335 3.50
52       2     1  214.2961347  49.87101 3.50
53       2     1  218.4954836  46.31360 3.50
54       2     1  222.6155418  49.24818 3.50
55       2     1  226.8828656  44.84754 3.50
56       2     1  229.5146364        NA 3.50
57       2     1  231.8150271  40.24792 3.50
58       2     1  234.9865114        NA 3.50
59       2     1  239.9865114  38.87511 3.50
60       2     1  244.3565635  32.07013 3.50
61       2     1  248.9292198        NA 3.50
62       2     1  253.4652885  36.21819 3.50
63       2     1  259.9482322  47.22663 3.50
64       2     1  264.9482322  49.13350 3.50
65       2     1  269.9482322  45.38506 3.50
66       2     1  274.9482322  45.59455 3.50
67       2     1  279.9482322  46.33443 3.50
68       2     1  283.4190597  47.65449 3.50
69       2     1  287.9484810  50.87595 3.50
70       2     1  292.0543403        NA 3.50
71       2     1  295.4940539  36.92994 3.50
72       2     1  300.2578560        NA 3.50
73       2     1  305.1172310        NA 3.50
74       2     1  310.1172310  36.05277 3.50
75       2     1  313.4943130  40.95762 3.50
76       2     1  316.9989992  45.09379 3.50
77       2     1  321.4726972        NA 3.50
78       2     1  324.9948326        NA 3.50
79       2     1  328.1072024  45.68984 3.50
80       2     1  330.4669680  41.06996 3.50
81       2     1  332.8121503        NA 3.50
82       2     1  336.0922284        NA 3.50
83       2     1  341.0922284        NA 3.50
84       2     1  346.0922284        NA 3.50
85       2     1  350.8031728        NA 3.50
86       2     1  355.7287005  46.56667 3.50
87       2     1  361.2688046  41.44623 3.50
88       2     1  366.2688046  39.18326 3.50
89       2     1  370.7729713  38.64956 3.50
90       2     1  375.4185305  39.97979 3.50
91       2     1  379.4878013  42.83741 3.50
92       2     1  382.9734784        NA 3.50
93       2     1  386.8842857  40.44965 3.50
94       2     1  391.5812909  42.01815 3.50
95       2     1  398.4208742  51.45372 3.50
96       2     1  403.0328534  61.60027 3.50
97       2     1  406.0613657  55.31032 3.50
98       2     1  408.5708676  49.40132 3.50
99       2     1  412.0758155  55.40103 3.50
100      2     1  417.0758155  52.08333 3.50
101      2     2    4.1525291  46.00760 5.00
102      2     2    5.3302635  40.52539 5.00
103      2     2    6.6385968        NA 5.00
104      2     2    7.8906802  51.57458 5.00
105      2     2    9.3175031  57.20750 5.00
106      2     2   10.9260968        NA 5.00
107      2     2   17.6859927  61.32104 5.00
108      2     2   20.3060447  54.57240 5.00
109      2     2   24.1078677  51.30035 5.00
110      2     2   27.3298729  50.65121 5.00
111      2     2   29.4982322  44.49601 5.00
112      2     2   32.7669822  40.24057 5.00
113      2     2   37.7669822  40.82126 5.00
114      2     2   42.7669822  48.72470 5.00
115      2     2   47.7669822  38.71897 5.00
116      2     2   53.9276593  50.16393 5.00
117      2     2   58.9276593  36.20609 5.00
118      2     2   63.9276593  42.06506 5.00
119      2     2   68.9276593  34.03491 5.00
120      2     2   72.6561650  30.96177 5.00
121      2     2   74.7463895  50.76021 5.00
122      2     2   79.5172228  57.03075 5.00
123      2     2   81.1006863        NA 5.00
124      2     2   83.3014773        NA 5.00
125      2     2   86.6287005  50.90503 5.00
126      2     2   91.6287005  46.94798 5.00
127      2     2   96.6287005  40.99774 5.00
128      2     2  101.6287005  39.47308 5.00
129      2     2  106.6287005        NA 5.00
130      2     2  111.6287005  37.57936 5.00
131      2     2  116.2086484  39.37887 5.00
132      2     2  121.7250546  57.30151 5.00
133      2     2  125.7220598        NA 5.00
134      2     2  129.8063046  54.09637 5.00
135      2     2  133.6430234  56.38914 5.00
136      2     2  137.5440651  49.50844 5.00
137      2     2  142.5440651  41.12952 5.00
138      2     2  146.3465410        NA 5.00
139      2     2  149.8956296  45.76235 5.00
140      2     2  154.8956296  49.08638 5.00
141      2     2  161.1889890        NA 5.00
142      2     2  163.8529213  45.08773 5.00
143      2     2  166.7314369  43.38024 5.00
144      2     2  170.5813067  36.55850 5.00
145      2     2  174.2856025  48.24663 5.00
146      2     2  178.3846901  43.89241 5.00
147      2     2  182.6128151  72.34256 5.00
148      2     2  185.6316953  76.62608 5.00
149      2     2  189.4925026  43.70362 5.00
150      2     2  194.4925026  39.09805 5.00
151      2     2  198.1878151  37.34391 5.00
152      2     2  202.1107317        NA 5.00
153      2     2  207.1107317  41.11715 5.00
154      2     2  212.1107317  41.57877 5.00
155      2     2  217.1107317  45.76724 5.00
156      2     2  222.1107317  37.99492 5.00
157      2     2  227.1107317  52.22856 5.00
158      2     2  232.1107317  44.35956 5.00
159      2     2  237.1107317  40.72324 5.00
160      2     2  241.8189359  42.04369 5.00
161      2     2  247.9302650  46.89638 5.00
162      2     2  252.9302650  40.15978 5.00
163      2     2  256.0589108  41.72088 5.00
164      2     2  259.7427650  51.77253 5.00
165      2     2  264.7427650  46.39692 5.00
166      2     2  269.1570864        NA 5.00
167      2     2  271.4611229  47.80331 5.00
168      2     2  275.8432843  42.48225 5.00
169      2     2  280.3740135  43.24485 5.00
170      2     2  284.9865135  45.40614 5.00
171      2     2  289.8637270  39.51530 5.00
172      2     2  294.8477114        NA 5.00
173      2     2  298.8816958  39.98121 5.00
174      2     2  303.1766177  51.24365 5.00
175      2     2  308.1766177  43.09495 5.00
176      2     2  311.5841697  54.61940 5.00
177      2     2  313.7642479        NA 5.00
178      2     2  318.2482322  53.76273 5.00
179      2     2  321.5408104  46.58874 5.00
180      2     2  324.3691892  49.79364 5.00
181      2     2  328.6467867  54.57691 5.00
182      2     2  332.3255628        NA 5.00
183      2     2  335.6159273  34.78257 5.00
184      2     2  340.1242607  42.77214 5.00
185      2     2  344.5424898  43.64396 5.00
186      2     2  348.6721773  61.66750 5.00
187      2     2  351.3840263  57.78891 5.00
188      2     2  355.4225751  55.69029 5.00
189      2     2  359.1813062  63.54395 5.00
190      2     2  361.2684155        NA 5.00
191      2     2  362.6464103  60.33171 5.00
192      2     2  365.7346916  66.63682 5.00
193      2     2  371.3050041  51.42185 5.00
194      2     2  376.3050041  46.78893 5.00
195      2     2  382.2461499  52.07635 5.00
196      2     2  387.2461499  44.50837 5.00
197      2     2  392.2461499  45.51166 5.00
198      2     2  397.2461499  46.96833 5.00
199      2     2  402.2461499  48.42021 5.00
200      2     2  407.2461499  47.51590 5.00
201      2     2  410.4435450  47.20983 5.00
202      2     2  412.2793515  59.36703 5.00
203      2     2  415.1491432  63.84255 5.00
204      2     2  418.1289609  64.09465 5.00
205      2     2  420.3129179        NA 5.00
206      2     3    1.1816139  46.40868 5.25
207      2     3    3.4683332  37.15417 5.25
208      2     3    5.6471092  42.05239 5.25
209      2     3    8.7895571  55.45929 5.25
210      2     3   10.5093488        NA 5.25
211      2     3   12.0929426        NA 5.25
212      2     3   15.6665103  54.56325 5.25
213      2     3   20.6665103  39.59843 5.25
214      2     3   25.6665103  35.73845 5.25
215      2     3   30.6665103  35.52867 5.25
216      2     3   35.6665103  34.45673 5.25
217      2     3   40.6665103  36.66559 5.25
218      2     3   45.6665103  42.65236 5.25
219      2     3   50.0157316  41.70734 5.25
220      2     3   55.5467237        NA 5.25
221      2     3   61.5799347  42.86054 5.25
222      2     3   65.9118436  47.72305 5.25
223      2     3   67.7880155        NA 5.25
224      2     3   70.8395780        NA 5.25
225      2     3   72.3680936  50.06972 5.25
226      2     3   75.6299426        NA 5.25
227      2     3   78.6153593  48.68654 5.25
228      2     3   80.4622343  54.09362 5.25
229      2     3   81.8816353  71.30965 5.25
230      2     3   87.6208280  62.70592 5.25
231      2     3   89.1440051  66.69897 5.25
232      2     3   91.2839780  47.37220 5.25
233      2     3   94.4692635  50.69288 5.25
234      2     3  101.3326749  51.34284 5.25
235      2     3  104.6205656  50.52030 5.25
236      2     3  108.6036385  43.22089 5.25
237      2     3  110.2236906  43.49837 5.25
238      2     3  113.5884041  52.48199 5.25
239      2     3  117.2647062  46.13908 5.25
240      2     3  121.0279874  48.61357 5.25
241      2     3  126.0279874  36.33651 5.25
242      2     3  130.7871030  42.47536 5.25
243      2     3  135.7391874  47.08082 5.25
244      2     3  140.7391874  35.10880 5.25
245      2     3  143.8164009        NA 5.25
246      2     3  145.4441353  43.26890 5.25
247      2     3  149.2334582  48.50415 5.25
248      2     3  154.2334582  45.02108 5.25
249      2     3  159.2334582  48.99710 5.25
250      2     3  163.4450463  45.67213 5.25
251      2     3  167.8300718  37.07085 5.25
252      2     3  171.5407489  45.71697 5.25
253      2     3  174.2876239  64.32510 5.25
254      2     3  177.5291603  55.16821 5.25
255      2     3  181.4467384  73.67892 5.25
256      2     3  184.4795441  80.38401 5.25
257      2     3  186.6859174  73.02115 5.25
258      2     3  189.1331831  68.57882 5.25
259      2     3  195.5339643  76.46542 5.25
260      2     3  198.1675581  60.31645 5.25
261      2     3  202.3446414  46.56870 5.25
262      2     3  204.9826622  46.84113 5.25
263      2     3  206.6088341        NA 5.25
264      2     3  208.0872195  43.64028 5.25
265      2     3  215.0348880  35.20545 5.25
266      2     3  218.0097577  29.52730 5.25
267      2     3  221.5464765        NA 5.25
268      2     3  224.4968671  37.65812 5.25
269      2     3  228.4942630  30.82410 5.25
270      2     3  231.3058515        NA 5.25
271      2     3  234.4800702  37.96443 5.25
272      2     3  237.8808515        NA 5.25
273      2     3  241.0087168  32.36756 5.25
274      2     3  243.2561134        NA 5.25
275      2     3  246.6365822  40.97436 5.25
276      2     3  251.6365822  31.63350 5.25
277      2     3  256.6365822  33.64339 5.25
278      2     3  261.6365822  31.55746 5.25
279      2     3  266.6365822  40.54693 5.25
280      2     3  271.6365822  36.92351 5.25
281      2     3  275.6813728  39.26135 5.25
282      2     3  279.7764239  43.04893 5.25
283      2     3  283.7445229  45.99230 5.25
284      2     3  288.8985593  53.55838 5.25
285      2     3  293.0663979  59.16905 5.25
286      2     3  297.4915281  50.84001 5.25
287      2     3  302.2122317  43.97083 5.25
288      2     3  306.4604093  40.06045 5.25
289      2     3  309.3583260  44.88669 5.25
290      2     3  312.0144458  58.61754 5.25
291      2     3  316.1152270  51.82001 5.25
292      2     3  320.3964770        NA 5.25
293      2     3  324.0376228  50.97637 5.25
294      2     3  329.2346281  51.96250 5.25
295      2     3  332.3135340  40.56408 5.25
296      2     3  335.8355390  46.90485 5.25
297      2     3  340.1985598  43.40768 5.25
298      2     3  344.2331952  39.76452 5.25
299      2     3  348.9287682  41.56611 5.25
300      2     3  353.9287682  43.30983 5.25
301      2     3  358.5945234  46.10351 5.25
302      2     3  362.5298032  43.49002 5.25
303      2     3  365.9856560        NA 5.25
304      2     3  369.3550570  51.85933 5.25
305      2     3  373.8290154  45.64736 5.25
306      2     3  378.4568799  58.25069 5.25
307      2     3  383.4568799  57.46009 5.25
308      2     3  389.0424268  35.34587 5.25
309      2     3  393.7748561  49.42514 5.25
310      2     3  397.6818947  37.98129 5.25
311      2     3  402.0610614  45.86796 5.25
312      2     3  406.0822853  36.61585 5.25
313      2     3  408.7295509        NA 5.25
314      2     3  411.1324155  48.73733 5.25
315      2     3  414.2520770  51.60695 5.25
316      2     3  417.0596291  59.47417 5.25
317      2     3  420.9035093  50.42973 5.25
318      2     3  425.9035093  48.24782 5.25
319      2     3  430.0415301  52.33759 5.25
320      2     3  433.1806609  60.74170 5.25
321      2     4    2.6318952  48.78384 4.00
322      2     4    7.6318952  42.72919 4.00
323      2     4   12.6318952  41.32000 4.00
324      2     4   17.6318952  37.97895 4.00
325      2     4   22.6318952  36.81140 4.00
326      2     4   27.6318952  43.55684 4.00
327      2     4   32.6318952  40.24578 4.00
328      2     4   37.6318952  42.19941 4.00
329      2     4   42.6318952  38.85525 4.00
330      2     4   46.2654892  39.57506 4.00
331      2     4   51.3652291  47.23809 4.00
332      2     4   54.9973811  47.07881 4.00
333      2     4   58.7310957  48.14769 4.00
334      2     4   62.1879967  49.89656 4.00
335      2     4   65.7114342        NA 4.00
336      2     4   70.6753665  53.30963 4.00
337      2     4   75.6753665  46.90781 4.00
338      2     4   80.6753665  40.82662 4.00
339      2     4   85.6753665  40.32084 4.00
340      2     4   88.8895696  38.68705 4.00
341      2     4   92.1956998        NA 4.00
342      2     4   97.1956998  49.10590 4.00
343      2     4  102.1956998  49.62790 4.00
344      2     4  106.2977832  40.06756 4.00
345      2     4  110.4587207  42.89710 4.00
346      2     4  114.2923139  37.90437 4.00
347      2     4  116.4670530        NA 4.00
348      2     4  118.5471311        NA 4.00
349      2     4  120.5770790  45.27036 4.00
350      2     4  122.1886676        NA 4.00
351      2     4  125.2647092        NA 4.00
352      2     4  128.9501259  55.46124 4.00
353      2     4  134.6118447  46.39563 4.00
354      2     4  138.3947874        NA 4.00
355      2     4  141.7499858  52.83255 4.00
356      2     4  146.1365644  58.30011 4.00
357      2     4  148.9232832  59.04046 4.00
358      2     4  152.1222415  47.65617 4.00
359      2     4  158.2204186  64.07723 4.00
360      2     4  162.3941165  51.12754 4.00
361      2     4  167.3941165  54.43728 4.00
362      2     4  172.3941165  63.32961 4.00
363      2     4  175.7408610  55.71844 4.00
364      2     4  179.5873451        NA 4.00
365      2     4  183.6232826  43.69958 4.00
366      2     4  187.7336993  46.25037 4.00
367      2     4  190.3792722  51.35992 4.00
368      2     4  193.0353920  55.21375 4.00
369      2     4  196.7842201  39.10310 4.00
370      2     4  198.1967201  41.60034 4.00
371      2     4  200.3239337  33.74978 4.00
372      2     4  204.4537516  43.89223 4.00
373      2     4  207.9698977  43.94289 4.00
374      2     4  211.4110436  45.80230 4.00
375      2     4  215.3904707  59.07046 4.00
376      2     4  219.0167727  54.18329 4.00
377      2     4  222.5592207  43.08125 4.00
378      2     4  226.4376061  40.70518 4.00
379      2     4  231.4376061  36.29787 4.00
380      2     4  235.0911217  39.29408 4.00
381      2     4  237.2740644        NA 4.00
382      2     4  241.1162519  46.82596 4.00
383      2     4  246.1162519  47.92294 4.00
384      2     4  249.7882571  52.46275 4.00
385      2     4  253.5644290  60.02655 4.00
386      2     4  258.8201582  55.91232 4.00
387      2     4  263.8201582  48.75128 4.00
388      2     4  267.9641792  32.18079 4.00
389      2     4  272.1917941  39.54999 4.00
390      2     4  277.1917941  40.72701 4.00
391      2     4  282.1917941  39.49414 4.00
392      2     4  287.1917941  37.93099 4.00
393      2     4  290.3614555  44.50494 4.00
394      2     4  295.1873655  39.12363 4.00
395      2     4  298.4259072  33.63309 4.00
396      2     4  300.4735634  60.60911 4.00
397      2     4  303.0217405  67.96922 4.00
398      2     4  307.0358030  72.71920 4.00
399      2     4  312.5149697  47.51901 4.00
400      2     4  317.5149697  45.33840 4.00
401      2     4  322.5149697  43.34069 4.00
402      2     4  328.5331856  60.33273 4.00
403      2     4  334.4837064  56.63154 4.00
404      2     4  338.4886543  48.92524 4.00
405      2     4  340.9824043  50.99365 4.00
406      2     4  343.3520658        NA 4.00
407      2     4  347.6938627  46.83772 4.00
408      2     4  351.5775930  42.62011 4.00
409      2     4  354.9033806        NA 4.00
410      2     4  357.2484327  52.18578 4.00
411      2     4  359.4627556        NA 4.00
412      2     4  364.4238233        NA 4.00
413      2     4  369.4490837  50.39296 4.00
414      2     4  373.1828752  45.91601 4.00
415  0slha     2    1.4235922  48.73615 3.75
416  0slha     2    4.5730713  52.24967 3.75
417  0slha     2    9.5730713  54.84329 3.75
418  0slha     2   14.5730713  45.09821 3.75
419  0slha     2   19.5730713  44.41347 3.75
420  0slha     2   24.4578369  50.24622 3.75
421  0slha     2   29.9993734        NA 3.75
422  0slha     2   34.9993734  44.58097 3.75
423  0slha     2   39.9993734  38.25976 3.75
424  0slha     2   44.9993734  41.18317 3.75
425  0slha     2   49.9993734  43.42080 3.75
426  0slha     2   54.9993734  41.01157 3.75
427  0slha     2   58.4828372  40.32140 3.75
428  0slha     2   60.6052333  78.29025 3.75
429  0slha     2   64.2564052  78.05198 3.75
430  0slha     2   69.2564052  39.03073 3.75
431  0slha     2   74.2564052  50.93858 3.75
432  0slha     2   79.8524989  44.40663 3.75
433  0slha     2   83.9260666  48.04451 3.75
434  0slha     2   87.2441656  44.99289 3.75
435  0slha     2   93.1860927  50.39956 3.75
436  0slha     2   98.1860927  40.39419 3.75
437  0slha     2  103.1860927  45.68570 3.75
438  0slha     2  108.1860927  46.71263 3.75
439  0slha     2  113.1860927  46.48849 3.75
440  0slha     2  119.5253957  69.73076 3.75
441  0slha     2  124.7951874  64.77957 3.75
442  0slha     2  129.7951874  51.66945 3.75
443  0slha     2  133.6251353  59.32489 3.75
444  0slha     2  137.8386770  46.24226 3.75
445  0slha     2  141.3023489  49.80747 3.75
446  0slha     2  145.8540624        NA 3.75
447  0slha     2  150.8540624  54.17375 3.75
448  0slha     2  155.8540624  52.18415 3.75
449  0slha     2  160.8540624  49.14334 3.75
450  0slha     2  165.0217708  46.38415 3.75
451  0slha     2  169.2978124  49.73163 3.75
452  0slha     2  175.2821874  29.27951 3.75
453  0slha     2  180.2230624  27.17288 3.75
454  0slha     2  184.8091197  37.36096 3.75
455  0slha     2  189.1007864  41.97012 3.75
456  0slha     2  193.9446666  34.79288 3.75
457  0slha     2  199.1123749  57.99789 3.75
458  0slha     2  203.2453270  53.85527 3.75
459  0slha     2  206.4232010  45.93125 3.75
460  0slha     2  211.2540604  43.30788 3.75
461  0slha     2  214.8112218  41.21432 3.75
462  0slha     2  218.4613521  48.17569 3.75
463  0slha     2  223.4613521  40.89873 3.75
464  0slha     2  228.4613521  44.63746 3.75
465  0slha     2  233.4583580  45.23365 3.75
466  0slha     2  237.0288015  52.12450 3.75
467  0slha     2  239.5347911  43.43392 3.75
468  0slha     2  242.7574473  46.20498 3.75
469  0slha     2  247.7574473  50.63589 3.75
470  0slha     2  252.7574473  42.61907 3.75
471  0slha     2  257.7574473  43.99981 3.75
472  0slha     2  262.2015885  40.46017 3.75
473  0slha     2  265.0940369        NA 3.75
474  0slha     2  269.0267192  49.45000 3.75
475  0slha     2  272.0376567  46.12495 3.75
476  0slha     2  277.9618754  55.36632 3.75
477  0slha     2  282.7082296  55.97778 3.75
478  0slha     2  285.8650004  60.79429 3.75
479  0slha     2  287.5582296        NA 3.75
480  0slha     2  291.1053650  59.17382 3.75
481  0slha     2  296.1053650  50.17528 3.75
482  0slha     2  301.1053650  47.65824 3.75
483  0slha     2  306.1053650  49.23745 3.75
484  0slha     2  311.1053650  50.45114 3.75
485  0slha     2  314.9824379  49.03484 3.75
486  0slha     2  319.7386775        NA 3.75
487  0slha     2  324.3362140  27.48053 3.75
488  0slha     2  327.0971619  31.71500 3.75
489  0slha     2  330.8699484  51.17931 3.75
490  0slha     2  335.2083598  56.49042 3.75
491  0slha     2  339.2504171        NA 3.75
492  0slha     2  344.0280213  62.23868 3.75
493  0slha     2  349.0280213  62.39093 3.75
494  0slha     2  353.1083598  73.09953 3.75
495  0slha     2  355.7853114  74.70306 3.75
496  0slha     2  357.4297124  58.36625 3.75
497  0slha     2  359.3543218        NA 3.75
498  0slha     2  362.1764572  51.92527 3.75
499  0slha     2  367.6738531  54.49384 3.75
500  0slha     2  372.6738531  52.17026 3.75
501  0slha     2  377.6738531  56.17264 3.75
502  0slha     2  382.6738531  55.55198 3.75
503  0slha     2  387.6738531  50.21320 3.75
504  0slha     2  392.6738531  49.02394 3.75
505  0slha     2  397.6738531  52.10578 3.75
506  0slha     2  402.6738531  52.90137 3.75
507  0slha     2  407.6738531  48.32781 3.75
508  0slha     3    2.6061926        NA 5.00
509  0slha     3   43.6043524  29.00936 5.00
510  0slha     3   45.6523993  25.27829 5.00
511  0slha     3   48.1951076  24.63252 5.00
512  0slha     3   51.9910711  24.42699 5.00
513  0slha     3   55.7651597  38.62351 5.00
514  0slha     3   59.5703680  33.51152 5.00
515  0slha     3   64.5595607  32.07641 5.00
516  0slha     3   69.5595607  30.58045 5.00
517  0slha     3   74.5595607  29.83060 5.00
518  0slha     3   79.5595607  34.31929 5.00
519  0slha     3   84.5595607  29.50773 5.00
520  0slha     3   88.8681616  33.10950 5.00
521  0slha     3   92.3159552  30.45007 5.00
522  0slha     3   96.6194708  41.14084 5.00
523  0slha     3  102.2926479  32.56938 5.00
524  0slha     3  105.5724653  23.67194 5.00
525  0slha     3  109.0694703  31.68135 5.00
526  0slha     3  112.2688193  29.20449 5.00
527  0slha     3  115.4082724  30.15134 5.00
528  0slha     3  118.6104859        NA 5.00
529  0slha     3  121.6673870  32.63725 5.00
530  0slha     3  125.9418661  36.13128 5.00
531  0slha     3  130.9418661  38.94652 5.00
532  0slha     3  135.9418661  37.09878 5.00
533  0slha     3  140.9418661  38.91555 5.00
534  0slha     3  145.9418661  37.41728 5.00
535  0slha     3  150.9418661  35.06895 5.00
536  0slha     3  155.9418661  34.92533 5.00
537  0slha     3  159.8893924  39.77262 5.00
538  0slha     3  163.9379599  48.09375 5.00
539  0slha     3  168.9379599  37.95299 5.00
540  0slha     3  173.9379599  38.45614 5.00
541  0slha     3  178.9379599  38.06417 5.00
542  0slha     3  183.9379599  44.30776 5.00
543  0slha     3  188.3041057  40.76383 5.00
544  0slha     3  191.4154338  66.23290 5.00
545  0slha     3  194.5977255  58.21758 5.00
546  0slha     3  198.2199911  63.62694 5.00
547  0slha     3  202.0009807  43.05667 5.00
548  0slha     3  207.0009807  32.47638 5.00
549  0slha     3  210.7625693  25.95949 5.00
550  0slha     3  213.4321005  39.33091 5.00
551  0slha     3  215.7806682        NA 5.00
552  0slha     3  218.0947307  42.55142 5.00
553  0slha     3  221.4378246  51.52025 5.00
554  0slha     3  223.8556581  40.45058 5.00
555  0slha     3  225.6491476        NA 5.00
556  0slha     3  228.8746685  40.78245 5.00
557  0slha     3  231.9969341  38.42486 5.00
558  0slha     3  233.4039653  51.65965 5.00
559  0slha     3  236.6608664  44.53314 5.00
560  0slha     3  241.6608664  44.04462 5.00
561  0slha     3  245.9237570  41.58796 5.00
562  0slha     3  249.3247987  52.69494 5.00
563  0slha     3  251.1158199  51.01573 5.00
564  0slha     3  252.9821015  69.74791 5.00
565  0slha     3  255.8537161  57.79291 5.00
566  0slha     3  259.0465546  47.00889 5.00
567  0slha     3  263.6512421  46.33351 5.00
568  0slha     3  269.8252005  69.01720 5.00
569  0slha     3  273.8804088  58.05517 5.00
570  0slha     3  278.8804088  48.67446 5.00
571  0slha     3  282.7166072  45.28185 5.00
572  0slha     3  286.6163473  50.99418 5.00
573  0slha     3  290.0638734  51.58079 5.00
574  0slha     3  292.2534567  64.50512 5.00
575  0slha     3  295.8145244  56.67741 5.00
576  0slha     3  300.8145244  47.91182 5.00
577  0slha     3  305.8145244  41.69644 5.00
578  0slha     3  310.8145244  44.99478 5.00
579  0slha     3  315.8145244  49.65282 5.00
580  0slha     3  320.8145244  45.92748 5.00
581  0slha     3  324.6874309  47.08123 5.00
582  0slha     3  328.0501812        NA 5.00
583  0slha     3  330.1056499  42.25585 5.00
584  0slha     3  335.0087749  26.81789 5.00
585  0slha     3  338.7298687  26.39059 5.00
586  0slha     3  341.9147747        NA 5.00
587  0slha     3  345.5449932  63.01414 5.00
588  0slha     3  349.4369202  50.93549 5.00
589  0slha     3  353.2283265  53.41717 5.00
590  0slha     3  354.8642640  58.23737 5.00
591  0slha     3  356.6236390  67.34798 5.00
592  0slha     3  359.0046286        NA 5.00
593  0slha     3  364.1285869  50.03964 5.00
594  0slha     3  367.1499411  53.49539 5.00
595  0slha     3  369.7753317  53.25370 5.00
596  0slha     3  371.5209049  56.86222 5.00
597  0slha     3  374.6796291  56.26815 5.00
598  0slha     3  379.6796291  48.60769 5.00
599  0slha     3  384.9832749  41.11580 5.00
600  0slha     3  389.3986395  40.42688 5.00
601  0slha     3  394.9051499  54.11229 5.00
602  0slha     3  399.9051499  60.72740 5.00
603  0slha     3  404.9051499  58.65908 5.00
604  0slha     3  409.9051499  55.45277 5.00
605  0slha     3  414.2728575  50.12437 5.00
606  0slha     3  418.7840546  58.22236 5.00
607  0slha     3  423.7840546  50.06831 5.00
608  0slha     3  428.7840546  48.84177 5.00
609  0slha     3  433.7840546  53.37057 5.00
610  0slha     3  438.7840546  46.09343 5.00
611  0slha     3  443.7840546  56.51283 5.00
612  0slha     3  449.9309164  53.18906 5.00
613  0slha     3  454.8611248        NA 5.00
614  0slha     4    1.1692170  43.72892 4.75
615  0slha     4    4.5780712  45.18059 4.75
616  0slha     4    8.5646597  48.09762 4.75
617  0slha     4   11.0550243  50.23768 4.75
618  0slha     4   14.5012482  62.64711 4.75
619  0slha     4   19.5012482  64.29883 4.75
620  0slha     4   24.5012482  52.53001 4.75
621  0slha     4   29.5012482  51.87386 4.75
622  0slha     4   34.5012482  47.94711 4.75
623  0slha     4   39.5012482  43.56960 4.75
624  0slha     4   44.5012482  49.28414 4.75
625  0slha     4   49.5012482  45.20736 4.75
626  0slha     4   54.5012482  49.10580 4.75
627  0slha     4   59.2211602  51.31254 4.75
628  0slha     4   63.9475826  51.72402 4.75
629  0slha     4   67.4699784  39.10361 4.75
630  0slha     4   72.4699784  26.43030 4.75
631  0slha     4   76.9034420  31.19294 4.75
632  0slha     4   80.1359940  27.66875 4.75
633  0slha     4   83.3405612  30.36117 4.75
634  0slha     4   88.4038524  41.71627 4.75
635  0slha     4   91.6921337  37.37901 4.75
636  0slha     4   93.1171337  40.45969 4.75
637  0slha     4   96.2155712  37.74683 4.75
638  0slha     4  101.2155712  33.59366 4.75
639  0slha     4  104.9737743  37.54141 4.75
640  0slha     4  109.4572378        NA 4.75
641  0slha     4  114.4572378  41.90564 4.75
642  0slha     4  119.4572378  46.22198 4.75
643  0slha     4  125.3147899  48.50924 4.75
644  0slha     4  130.3147899  41.59484 4.75
645  0slha     4  135.3147899  38.57584 4.75
646  0slha     4  140.3147899  38.19125 4.75
647  0slha     4  145.3147899  40.28023 4.75
648  0slha     4  148.7321084        NA 4.75
649  0slha     4  152.2384894  50.42179 4.75
650  0slha     4  157.2384894  46.72492 4.75
651  0slha     4  160.8287237  45.36610 4.75
652  0slha     4  163.4440883        NA 4.75
653  0slha     4  166.0546352        NA 4.75
654  0slha     4  168.8267706  42.57686 4.75
655  0slha     4  170.5199998  31.88834 4.75
656  0slha     4  173.3265105  37.73552 4.75
657  0slha     4  176.3916149  41.59527 4.75
658  0slha     4  179.4936982        NA 4.75
659  0slha     4  182.8948701  50.08961 4.75
660  0slha     4  185.7433076  42.24590 4.75
661  0slha     4  187.6809378  50.83363 4.75
662  0slha     4  189.1753388  44.52846 4.75
663  0slha     4  191.6038545  42.57925 4.75
664  0slha     4  194.8391409  48.40414 4.75
665  0slha     4  196.9651826  46.41099 4.75
666  0slha     4  199.3763805  49.24049 4.75
667  0slha     4  201.9183076  47.62977 4.75
668  0slha     4  205.4554170  56.06016 4.75
669  0slha     4  211.1761175        NA 4.75
670  0slha     4  213.1795030        NA 4.75
671  0slha     4  214.6334092  56.43750 4.75
672  0slha     4  218.1375759  55.77184 4.75
673  0slha     4  221.6474717  52.13678 4.75
674  0slha     4  226.1317165  50.41678 4.75
675  0slha     4  231.1317165  50.51464 4.75
676  0slha     4  236.1317165  48.72137 4.75
677  0slha     4  239.6582691  51.65199 4.75
678  0slha     4  243.5973217        NA 4.75
679  0slha     4  248.5973217  70.86728 4.75
680  0slha     4  253.5973217        NA 4.75
681  0slha     4  258.5973217  65.36943 4.75
682  0slha     4  262.1530508  63.64217 4.75
683  0slha     4  264.1279204        NA 4.75
684  0slha     4  268.0246649  65.82930 4.75
685  0slha     4  270.3555243  51.48911 4.75
686  0slha     4  272.8099514  43.36881 4.75
687  0slha     4  276.3395086        NA 4.75
688  0slha     4  280.2595607  44.10655 4.75
689  0slha     4  282.2613836  39.59675 4.75
690  0slha     4  285.4145086        NA 4.75
691  0slha     4  288.8404201        NA 4.75
692  0slha     4  290.7121649  44.74186 4.75
693  0slha     4  294.0121753  60.86341 4.75
694  0slha     4  297.9434357  59.21322 4.75
695  0slha     4  300.7425243  49.21320 4.75
696  0slha     4  303.7641389        NA 4.75
697  0slha     4  306.8271597  50.37849 4.75
698  0slha     4  311.0447378  48.65906 4.75
699  0slha     4  315.1473689  48.62543 4.75
700      3     1    2.5883003        NA 4.00
701      3     1    6.2448107  39.14921 4.00
702      3     1    9.5164253  36.52310 4.00
703      3     1   13.0510607  38.40450 4.00
704      3     1   18.0510607  37.63289 4.00
705      3     1   23.0510607  40.10735 4.00
706      3     1   28.0510607  40.16343 4.00
707      3     1   33.0510607  40.14068 4.00
708      3     1   38.0510607  40.06846 4.00
709      3     1   43.0510607  36.69722 4.00
710      3     1   48.0510607  38.61600 4.00
711      3     1   52.9026235  33.04575 4.00
712      3     1   57.0827019  33.61849 4.00
713      3     1   60.3678581  30.16267 4.00
714      3     1   64.5359571  24.05811 4.00
715      3     1   69.5359571  23.74284 4.00
716      3     1   74.5359571  23.78408 4.00
717      3     1   79.5359571  23.54542 4.00
718      3     1   84.5359571  23.78652 4.00
719      3     1   89.5359571  24.51398 4.00
720      3     1   94.7812716  27.36517 4.00
721      3     1   99.7812716  26.14563 4.00
722      3     1  104.6557508  26.27915 4.00
723      3     1  109.4523654  27.65432 4.00
724      3     1  114.7411674  31.06069 4.00
725      3     1  119.7411674  28.64156 4.00
726      3     1  123.9834839  25.85446 4.00
727      3     1  130.8422066  26.06616 4.00
728      3     1  135.8422066  35.62370 4.00
729      3     1  140.8422066  33.91210 4.00
730      3     1  145.8422066  34.44751 4.00
731      3     1  150.8422066  33.61879 4.00
732      3     1  155.8422066  33.62092 4.00
733      3     1  160.8422066  25.51067 4.00
734      3     1  165.8422066  27.01391 4.00
735      3     1  170.0505409  31.42133 4.00
736      3     1  174.4192919  31.33176 4.00
737      3     1  178.0854286  29.26029 4.00
738      3     1  181.8067736  28.19702 4.00
739      3     1  187.6981799  32.76573 4.00
740      3     1  192.6981799  34.34362 4.00
741      3     1  197.0579455  33.52773 4.00
742      3     1  200.5919299  28.78843 4.00
743      3     1  202.9196643  26.77541 4.00
744      3     1  206.1981799  27.60891 4.00
745      3     1  211.1981799  23.15100 4.00
746      3     1  216.1981799  23.25900 4.00
747      3     1  221.1981799  23.00503 4.00
748      3     1  226.1981799  22.57456 4.00
749      3     1  231.1981799  22.51737 4.00
750      3     1  236.1981799  23.09291 4.00
751      3     1  240.3946643  24.42132 4.00
752      3     1  244.6796903  24.31530 4.00
753      3     1  249.6796903  23.36226 4.00
754      3     1  254.6796903  25.00062 4.00
755      3     1  259.6796903  23.66569 4.00
756      3     1  263.2282677  23.42426 4.00
757      3     1  266.8989805  22.83308 4.00
758      3     1  271.2265846        NA 4.00
759      3     1  275.3508034  22.25065 4.00
760      3     1  279.1558815  23.41457 4.00
761      3     1  282.7635638        NA 4.00
762      3     1  287.7635638  25.25269 4.00
763      3     1  292.7635638  22.90818 4.00
764      3     1  297.7635638  22.63254 4.00
765      3     1  302.7635638        NA 4.00
766      3     1  307.7635638  22.49611 4.00
767      3     1  312.7635638        NA 4.00
768      3     1  317.7635638  23.92802 4.00
769      3     1  322.7635638  26.90720 4.00
770      3     1  327.7635638  24.62748 4.00
771      3     1  332.7635638  24.37994 4.00
772      3     1  338.2794467  23.59181 4.00
773      3     1  343.2794467  21.67346 4.00
774      3     1  348.2794467  22.23828 4.00
775      3     1  353.2794467  21.96525 4.00
776      3     1  357.6699351  21.78544 4.00
777      3     1  362.9794339  19.34822 4.00
778      3     1  367.9794339  23.18854 4.00
779      3     1  372.9794339  23.89147 4.00
780      3     1  377.9794339  24.33307 4.00
781      3     1  382.9794339  25.91346 4.00
782      3     1  387.8031314  25.97408 4.00
783      3     1  392.8049538  21.73158 4.00
784      3     1  397.8049538  22.15894 4.00
785      3     1  402.8049538  23.17887 4.00
786      3     1  407.7612038  22.19527 4.00
787      3     1  411.9858131  18.59011 4.00
788      3     1  415.8477926  19.00875 4.00
789      3     1  418.6524803        NA 4.00
790      3     1  420.3548241        NA 4.00
791      3     1  423.8763084  20.99024 4.00
792      3     1  431.3065168  17.05263 4.00
793      3     1  436.3065168  16.77588 4.00
794      3     1  442.2742251  17.32401 4.00
795      3     1  447.2742251  21.54983 4.00
796      3     1  452.2742251  21.52858 4.00
797      3     1  456.1149872  22.88393 4.00
798      3     1  458.7553586  18.60680 4.00
799      3     1  462.4225461  23.60426 4.00
800      3     1  467.5138222  21.28622 4.00
801      3     1  471.9235778  22.98132 4.00
802      3     2    3.7784070  28.61785 2.75
803      3     2    8.7784070  26.86461 2.75
804      3     2   13.1218788  29.29637 2.75
805      3     2   16.9531288  24.90947 2.75
806      3     2   22.0565142  27.32611 2.75
807      3     2   27.0565142  29.77813 2.75
808      3     2   32.0565142  27.51349 2.75
809      3     2   37.0565142  28.19213 2.75
810      3     2   42.0565142  27.09539 2.75
811      3     2   47.0565142  26.38712 2.75
812      3     2   52.0565142  24.83690 2.75
813      3     2   57.0565142  24.24925 2.75
814      3     2   62.0565142  25.21775 2.75
815      3     2   67.0565142  22.14362 2.75
816      3     2   72.0565142  19.10926 2.75
817      3     2   77.0565142  19.33062 2.75
818      3     2   82.0565142  19.76304 2.75
819      3     2   87.0565142  19.32037 2.75
820      3     2   92.0565142  16.85847 2.75
821      3     2   97.0565142  20.44016 2.75
822      3     2  102.0565142  20.09462 2.75
823      3     2  107.0565142  20.98489 2.75
824      3     2  112.0565142  20.59817 2.75
825      3     2  117.0565142  21.19227 2.75
826      3     2  122.0565142  23.56022 2.75
827      3     2  126.1008029  20.94214 2.75
828      3     2  131.7239799  25.13431 2.75
829      3     2  136.7239799  24.27076 2.75
830      3     2  140.6851735  29.81897 2.75
831      3     2  144.7481901  31.15296 2.75
832      3     2  149.7481901  25.15718 2.75
833      3     2  154.6606901  25.97248 2.75
834      3     2  159.6950651  24.47007 2.75
835      3     2  164.6950651  27.08569 2.75
836      3     2  169.6950651  30.29106 2.75
837      3     2  174.6950651  31.55052 2.75
838      3     2  179.2463626  29.37448 2.75
839      3     2  184.0346392  31.23514 2.75
840      3     2  189.0346392  29.36963 2.75
841      3     2  194.0346392  31.37129 2.75
842      3     2  199.0346392  28.01317 2.75
843      3     2  204.0346392  30.15665 2.75
844      3     2  209.0346392  24.76552 2.75
845      3     2  214.0346392  26.03916 2.75
846      3     2  219.0346392  24.06390 2.75
847      3     2  224.0346392  24.72086 2.75
848      3     2  229.0346392  23.61655 2.75
849      3     2  234.0346392  23.16687 2.75
850      3     2  238.1722794  22.21188 2.75
851      3     2  240.6893466  20.98169 2.75
852      3     2  243.9284091  21.46504 2.75
853      3     2  248.9284091  21.65903 2.75
854      3     2  251.9665535  23.89647 2.75
855      3     2  254.8533959  19.30656 2.75
856      3     2  258.2738386  23.84892 2.75
857      3     2  261.7341250  30.40602 2.75
858      3     2  266.7341250  33.41186 2.75
859      3     2  271.7341250  33.55695 2.75
860      3     2  276.7341250  33.57954 2.75
861      3     2  281.7341250  32.83490 2.75
862      3     2  287.2403689  35.93826 2.75
863      3     2  292.2403689  32.98154 2.75
864      3     2  296.4641970  32.68203 2.75
865      3     2  300.8776085  29.68302 2.75
866      3     2  305.8776085  30.39036 2.75
867      3     2  310.8776085  26.31077 2.75
868      3     2  315.8776085  25.79082 2.75
869      3     2  320.8776085  25.94541 2.75
870      3     2  325.8776085  25.84293 2.75
871      3     2  330.8776085  26.28387 2.75
872      3     2  335.8776085  24.91475 2.75
873      3     2  340.8776085  24.85614 2.75
874      3     2  345.8776085  24.38058 2.75
875      3     2  349.1140760  23.65583 2.75
876      3     2  352.5754133  17.19673 2.75
877      3     2  359.1218976  17.85675 2.75
878      3     2  364.1218976  14.58875 2.75
879      3     2  369.1218976  15.19132 2.75
880      3     2  374.1218976  16.59768 2.75
881      3     2  379.1218976  17.16877 2.75
882      3     2  383.3995048  15.49578 2.75
883      3     2  385.5945569  19.83717 2.75
884      3     2  386.8436455        NA 2.75
885      3     2  390.0849215  21.40221 2.75
886      3     2  393.6752861  21.99085 2.75
887      3     2  397.4005465  19.08531 2.75
888      3     2  401.2552340        NA 2.75
889      3     2  403.2932340  20.57621 2.75
890      3     2  406.3203173  17.96462 2.75
891      3     2  411.2518277  16.12014 2.75
892      3     2  416.2518277  18.71065 2.75
893      3     2  421.2518277  23.15208 2.75
894      3     2  425.4765673  19.82015 2.75
895      3     2  431.2140673  20.21674 2.75
896      3     2  436.2140673  23.25607 2.75
897      3     2  441.2140673  23.39905 2.75
898      3     2  446.2140673  22.35648 2.75
899      3     2  451.2140673  22.67810 2.75
900      3     2  455.4332184  22.37290 2.75
901      3     2  459.3031507  23.07735 2.75
902      3     2  466.1539167  28.33705 2.75
903      3     2  471.1539167  26.37677 2.75
904      3     2  475.5558698  30.16564 2.75
905      3     3    2.6805285  34.10193 2.50
906      3     3    7.6805285  37.15905 2.50
907      3     3   12.6805285  36.24565 2.50
908      3     3   17.6805285  32.25970 2.50
909      3     3   22.6805285  27.90036 2.50
910      3     3   27.6805285  24.30587 2.50
911      3     3   32.6805285  21.11521 2.50
912      3     3   37.6805285  21.59481 2.50
913      3     3   42.6805285  22.60115 2.50
914      3     3   45.8393878  16.73017 2.50
915      3     3   49.1406949  19.71725 2.50
916      3     3   52.7207731  19.23794 2.50
917      3     3   57.1084033  18.45153 2.50
918      3     3   62.1084033  15.97041 2.50
919      3     3   67.1084033  19.64276 2.50
920      3     3   72.1084033  15.98031 2.50
921      3     3   76.1682996  19.70717 2.50
922      3     3   83.0982480  21.05700 2.50
923      3     3   88.0982480  23.66965 2.50
924      3     3   93.0982480  24.62821 2.50
925      3     3   98.0982480  25.70114 2.50
926      3     3  102.4465449  25.31539 2.50
927      3     3  106.9346855  23.29001 2.50
928      3     3  111.9346855  24.46007 2.50
929      3     3  116.1883313  27.72776 2.50
930      3     3  118.7251905  23.06708 2.50
931      3     3  120.5887423  25.24296 2.50
932      3     3  122.3787163  25.26647 2.50
933      3     3  125.5300184  22.53503 2.50
934      3     3  130.5300184  22.53166 2.50
935      3     3  135.9268934  32.33238 2.50
936      3     3  140.9268934  35.61806 2.50
937      3     3  145.9268934  33.11249 2.50
938      3     3  150.9268934  35.45370 2.50
939      3     3  156.5581423  26.58049 2.50
940      3     3  161.5581423  25.48448 2.50
941      3     3  166.5581423  26.53458 2.50
942      3     3  171.5581423  23.09441 2.50
943      3     3  176.5581423  26.13148 2.50
944      3     3  181.5581423  26.82508 2.50
945      3     3  186.5581423  26.78018 2.50
946      3     3  191.5581423  25.57103 2.50
947      3     3  196.5581423  25.49850 2.50
948      3     3  201.5581423  24.86746 2.50
949      3     3  205.5516327  24.61599 2.50
950      3     3  209.6878314  30.12039 2.50
951      3     3  214.6878314  28.78317 2.50
952      3     3  219.6878314  29.72313 2.50
953      3     3  228.2211525  20.25735 2.50
954      3     3  232.8020119  17.38091 2.50
955      3     3  237.4945900  21.02631 2.50
956      3     3  241.7823461  25.09116 2.50
957      3     3  246.1221855  23.70580 2.50
958      3     3  251.1221855  22.38110 2.50
959      3     3  254.8997897  23.87837 2.50
960      3     3  258.7185397  23.45537 2.50
961      3     3  263.4885918  22.74033 2.50
962      3     3  267.3169874  22.74614 2.50
963      3     3  270.7728569  30.63511 2.50
964      3     3  274.7714246  35.63741 2.50
965      3     3  279.7714246  35.72633 2.50
966      3     3  283.0828829  35.45699 2.50
967      3     3  288.6414767  34.62856 2.50
968      3     3  293.6414767  38.53903 2.50
969      3     3  298.6414767  35.65059 2.50
970      3     3  303.6414767  35.43901 2.50
971      3     3  308.6414767  36.85486 2.50
972      3     3  313.6414767  39.30202 2.50
973      3     3  318.6026644  35.37402 2.50
974      3     3  323.7560397  36.35457 2.50
975      3     3  328.6436699  30.46694 2.50
976      3     3  333.6591647  27.01491 2.50
977      3     3  338.6591647  31.18332 2.50
978      3     3  342.2257011  31.75345 2.50
979      3     3  345.8555188  30.21664 2.50
980      3     3  350.7832532  28.39197 2.50
981      3     3  355.7576022  25.36431 2.50
982      3     3  360.7943209  22.87925 2.50
983      3     3  365.7943209  23.42888 2.50
984      3     3  369.4449816  21.42365 2.50
985      3     3  371.8211632  22.35770 2.50
986      3     3  374.8919965  21.43007 2.50
987      3     3  379.8919965  22.13376 2.50
988      3     3  384.8919965  23.28655 2.50
989      3     3  389.8919965  23.26562 2.50
990      3     3  395.8102130  23.67094 2.50
991      3     3  400.8102130  23.24348 2.50
992      3     3  405.8102130        NA 2.50
993      3     3  408.9586505  24.32713 2.50
994      3     3  413.4193275  24.71848 2.50
995      3     3  417.7936732  27.15869 2.50
996      3     3  422.3888522  31.69023 2.50
997      3     3  427.3888522  31.35297 2.50
998      3     3  432.3888522  26.88764 2.50
999      3     3  437.3888522  28.67463 2.50
1000     3     3  442.3888522  24.41867 2.50
1001     3     3  446.3371595  26.18944 2.50
1002     3     3  450.3617688  27.72688 2.50
1003     3     3  454.0637255  26.82002 2.50
1004     3     3  457.8177656  25.70722 2.50
1005     3     3  462.8177656  25.72958 2.50
1006     3     3  467.6588828  28.70496 2.50
1007     3     4    4.9654330  34.66316 2.75
1008     3     4    9.7296257  37.89237 2.75
1009     3     4   14.7281934        NA 2.75
1010     3     4   19.7281934        NA 2.75
1011     3     4   24.7281934        NA 2.75
1012     3     4   31.4000664  34.86134 2.75
1013     3     4   36.4000664  36.01734 2.75
1014     3     4   41.4000664  31.09311 2.75
1015     3     4   46.4000664  33.91253 2.75
1016     3     4   51.4000664  35.00590 2.75
1017     3     4   56.4000664  32.84030 2.75
1018     3     4   61.4000664  28.74218 2.75
1019     3     4   66.4000664  25.39488 2.75
1020     3     4   71.4000664  23.30854 2.75
1021     3     4   76.4000664  22.71949 2.75
1022     3     4   81.4000664  23.25529 2.75
1023     3     4   85.2270200  21.07524 2.75
1024     3     4   88.4344419  22.08696 2.75
1025     3     4   93.4344419  24.37888 2.75
1026     3     4   99.0318377  22.07467 2.75
1027     3     4  104.0318377  22.13213 2.75
1028     3     4  109.0205099  21.75697 2.75
1029     3     4  112.4985049  21.98163 2.75
1030     3     4  115.8500674  20.01373 2.75
1031     3     4  120.8500674  22.20832 2.75
1032     3     4  125.8500674  23.04527 2.75
1033     3     4  130.6837914  23.49739 2.75
1034     3     4  135.5948591  24.00893 2.75
1035     3     4  140.5948591  25.83719 2.75
1036     3     4  145.5948591  24.97348 2.75
1037     3     4  150.5948591  24.80013 2.75
1038     3     4  156.5857440  23.61678 2.75
1039     3     4  161.5857440  23.60707 2.75
1040     3     4  164.9943380  23.98203 2.75
1041     3     4  167.6375674        NA 2.75
1042     3     4  172.8638695  24.39597 2.75
1043     3     4  174.1935570  20.69043 2.75
1044     3     4  177.8472028  21.44128 2.75
1045     3     4  182.8472028  20.57127 2.75
1046     3     4  187.8472028  24.22295 2.75
1047     3     4  192.8472028  25.19740 2.75
1048     3     4  197.8472028  25.01254 2.75
1049     3     4  202.8472028  25.12045 2.75
1050     3     4  207.8472028  25.19909 2.75
1051     3     4  211.9156929  26.69874 2.75
1052     3     4  218.0479851        NA 2.75
1053     3     4  223.0479851  25.10513 2.75
1054     3     4  227.4038345  27.48769 2.75
1055     3     4  231.1651527        NA 2.75
1056     3     4  233.4638507  23.83089 2.75
1057     3     4  236.6544757  24.22148 2.75
1058     3     4  241.6544757  25.78246 2.75
1059     3     4  246.6544757  28.10715 2.75
1060     3     4  251.6544757  28.41992 2.75
1061     3     4  256.6180171        NA 2.75
1062     3     4  261.6818189  33.42562 2.75
1063     3     4  266.6818189  34.32346 2.75
1064     3     4  271.6818189  29.86235 2.75
1065     3     4  277.2010897  26.48546 2.75
1066     3     4  282.2010897  26.88359 2.75
1067     3     4  287.2010897  27.50781 2.75
1068     3     4  292.2010897  27.18669 2.75
1069     3     4  297.2010897  23.17942 2.75
1070     3     4  302.2010897  25.56913 2.75
1071     3     4  307.2010897  26.39886 2.75
1072     3     4  312.2010897  24.22576 2.75
1073     3     4  317.2010897  26.02765 2.75
1074     3     4  322.2010897  24.25413 2.75
1075     3     4  327.2010897  25.48775 2.75
1076     3     4  332.2010897  24.76826 2.75
1077     3     4  337.9904116  25.97082 2.75
1078     3     4  342.1806460  24.11101 2.75
1079     3     4  344.6633382        NA 2.75
1080     3     4  346.3722023  23.84212 2.75
1081     3     4  349.9912127  22.14684 2.75
1082     3     4  354.9912127  24.13352 2.75
1083     3     4  358.8284523  22.01167 2.75
1084     3     4  362.8688169  24.73069 2.75
1085     3     4  367.8688169  24.91569 2.75
1086     3     4  372.2034523  25.68734 2.75
1087     3     4  375.3018898  20.27668 2.75
1088     3     4  378.8445981  20.65750 2.75
1089     3     4  383.8445981  16.98627 2.75
1090     3     4  388.8445981  18.32249 2.75
1091     3     4  394.7464211  19.37402 2.75
1092     3     4  398.0573586  16.68136 2.75
1093     3     4  401.4430356  18.91477 2.75
1094     3     4  406.4430356  20.35419 2.75
1095     3     4  411.4430356  22.89685 2.75
1096     3     4  416.4430356  20.95532 2.75
1097     3     4  419.7322278  21.13180 2.75
1098     3     4  423.1987638  20.65403 2.75
1099     3     4  428.1987638  18.53784 2.75
1100     3     4  431.7807950  23.32445 2.75
1101     3     4  434.8848323  20.12561 2.75
1102     3     4  439.6753278  21.03132 2.75
1103     3     4  443.4350934  21.40020 2.75
1104     3     4  447.3253278  20.09263 2.75
1105     3     4  452.3253278  20.12804 2.75
1106     3     4  457.3253278  21.43300 2.75
1107     3     4  462.3253278  20.69441 2.75
1108     3     4  467.3253278  19.32829 2.75
1109     3     4  470.7043306        NA 2.75
1110     4     2    1.1782132  86.03386 1.00
1111     4     2    4.4767809  59.33087 1.00
1112     4     2    9.4767809  78.30009 1.00
1113     4     2   18.7009809  89.32662 1.00
1114     4     2   23.7009809  36.99036 1.00
1115     4     2   28.2934288  36.12573 1.00
1116     4     2   34.0978559  37.95938 1.00
1117     4     2   39.0978559  34.17272 1.00
1118     4     2   44.0978559  36.20614 1.00
1119     4     2   49.0978559  28.78402 1.00
1120     4     2   52.3126994  28.51204 1.00
1121     4     2   53.7909543  46.06602 1.00
1122     4     2   56.8882199  80.41336 1.00
1123     4     2   61.8882199  72.92263 1.00
1124     4     2   66.8882199  66.73831 1.00
1125     4     2   70.6840629  71.63163 1.00
1126     4     2   74.6968330  53.29772 1.00
1127     4     2   79.6968330  44.69230 1.00
1128     4     2   83.1851143  31.15268 1.00
1129     4     2   86.8187080  47.34939 1.00
1130     4     2   91.8187080  30.97808 1.00
1131     4     2   96.8187080  35.68781 1.00
1132     4     2  100.7155833  28.36599 1.00
1133     4     2  104.8345939  37.86727 1.00
1134     4     2  109.8345939  37.73759 1.00
1135     4     2  114.8345939  39.41504 1.00
1136     4     2  120.6387606  51.58532 1.00
1137     4     2  125.6387606  40.56102 1.00
1138     4     2  130.4882403  45.23591 1.00
1139     4     2  134.8140220  46.93865 1.00
1140     4     2  139.8140220  46.54723 1.00
1141     4     2  144.8140220  42.95747 1.00
1142     4     2  149.8140220  41.57130 1.00
1143     4     2  154.8140220  41.89293 1.00
1144     4     2  159.8140220  40.54690 1.00
1145     4     2  163.0176676  40.29494 1.00
1146     4     2  167.5101153  54.26005 1.00
1147     4     2  170.5215736  59.75846 1.00
1148     4     2  172.2435788  59.58430 1.00
1149     4     2  176.0681882  49.00846 1.00
1150     4     2  181.0681882  51.20731 1.00
1151     4     2  186.0681882  39.97080 1.00
1152     4     2  191.0681882  52.82040 1.00
1153     4     2  196.0681882        NA 1.00
1154     4     2  199.1930481  80.64091 1.00
1155     4     2  200.6871788  84.21831 1.00
1156     4     2  204.1061892  66.00580 1.00
1157     4     2  209.1061892  62.83393 1.00
1158     4     2  214.1061892  63.59736 1.00
1159     4     2  217.7121788  63.90331 1.00
1160     4     2  221.5192100  60.95282 1.00
1161     4     2  226.5192100  65.43835 1.00
1162     4     2  231.5192100  64.52089 1.00
1163     4     2  235.0929186  65.80489 1.00
1164     4     2  238.7684501  75.58272 1.00
1165     4     2  243.7684501  70.09091 1.00
1166     4     2  248.7684501  64.29938 1.00
1167     4     2  253.7684501        NA 1.00
1168     4     2  257.8357460  53.88360 1.00
1169     4     2  260.5968137  79.65157 1.00
1170     4     2  264.9137408        NA 1.00
1171     4     2  269.0878293  66.41644 1.00
1172     4     2  274.4173866        NA 1.00
1173     4     2  279.4173866  43.57379 1.00
1174     4     2  284.4173866  54.41310 1.00
1175     4     2  289.4173866  53.66427 1.00
1176     4     2  294.4173866  47.06877 1.00
1177     4     2  299.4173866  40.02311 1.00
1178     4     2  304.4173866  46.25009 1.00
1179     4     2  309.4173866  67.14866 1.00
1180     4     2  313.0446096  66.99022 1.00
1181     4     2  316.9249575        NA 1.00
1182     4     2  319.9956606  70.53664 1.00
1183     4     2  323.2528221  84.53533 1.00
1184     4     2  328.2528221  99.84044 1.00
1185     4     2  333.2528221  64.94389 1.00
1186     4     2  338.2528221  53.48114 1.00
1187     4     2  343.2528221  36.42928 1.00
1188     4     2  348.5663454  53.81829 1.00
1189     4     2  352.8207725  55.39692 1.00
1190     4     2  356.0925173  48.78905 1.00
1191     4     2  358.0334027        NA 1.00
1192     4     2  361.8166059  65.36091 1.00
1193     4     2  365.1403038  60.06277 1.00
1194     4     2  368.7452517  54.14627 1.00
1195     4     2  373.7452517  71.58443 1.00
1196     4     2  378.7452517  65.13375 1.00
1197     4     2  383.7452517  53.80041 1.00
1198     4     2  388.7452517  47.56185 1.00
1199     4     2  393.7452517  58.51750 1.00
1200     4     2  397.5567194  41.97212 1.00
1201     4     2  400.7224841  39.43478 1.00
1202     4     2  403.7434476  95.64413 1.00
1203     4     2  407.3700101 103.96135 1.00
1204     4     2  411.6157132  91.19248 1.00
1205     4     2  415.9447497        NA 1.00
1206     4     2  420.9447497  97.45943 1.00
1207     4     2  424.6679268  81.08808 1.00
1208     4     2  428.6148018  56.34400 1.00
1209     4     2  433.6148018  65.35674 1.00
1210     4     2  438.6148018  56.15657 1.00
1211     4     2  443.6148018  61.29213 1.00
1212     4     3    2.6639199  48.65465 1.00
1213     4     3    7.6639199  36.36217 1.00
1214     4     3   12.6639199  42.05042 1.00
1215     4     3   17.6639199  57.77087 1.00
1216     4     3   22.6639199  69.14012 1.00
1217     4     3   27.9146925  79.83384 1.00
1218     4     3   32.9146925  58.66704 1.00
1219     4     3   37.9146925  41.92041 1.00
1220     4     3   42.9146925  31.98599 1.00
1221     4     3   46.7256300  34.85111 1.00
1222     4     3   51.4861886  33.99376 1.00
1223     4     3   56.3610701  31.28055 1.00
1224     4     3   61.3610701  38.85986 1.00
1225     4     3   66.3610701  39.35115 1.00
1226     4     3   73.7407576        NA 1.00
1227     4     3   80.8707055  47.54916 1.00
1228     4     3   86.6180983  26.88740 1.00
1229     4     3   89.8489577  25.91113 1.00
1230     4     3   92.7509108  31.27585 1.00
1231     4     3   97.2705722  26.54692 1.00
1232     4     3  102.1561191  44.22089 1.00
1233     4     3  107.1561191        NA 1.00
1234     4     3  112.1561191  40.44356 1.00
1235     4     3  116.3973949  34.34093 1.00
1236     4     3  119.1981759        NA 1.00
1237     4     3  122.5699207  38.50144 1.00
1238     4     3  127.5248686  36.03957 1.00
1239     4     3  132.5248686  26.22332 1.00
1240     4     3  137.5248686  24.33515 1.00
1241     4     3  142.5248686  23.15146 1.00
1242     4     3  145.8684818  27.88683 1.00
1243     4     3  149.3576679  30.86343 1.00
1244     4     3  154.3576679  34.85812 1.00
1245     4     3  158.6230325  35.94250 1.00
1246     4     3  164.1515481  60.56443 1.00
1247     4     3  168.6725116  52.11696 1.00
1248     4     3  173.6725116  46.72620 1.00
1249     4     3  177.0412680  47.96989 1.00
1250     4     3  180.4996077  38.10423 1.00
1251     4     3  183.8977848  32.07295 1.00
1252     4     3  188.1998681  54.64663 1.00
1253     4     3  193.8225243  71.51560 1.00
1254     4     3  200.1785160  47.16265 1.00
1255     4     3  205.0055993        NA 1.00
1256     4     3  210.0709639  48.09975 1.00
1257     4     3  214.3078128  50.07756 1.00
1258     4     3  218.7220056  66.79103 1.00
1259     4     3  223.7220056  60.09489 1.00
1260     4     3  227.1475259  60.23119 1.00
1261     4     3  230.2727858  67.15488 1.00
1262     4     3  234.7480462  62.75546 1.00
1263     4     3  239.7480462  62.65836 1.00
1264     4     3  244.0505202  56.91743 1.00
1265     4     3  248.4069004        NA 1.00
1266     4     3  253.3294264        NA 1.00
1267     4     3  258.0253800  78.01389 1.00
1268     4     3  260.8342243        NA 1.00
1269     4     3  263.7920368  53.04113 1.00
1270     4     3  267.2809691  70.12356 1.00
1271     4     3  270.9615680  72.26426 1.00
1272     4     3  275.9615680  63.82603 1.00
1273     4     3  279.1937295  82.87509 1.00
1274     4     3  281.2710732  57.54120 1.00
1275     4     3  285.1464639  58.42471 1.00
1276     4     3  290.1464639        NA 1.00
1277     4     3  294.7339639  46.22043 1.00
1278     4     3  299.8825316  90.94451 1.00
1279     4     3  304.4855264  78.31299 1.00
1280     4     3  309.4855264  80.70148 1.00
1281     4     3  314.4855264  78.99159 1.00
1282     4     3  318.1188594  66.90564 1.00
1283     4     3  321.7958123  78.69867 1.00
1284     4     3  326.7456821  74.33036 1.00
1285     4     3  331.7456821  90.84978 1.00
1286     4     3  336.7456821  60.08971 1.00
1287     4     3  340.4408644  77.98514 1.00
1288     4     3  344.3482863  96.83202 1.00
1289     4     3  349.3482863  54.26796 1.00
1290     4     3  352.7444009 145.73258 1.00
1291     4     3  354.0717446        NA 1.00
1292     4     3  357.3403644 122.69508 1.00
1293     4     3  362.3819009        NA 1.00
1294     4     3  367.3819009        NA 1.00
1295     4     3  371.4731769 102.33988 1.00
1296     4     3  374.9790363 102.01648 1.00
1297     4     3  379.9790363  58.73870 1.00
1298     4     3  384.9790363  60.47364 1.00
1299     4     3  389.9790363  58.97530 1.00
1300     4     3  394.9790363  53.89380 1.00
1301     4     3  399.9790363  65.59709 1.00
1302     4     3  404.9790363  52.96003 1.00
1303     4     3  409.9790363  48.13798 1.00
1304     4     3  413.0984274  39.18281 1.00
1305     4     3  416.4032352  55.40733 1.00
1306     4     3  422.5154748  47.47970 1.00
1307     4     3  427.5154748  60.39797 1.00
1308     4     3  430.9645633  57.91189 1.00
1309     4     3  434.6602665        NA 1.00
1310     4     3  438.0510323        NA 1.00
1311     4     3  441.0281264        NA 1.00
1312     4     3  444.4566420        NA 1.00
1313     4     3  448.4569024        NA 1.00
1314     4     3  451.9963555  47.68241 1.00
1315     4     3  455.6472670  46.94054 1.00
1316     4     3  460.6472670  48.17960 1.00
1317     4     3  463.9151055  59.57916 1.00
1318     4     3  466.4125014  53.25728 1.00
1319     4     3  470.5983087  64.16065 1.00
1320     4     3  475.5983087  72.65448 1.00
1321     4     3  480.5983087  67.73958 1.00
1322     4     3  485.4059889        NA 1.00
1323     4     3  489.1399733  86.99002 1.00
1324     4     4    0.9656279  69.27966 1.00
1325     4     4    2.5860706  61.14568 1.00
1326     4     4    5.8660185  60.33100 1.00
1327     4     4    9.0304716  52.38385 1.00
1328     4     4   11.5612008  56.53171 1.00
1329     4     4   14.0056018  53.97485 1.00
1330     4     4   18.4615914        NA 1.00
1331     4     4   23.4615914        NA 1.00
1332     4     4   31.2686227  36.90325 1.00
1333     4     4   36.2686227  32.95500 1.00
1334     4     4   41.2348987  32.87785 1.00
1335     4     4   50.6809925  35.08726 1.00
1336     4     4   53.8832060  45.23991 1.00
1337     4     4   58.8764349        NA 1.00
1338     4     4   64.0134138  43.42536 1.00
1339     4     4   69.0134138  49.83890 1.00
1340     4     4   72.9773400  51.84814 1.00
1341     4     4   77.2191308        NA 1.00
1342     4     4   81.6601464  49.71445 1.00
1343     4     4   86.2264224  30.14202 1.00
1344     4     4   89.7509016  28.30249 1.00
1345     4     4   92.8781220  41.29866 1.00
1346     4     4   96.0118528  33.24177 1.00
1347     4     4  100.8774778  37.34426 1.00
1348     4     4  105.3833372  33.49165 1.00
1349     4     4  109.2201862        NA 1.00
1350     4     4  113.3490924  49.69949 1.00
1351     4     4  118.3490924  51.19814 1.00
1352     4     4  121.9442747  62.77138 1.00
1353     4     4  123.9076859  31.10220 1.00
1354     4     4  126.6566440  35.88448 1.00
1355     4     4  130.9738315  30.17890 1.00
1356     4     4  135.9738315  26.51761 1.00
1357     4     4  140.9738315  27.98452 1.00
1358     4     4  145.9738315  32.65394 1.00
1359     4     4  150.9738315  36.07506 1.00
1360     4     4  155.9738315  32.42257 1.00
1361     4     4  160.9738315  37.07961 1.00
1362     4     4  163.9855442  34.63701 1.00
1363     4     4  165.4298089        NA 1.00
1364     4     4  169.7925693  49.78259 1.00
1365     4     4  175.0829339  38.99475 1.00
1366     4     4  180.0829339  48.33659 1.00
1367     4     4  185.0829339  42.38764 1.00
1368     4     4  189.0588377  41.09831 1.00
1369     4     4  192.8717283  49.87026 1.00
1370     4     4  197.7369627  29.78145 1.00
1371     4     4  202.7264158  27.73759 1.00
1372     4     4  207.7264158  27.27809 1.00
1373     4     4  212.7264158  28.89180 1.00
1374     4     4  216.2204263  38.29963 1.00
1375     4     4  218.9463377  55.01159 1.00
1376     4     4  222.1960773  55.85801 1.00
1377     4     4  224.9886554  66.08995 1.00
1378     4     4  228.6100096  49.82838 1.00
1379     4     4  233.6100096  43.47307 1.00
1380     4     4  238.2318846  44.48165 1.00
1381     4     4  242.9193846  58.90860 1.00
1382     4     4  246.5579359  69.87712 1.00
1383     4     4  250.3707060  56.71953 1.00
1384     4     4  255.3707060  48.32082 1.00
1385     4     4  260.1837268  41.50994 1.00
1386     4     4  263.6779977  40.29952 1.00
1387     4     4  265.3944039  47.10796 1.00
1388     4     4  268.4985706  44.52311 1.00
1389     4     4  273.4985706  44.66988 1.00
1390     4     4  279.4867018  59.50001 1.00
1391     4     4  282.7394362  51.63212 1.00
1392     4     4  285.9540195  52.08267 1.00
1393     4     4  290.9540195  40.80421 1.00
1394     4     4  295.9540195  43.20888 1.00
1395     4     4  300.9540195  52.89889 1.00
1396     4     4  305.9540195  52.71085 1.00
1397     4     4  309.0660017  59.73911 1.00
1398     4     4  310.5486871  60.42686 1.00
1399     4     4  313.9019423  65.49562 1.00
1400     4     4  319.0140516  47.00295 1.00
1401     4     4  322.9119683  56.28868 1.00
1402     4     4  327.7563693  58.75290 1.00
1403     4     4  332.7233036  67.22900 1.00
1404     4     4  337.0096388  55.33710 1.00
1405     4     4  340.4864617  45.69835 1.00
1406     4     4  344.9058628  54.79849 1.00
1407     4     4  347.9290399  51.49406 1.00
1408     4     4  350.7037794  52.95666 1.00
1409     4     4  355.4662794  53.53499 1.00
1410     4     4  359.3983107  56.36524 1.00
1411     4     4  363.5477899  44.92396 1.00
1412     4     4  366.9731802  48.34370 1.00
1413     4     4  369.7559925  62.22538 1.00
1414     4     4  372.2002633  74.81623 1.00
1415     4     4  375.3667998        NA 1.00
1416     4     4  380.1938831  68.78530 1.00
1417     4     4  385.1938831  58.12079 1.00
1418     4     4  390.1938831  52.35564 1.00
1419     4     4  395.1938831  47.51554 1.00
1420     4     4  398.6492221  43.84755 1.00
1421     4     4  402.2868528  52.40983 1.00
1422     4     4  406.1757851  61.98957 1.00
1423     4     4  409.6996133        NA 1.00
1424     4     4  414.2183633  70.17542 1.00
1425     4     4  419.3113320        NA 1.00
1426     4     4  424.3113320        NA 1.00
1427     4     4  427.8114612        NA 1.00
1428     4     4  431.4774758  65.98424 1.00
1429     4     4  436.9332050  51.07158 1.00
1430     4     4  440.8416025  42.30593 1.00
1431     5     1    1.3781331  15.43611 3.75
1432     5     1    3.9171921  18.84446 3.75
1433     5     1   11.7697962  22.89187 3.75
1434     5     1   14.3862025  23.11823 3.75
1435     5     1   18.2696660        NA 3.75
1436     5     1   23.2696660  21.64939 3.75
1437     5     1   28.2696660  19.99465 3.75
1438     5     1   33.2696660  24.49211 3.75
1439     5     1   36.8536601        NA 3.75
1440     5     1   39.3321854  22.38492 3.75
1441     5     1   41.9668208  20.87378 3.75
1442     5     1   45.3043208  23.64057 3.75
1443     5     1   49.8052322  20.64590 3.75
1444     5     1   54.3157791  21.42362 3.75
1445     5     1   59.1147374  20.68670 3.75
1446     5     1   64.1147374  23.51355 3.75
1447     5     1   69.1147374  16.97626 3.75
1448     5     1   72.2672017  16.19043 3.75
1449     5     1   77.6990931  22.11681 3.75
1450     5     1   82.6990931  19.80243 3.75
1451     5     1   87.6990931  19.09037 3.75
1452     5     1   92.6990931  19.15460 3.75
1453     5     1   97.6990931  19.24415 3.75
1454     5     1  102.6990931  18.58668 3.75
1455     5     1  107.6990931  16.65326 3.75
1456     5     1  111.2816452  20.32938 3.75
1457     5     1  113.6381556        NA 3.75
1458     5     1  117.5694056        NA 3.75
1459     5     1  121.3949264  24.27715 3.75
1460     5     1  126.3949264  22.38698 3.75
1461     5     1  131.3949264  22.37410 3.75
1462     5     1  136.3949264  21.34898 3.75
1463     5     1  141.3949264  22.42231 3.75
1464     5     1  146.3949264  22.60281 3.75
1465     5     1  149.4125147  25.56454 3.75
1466     5     1  152.6879155        NA 3.75
1467     5     1  156.5043116        NA 3.75
1468     5     1  158.9824264  22.98526 3.75
1469     5     1  162.6993535  22.09824 3.75
1470     5     1  167.9378952  26.33309 3.75
1471     5     1  172.9378952  26.98014 3.75
1472     5     1  177.9378952  22.86815 3.75
1473     5     1  182.9378952  20.32630 3.75
1474     5     1  187.9378952  18.41002 3.75
1475     5     1  192.9378952  16.84048 3.75
1476     5     1  197.0544423  18.95310 3.75
1477     5     1  200.0630468  39.38742 3.75
1478     5     1  202.6268488  39.19189 3.75
1479     5     1  206.9949478  25.84936 3.75
1480     5     1  211.9949478  23.47617 3.75
1481     5     1  216.9949478  25.10773 3.75
1482     5     1  221.9949478  23.90731 3.75
1483     5     1  226.9949478  23.05045 3.75
1484     5     1  231.9949478  22.22445 3.75
1485     5     1  236.9949478  21.51003 3.75
1486     5     1  241.9949478  20.75634 3.75
1487     5     1  245.6843943  19.95052 3.75
1488     5     1  247.7931117        NA 3.75
1489     5     1  251.0925908        NA 3.75
1490     5     1  256.0925908  25.17147 3.75
1491     5     1  261.0925908  20.54615 3.75
1492     5     1  264.9481898        NA 3.75
1493     5     1  268.2134242  37.75009 3.75
1494     5     1  271.4433721        NA 3.75
1495     5     1  274.8087367  39.55226 3.75
1496     5     1  279.8087367  36.55944 3.75
1497     5     1  284.8087367  35.72937 3.75
1498     5     1  289.8087367  42.91369 3.75
1499     5     1  294.8087367  42.06316 3.75
1500     5     1  298.1994975  40.25178 3.75
1501     5     1  300.8174718  39.15474 3.75
1502     5     1  304.7168208        NA 3.75
1503     5     1  309.3441650        NA 3.75
1504     5     1  313.4148687  28.13233 3.75
1505     5     1  317.8832280        NA 3.75
1506     5     1  322.8832280  19.73523 3.75
1507     5     1  327.8832280  19.70511 3.75
1508     5     1  332.8832280  21.99142 3.75
1509     5     1  337.3898483  28.73703 3.75
1510     5     1  341.2795618  26.34398 3.75
1511     5     1  346.2795618        NA 3.75
1512     5     1  351.2795618  23.13365 3.75
1513     5     1  356.2795618  22.17842 3.75
1514     5     1  360.8168017  24.34468 3.75
1515     5     1  365.6243540        NA 3.75
1516     5     1  370.6243540  26.69660 3.75
1517     5     1  375.6243540  25.48351 3.75
1518     5     1  380.6243540  25.27642 3.75
1519     5     1  385.6243540  22.99133 3.75
1520     5     1  390.6243540  21.90641 3.75
1521     5     1  395.6243540  23.72722 3.75
1522     5     1  400.4371770  25.88032 3.75
1523     5     2    1.8121348  24.61347 3.75
1524     5     2    5.8413004  21.24662 3.75
1525     5     2   10.8413004  17.68135 3.75
1526     5     2   14.3952067  20.99438 3.75
1527     5     2   18.0090088  16.65983 3.75
1528     5     2   21.4669515  17.54733 3.75
1529     5     2   24.9133056  25.05038 3.75
1530     5     2   28.8722900  25.06116 3.75
1531     5     2   32.8795817  21.56415 3.75
1532     5     2   37.8795817  22.14621 3.75
1533     5     2   42.8795817  20.13668 3.75
1534     5     2   47.8795817  19.61502 3.75
1535     5     2   52.8795817  19.61983 3.75
1536     5     2   57.8795817  20.36909 3.75
1537     5     2   62.8795817  19.73289 3.75
1538     5     2   67.4364822  20.83784 3.75
1539     5     2   72.2246328  27.33312 3.75
1540     5     2   75.5065338  23.26489 3.75
1541     5     2   78.9691640  24.82037 3.75
1542     5     2   83.9691640  19.53049 3.75
1543     5     2   88.9691640  21.10270 3.75
1544     5     2   93.9691640  21.66128 3.75
1545     5     2   98.9691640  20.51451 3.75
1546     5     2  102.9040614  23.50784 3.75
1547     5     2  107.0754170        NA 3.75
1548     5     2  110.8289327  15.92592 3.75
1549     5     2  114.3815368  21.63838 3.75
1550     5     2  117.4837504        NA 3.75
1551     5     2  121.2485934  24.92567 3.75
1552     5     2  125.9636968  27.40850 3.75
1553     5     2  130.9636968  30.26751 3.75
1554     5     2  135.9636968  29.98673 3.75
1555     5     2  140.9636968  27.32708 3.75
1556     5     2  145.9636968  28.17149 3.75
1557     5     2  150.9636968  27.44493 3.75
1558     5     2  154.4260597  26.50207 3.75
1559     5     2  158.0675893  26.96151 3.75
1560     5     2  163.0675893  25.56972 3.75
1561     5     2  166.4139435  25.40135 3.75
1562     5     2  169.9894643  28.04409 3.75
1563     5     2  174.0539174        NA 3.75
1564     5     2  178.3121205  31.64240 3.75
1565     5     2  183.3121205  24.98583 3.75
1566     5     2  189.1670822  29.88992 3.75
1567     5     2  193.8165614  33.21180 3.75
1568     5     2  198.6457280  35.61962 3.75
1569     5     2  203.6457280  34.34588 3.75
1570     5     2  207.3432541  31.51016 3.75
1571     5     2  210.7286705        NA 3.75
1572     5     2  215.2975504  38.05813 3.75
1573     5     2  220.2975504  42.40846 3.75
1574     5     2  225.2975504  40.87192 3.75
1575     5     2  230.2975504  36.98143 3.75
1576     5     2  235.2975504  35.67290 3.75
1577     5     2  239.8967692  28.55962 3.75
1578     5     2  244.8665608        NA 3.75
1579     5     2  249.8665608  27.08319 3.75
1580     5     2  255.4958582  30.78873 3.75
1581     5     2  260.3399989  35.71680 3.75
1582     5     2  266.0907801  30.76395 3.75
1583     5     2  271.1657801  38.38847 3.75
1584     5     2  275.0666913  26.84128 3.75
1585     5     2  278.1767171  29.06724 3.75
1586     5     2  282.4715088  35.83827 3.75
1587     5     2  287.4715088  28.78080 3.75
1588     5     2  292.4715088  34.88622 3.75
1589     5     2  297.4715088  32.53160 3.75
1590     5     2  301.6113464  31.79554 3.75
1591     5     2  306.0936320  42.75714 3.75
1592     5     2  311.0936320  24.76493 3.75
1593     5     2  316.0936320  22.50079 3.75
1594     5     2  321.0936320  22.85583 3.75
1595     5     2  326.0936320  26.57772 3.75
1596     5     2  329.7613403  29.53635 3.75
1597     5     2  331.9601750  38.29311 3.75
1598     5     2  333.9234629  31.73234 3.75
1599     5     2  336.4475514  37.78414 3.75
1600     5     2  340.4590098  23.18757 3.75
1601     5     2  344.0806244  22.79525 3.75
1602     5     2  347.9181244        NA 3.75
1603     5     2  351.9583587  18.17437 3.75
1604     5     2  356.2105723  44.73161 3.75
1605     5     2  359.5389577        NA 3.75
1606     5     2  362.5715093  46.03059 3.75
1607     5     2  367.2017171  44.29711 3.75
1608     5     2  370.5022379  38.17413 3.75
1609     5     2  374.1332275  38.18731 3.75
1610     5     2  379.1332275  25.87437 3.75
1611     5     2  384.1332275  24.60035 3.75
1612     5     2  389.1332275  23.27914 3.75
1613     5     2  392.8582804  23.48217 3.75
1614     5     3    2.5905445  24.18099 1.75
1615     5     3    7.5905445  23.30870 1.75
1616     5     3   12.5905445  25.72023 1.75
1617     5     3   17.5905445  25.05359 1.75
1618     5     3   22.5905445  24.39268 1.75
1619     5     3   27.5905445  25.05061 1.75
1620     5     3   32.5905445  22.91318 1.75
1621     5     3   37.5905445  24.51685 1.75
1622     5     3   42.5905445  23.82389 1.75
1623     5     3   47.5905445  22.54734 1.75
1624     5     3   52.5905445  22.57751 1.75
1625     5     3   57.5905445  23.06304 1.75
1626     5     3   62.5905445  22.32126 1.75
1627     5     3   67.5905445  23.31597 1.75
1628     5     3   72.5905445  18.24164 1.75
1629     5     3   75.9130703  18.39749 1.75
1630     5     3   79.0331222  24.20089 1.75
1631     5     3   83.7902836  26.67968 1.75
1632     5     3   87.3615076        NA 1.75
1633     5     3   89.9707524  27.54063 1.75
1634     5     3   94.1556482        NA 1.75
1635     5     3   97.3529138  25.97945 1.75
1636     5     3  100.6720544  27.36071 1.75
1637     5     3  105.6720544  25.30126 1.75
1638     5     3  110.6720544  23.22218 1.75
1639     5     3  115.6720544  24.24376 1.75
1640     5     3  120.6720544  23.76740 1.75
1641     5     3  125.6720544  23.64624 1.75
1642     5     3  130.6720544  24.93048 1.75
1643     5     3  135.6720544  25.05003 1.75
1644     5     3  140.6720544  24.27334 1.75
1645     5     3  145.6720544  24.62893 1.75
1646     5     3  150.6720544  25.22664 1.75
1647     5     3  155.6720544  27.99642 1.75
1648     5     3  160.6720544  27.68924 1.75
1649     5     3  165.6720544  27.74657 1.75
1650     5     3  170.6720544  25.89362 1.75
1651     5     3  175.6720544  27.61559 1.75
1652     5     3  180.6720544  26.11608 1.75
1653     5     3  185.6049982  26.33515 1.75
1654     5     3  188.9061711        NA 1.75
1655     5     3  192.0171086  32.46239 1.75
1656     5     3  196.2427596        NA 1.75
1657     5     3  198.5151554        NA 1.75
1658     5     3  202.4467961  37.30781 1.75
1659     5     3  207.4467961        NA 1.75
1660     5     3  212.4467961  33.58729 1.75
1661     5     3  217.4467961        NA 1.75
1662     5     3  222.9756993  24.92253 1.75
1663     5     3  227.9756993  27.26930 1.75
1664     5     3  232.9756993  26.75681 1.75
1665     5     3  237.9756993  29.97713 1.75
1666     5     3  241.7895013  26.70607 1.75
1667     5     3  245.7501784        NA 1.75
1668     5     3  250.7501784  35.76286 1.75
1669     5     3  255.7501784  37.75715 1.75
1670     5     3  260.7501784  37.79549 1.75
1671     5     3  265.7501784        NA 1.75
1672     5     3  269.7654128        NA 1.75
1673     5     3  273.1535638  49.14746 1.75
1674     5     3  277.5577305  37.49280 1.75
1675     5     3  282.5577305  22.43433 1.75
1676     5     3  285.8565586  23.82809 1.75
1677     5     3  289.2788243  39.70623 1.75
1678     5     3  294.9564284  30.07186 1.75
1679     5     3  299.5564297        NA 1.75
1680     5     3  304.4806497        NA 1.75
1681     5     3  309.4806497  25.46426 1.75
1682     5     3  314.4806497  27.01298 1.75
1683     5     3  319.4806497  23.03676 1.75
1684     5     3  323.7788266  25.68857 1.75
1685     5     3  328.1353367        NA 1.75
1686     5     3  333.1353367  25.48893 1.75
1687     5     3  338.1353367  25.79889 1.75
1688     5     3  344.2056492        NA 1.75
1689     5     3  349.2056492  24.80243 1.75
1690     5     3  354.2056492  25.23790 1.75
1691     5     3  359.2056492  25.08827 1.75
1692     5     4    3.1639831        NA   NA
1693     5     4    8.5746601  40.58774   NA
1694     5     4   13.5746601  34.53555   NA
1695     5     4   18.5746601  28.17518   NA
1696     5     4   23.5746601  28.87720   NA
1697     5     4   28.5746601  30.60316   NA
1698     5     4   33.5746601  30.40409   NA
1699     5     4   38.5746601  26.44941   NA
1700     5     4   43.5746601  25.18089   NA
1701     5     4   48.4044781  24.51680   NA
1702     5     4   51.9922388        NA   NA
1703     5     4   58.0105982        NA   NA
1704     5     4   63.0105982  24.21124   NA
1705     5     4   68.0105982  20.02678   NA
1706     5     4   73.0105982  26.45576   NA
1707     5     4   78.0105982  25.19682   NA
1708     5     4   83.0105982  25.86990   NA
1709     5     4   88.0105982  23.41407   NA
1710     5     4   93.0105982  31.94997   NA
1711     5     4   98.0105982  25.00751   NA
1712     5     4  103.0105982  25.55207   NA
1713     5     4  108.0105982  26.90420   NA
1714     5     4  113.0105982  28.25210   NA
1715     5     4  118.0105982  24.56583   NA
1716     5     4  123.0105982  25.35801   NA
1717     5     4  129.4186706  28.52201   NA
1718     5     4  134.4186706  23.81518   NA
1719     5     4  139.4186706  20.75909   NA
1720     5     4  144.4186706  20.25748   NA
1721     5     4  149.4186706  19.32338   NA
1722     5     4  153.8201026  22.22228   NA
1723     5     4  158.5483576  25.27086   NA
1724     5     4  163.3531753  20.54579   NA
1725     5     4  167.3664565  18.64197   NA
1726     5     4  171.1751805  32.12251   NA
1727     5     4  173.8184096  32.61432   NA
1728     5     4  176.0083836  30.05350   NA
1729     5     4  179.7280451  60.45718   NA
1730     5     4  184.7280451  42.06931   NA
1731     5     4  189.7280451  42.05800   NA
1732     5     4  194.7280451  41.60121   NA
1733     5     4  199.7280451  40.28733   NA
1734     5     4  204.7280451  40.68617   NA
1735     5     4  209.7280451  38.41300   NA
1736     5     4  214.7280451  36.62801   NA
1737     5     4  219.7280451  38.33945   NA
1738     5     4  224.7280451  39.72860   NA
1739     5     4  229.7280451  37.68280   NA
1740     5     4  234.7280451  37.33533   NA
1741     5     4  240.6970550  69.86100   NA
1742     5     4  245.6970550  54.35463   NA
1743     5     4  250.6970550  55.86051   NA
1744     5     4  254.2684091  50.64028   NA
1745     5     4  257.0939300        NA   NA
1746     5     4  260.7723154  47.80107   NA
1747     5     4  264.7902841  52.70598   NA
1748     5     4  268.4861175  38.56062   NA
1749     5     4  273.4861175  40.51936   NA
1750     5     4  278.4861175  37.87000   NA
1751     5     4  283.4861175  40.67165   NA
1752     5     4  288.4861175  43.08279   NA
1753     5     4  293.4861175  39.05208   NA
1754     5     4  298.4861175  41.42834   NA
1755     5     4  303.4861175  39.10268   NA
1756     5     4  308.4861175  40.20213   NA
1757     5     4  313.4861175  41.09388   NA
1758     5     4  318.4861175  43.88723   NA
1759     5     4  322.2803885  40.52654   NA
1760     5     4  326.3108576        NA   NA
1761     5     4  331.3108576  38.94509   NA
1762     5     4  336.3108576  38.20746   NA
1763     5     4  341.3108576  36.83599   NA
1764     5     4  346.4776544        NA   NA
1765     5     4  350.0212742        NA   NA
1766     5     4  351.8141128        NA   NA
1767     5     4  355.1512221        NA   NA
1768     5     4  360.1512221        NA   NA
1769     5     4  365.1512221        NA   NA
1770     5     4  370.1512221        NA   NA
1771     5     4  373.1585141  38.76503   NA
1772     5     4  376.2681497  40.75842   NA
1773     5     4  380.4802591  38.77399   NA
1774     5     4  384.8743997  41.35999   NA
1775     5     4  389.8743997  38.22246   NA
1776     5     4  394.8743997  44.52273   NA
1777     5     4  400.2439300  42.22794   NA
1778     5     4  405.2439300  44.11162   NA
1779     5     4  410.2439300        NA   NA
1780     5     4  415.2439300  42.52673   NA
1781     5     4  420.2439300  43.77683   NA
1782     5     4  424.6332534        NA   NA
1783     5     4  428.7600763  34.32553   NA
1784     5     4  432.0368992        NA   NA
1785     5     4  435.5079930  34.87141   NA
1786     5     4  439.6154148  35.74780   NA
1787     5     4  442.6574721  42.76775   NA
1788     5     4  445.9738784  34.61974   NA
1789     5     4  450.3400166  34.21032   NA
1790     5     4  454.1146183  41.44483   NA
1791     5     4  458.3599308  39.90589   NA
1792     5     4  462.4686548  40.09580   NA
1793     5     4  465.5130558        NA   NA
1794     5     4  467.5667017  34.90790   NA
1795     5     4  471.8836287  41.45812   NA
1796     5     4  474.0663110        NA   NA
1797     5     4  475.8512069        NA   NA
1798     5     4  479.4768658  37.29084   NA
1799     5     4  482.5660664  33.45888   NA
1800     5     4  485.5349466  32.63537   NA
1801     5     4  488.4659362        NA   NA
1802     5     4  490.9954935  48.67698   NA
1803     5     4  494.4350768        NA   NA
1804     5     4  499.5908060        NA   NA
1805     5     4  503.0943216        NA   NA
1806     5     4  506.7533060        NA   NA
1807     5     4  510.7924082  44.28544   NA

Example: Overnight heart rate variability (rmssd) measured each 5 minutes from sleep onset within multiple nights, in their turn nested within participants (ID).

lmer( rmssd ~ 
        TASW_c + 
        (TASW_c | ID / night), 
      data=dat)

Incorporating time in your model

Growth Curve Models
Modelling individual change over time, with each subject having their own unique trajectory (random slope) interacting with other predictors.

m1 <- lmer(Y ~ Time + (Time | ID), 
           data = mydataset)
m2 <- lmer(Y ~ Time * x1 + (Time | ID), 
           data = mydataset)

Fixed Intercept: Average starting level (baseline)
Fixed Slope: Average rate of change (growth rate) over time
Random Effects: Individual variability around the starting point and growth rate

Cross-lagged Models
Modelling temporal change: $x_{t-1}$ predicts $y_t$ controlling for $y_{t-1}$

# lagging variables
library(dplyr)
dat <- dat %>% group_by(ID) %>% 
  mutate(SBP_lag_pmc = lag(SBP_aft_pmc, n=1),
         SW_lag_pmc = lag(SW_pmc, n=1))
dat[1:3,c("ID","day","SW_pmc","SW_lag_pmc")]

# A tibble: 3 × 4
# Groups:   ID [1]
  ID      day SW_pmc SW_lag_pmc
  <chr> <int>  <dbl>      <dbl>
1 S001      1 -0.883     NA    
2 S001      2  1.95      -0.883
3 S001      3  0.783      1.95

# cross-lagged model
m <- lmer(SBP_aft ~ 
            SBP_lag_pmc + 
            SW_lag_pmc + 
            (1|ID), data = dat)

Within-person mediation (1/2)

The lme4 package is not designed for testing mediation models

However, the mediation package allows to estimate the
average causal mediation effect (ACME) with quasi-Bayesian confidence intervals

library(mediation)
mmed <- lmer(SBP_aft ~ SW_pmc + (1 | ID), data = dat) # mediator model
mout <- lmer(SBP_eve ~ SBP_aft + SBP_aft_pm + SW_pmc + (1 | ID), data = dat) # outcome model

# indirect effect
m <- mediate(model.m = mmed, model.y = mout, sims = 50, treat = "SW_pmc", mediator = "SBP_aft")
summary(m) # results


Causal Mediation Analysis 

Quasi-Bayesian Confidence Intervals

Mediator Groups: ID 

Outcome Groups: ID 

Output Based on Overall Averages Across Groups 

                 Estimate 95% CI Lower 95% CI Upper p-value    
ACME             0.359390     0.094012     0.674259  <2e-16 ***
ADE              0.144395    -0.510656     0.779417    0.72    
Total Effect     0.503784    -0.224774     1.261319    0.36    
Prop. Mediated   0.522197   -18.092613     2.838744    0.36    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Sample Size Used: 660 


Simulations: 50

Within-person mediation (1/2)

Alternatively, we can move to SEM or path analysis with the lavaan package.

# Define the 2-level mediation model
m <- "level: 1 
      SBP_aft ~ a * SW_pmc
      SBP_eve ~ b * SBP_aft + cp * SW_pmc
      indirect_W := a * b
      
      # between-level saturated model
      level: 2 
      SBP_eve ~ SBP_aft_pm
      SBP_aft ~~ SBP_eve"

# Fit the model
library(lavaan)
fit <- sem(model = m, data = dat, cluster = "ID")
standardizedsolution(fit)[1:3,] # standardized parameters

      lhs op     rhs label est.std    se     z pvalue ci.lower ci.upper
1 SBP_aft  ~  SW_pmc     a   0.123 0.039 3.118  0.002    0.046    0.200
2 SBP_eve  ~ SBP_aft     b   0.247 0.041 6.032  0.000    0.166    0.327
3 SBP_eve  ~  SW_pmc    cp   0.011 0.039 0.295  0.768   -0.065    0.088

Serial mediation

serial_msem <- "level: 1
                # 1. Predicting the FIRST mediator
                M1 ~ a1 * X

                # 2. Predicting the SECOND mediator by X and M1
                M2 ~ a2 * X + d * M1
            
                # 3. Predicting the OUTCOME by X and both mediators
                Y ~ cp * X + b1 * M1 + b2 * M2
                
                # effects calculation (User-defined via ':=')
                # -------------------------------------------
                
                # indirect effects
                ind_M1 := a1 * b1 # Path: X -> M1 -> Y
                ind_M2 := a2 * b2 # Path: X -> M2 -> Y
                
                # SERIAL indirect effect (X -> M1 -> M2 -> Y)
                ind_serial := a1 * d * b2 
                
                # Overall indirect and total effects
                total_ind := ind_M1 + ind_M2 + ind_serial
                total_eff := cp + total_ind
                
                level: 2
                # saturated model at the between level
                Y ~~ M1 + M2
                M1 ~~ M2"

Generalized linear mixed-effects regression (GLMER)

Generalization of LMER:

In addition to modeling normally distributed quantitative dependent variables (like ‘standard’ LMER), they can also manage non-normally distributed variables such as:
- Quantitative variables that only take positive values $\rightarrow$ Gamma
- Count variables $\rightarrow$ Poisson
- Binary/Dichotomic variables $\rightarrow$ Binomial
This is done by integrating 3 components:
1. Probability distribution for the expected value of the $y$ variable
  (e.g., Gaussian, Gamma, Poisson, binomial)
2. Linear model of the predictors, including both fixed and random effects (LMER)
3. Link function that translates the expected values of the $y$ variable into the values predicted by the linear model (e.g., identity, log, logit, inverse)

m <- glmer(nightwork_YesNo ~ workload_pmc + (1 | ID), 
           family = binomial( link = "logit" ),
           data = mydataset)

We are done!

Additional resources

Bates, D. (2022). lme4: Mixed-effects modeling with R. stat.ethz.ch/~maechler/MEMo-pages/lMMwR.pdf
Bliese, P. (2022). Multilevel modeling in R (2.7). cran.r-project.org/doc/contrib/Bliese_Multilevel.pdf
Menghini, L., Perinelli, E., Balducci, C. (2025). Manipulation of Intensive Longitudinal Data: A Tutorial in R with Applications on the Job Demand‐Control Model. International Journal of Psychology, 60(2), e70040. Link to R pipeline
Menghini, L. (2023). Introduction to multilevel modeling (full slides presented at the “Advanced data analysis for psychological science” master course). github.com/Luca-Menghini/advancedDataAnalysis-course

PSICOSTAT

We are an interdisciplinary research group interested in Psychology and Statistics, working in areas related to quantitative psychology, psychometrics, psychological testing and statistics. Our goal is to promote the connection between the two fields in order to benefit the progress of scientific research.

Multilevel modelling with R

Course material

About myself

About yourselfs

Workshop outline

Intensive Longitudinal Designs in Occupational Health Psychology

Intensive Longitudinal Designs (ILD)

ILD landscape

Which designs?

Advanced designs

Wearable technology

Laboratory vs. Ambulatory assessment

Laboratory vs. Ambulatory assessment

From ILD to Multilevel modelling

Short introduction to R

Why ?

RStudio

Some basic commands

Relational & logical operators

Types of R objects (classes)

Types of R objects: data.frame

How to load your data: set the work directory

How to load your data: data reading

Which dataset is it?

The dataset

Workspace: Functions & packages

Time for a (micro) break!

LMER intro: From linear models to multilevel modelling

Linear models (LM)

LM core assumptions

Linear models in

Nested data & Local dependencies

Linear mixed-effects regression models (LMER)

From LM to LMER

Random intercept

Random slope

From LMER to multilevel modelling

HandZone: From data pre-processing to cross-level interactions

The dataset

From data pre-processing to cross-level interactions

1. Data pre-processing (1/3)

1. Data pre-processing (2/3)

1. Data pre-processing (3/3)

2. Level-specific correlations

3. Null model & ICC

4. Main effects (random intercept model)

Why centering level-1 predictors?

5. Random slope model

6. Cross-level interaction

Ok, but where the hell are my p-values!?

One (fundamental) step back: Model assumptions

Cluster-level influential cases

From data pre-processing to cross-level interactions

LMER advanced 3-level models, growth curve and cross-lagged models, mediation, GLMER

3-level models

Incorporating time in your model

Within-person mediation (1/2)

Within-person mediation (1/2)

Serial mediation

Generalized linear mixed-effects regression (GLMER)

We are done!

Additional resources

PSICOSTAT

THE END

Intensive Longitudinal Designs
in Occupational Health Psychology

Types of R objects: `data.frame`

LMER intro:
From linear models
to multilevel modelling

HandZone:
From data pre-processing
to cross-level interactions

LMER advanced
3-level models, growth curve and cross-lagged models, mediation, GLMER