title	The Art of Modeling. An Introduction to Linear Mixed Effects Models with R.
author	Klaus Frieler, Max Planck Institute for Empirical Aesthetics, Frankfurt/Main
date	02.05.2025

Materials for a Linear Mixed Effects Models Workshop

Data Sets

The project includes several data sets that are used during the workshop.

Simulating random effects data

Central are simulated data, which can be generated using simulate_lmm() in simulate_lmm.R. The generated data are coming from a fully crossed design of n_rater ratings for n_item items with respect to liking. The items are presented in two conditions, audio-only (AO) and audio-visual (AV). The effect of condition on liking can be set be with the parameter fixef_beta, the residual error with the parameter eps, the global intercept with y0. The random effects are set with the parameter ranef which needs to be a nested list. The parameter list has three lists with names intercept, beta, and cor on the top level, which
need to be lists with entries ratersand ìtems, containing the corresponding random effects parameters.

Variable	Type	Values
rater	factor	[ r01 | r02 | r03 | r04 | ... ]
item	factor	[ i01 | i02 | i03 | i04 | ... ]
condition	factor	[ AO | AV ]
betas	numeric
y1	numeric
liking	numeric

mer (Music Emotion Recognition)

This is an abridged version of the original data from Lange & Frieler, 2016. The data come from an experiment where 20 audio engineers (column p_id) rated 60 items (column s_id) on several scales. The data set is filtered to included only cases which have a definite tempo (column MIR.tempo), which are 53 in total.

The main ratings were perceived emotional expressions (columns angry, sad, happy, peacef, tender, fearf) on a scale from 1 to 7. These were aggregated with factor analysis to two variables representing valence and arousal (columns AROUSAL and VALENCE.)

Besides that, for each item there are 11 audio features extracted, where MIR.tempo was manually annotated (see table below).

Finally, there is a categorial variable (column emo), which contains a emotion label, derived as the emotion variable with the highest mean across participant for this item.

Variable	Type	Values
p_id	integer	1–20
s_id	integer	1–60
AROUSAL	numeric
VALENCE	numeric
angry	integer	1–7
sad	integer	1–7
happy	integer	1–7
peacef	integer	1–7
tender	integer	1–7
fearf	integer	1–7
MIR.low_energy_mean	numeric
MIR.pitch_mean	numeric
MIR.rms_mean	numeric
MIR.regularity_mean	numeric
MIR.keyclarity_mean	numeric
MIR.mode_mean	numeric
MIR.pulse_clarity_mean	numeric
MIR.spectral_novelty_mean	numeric
MIR.mode_std	numeric
MIR.attacktime_std	numeric
MIR.tempo	numeric
emo	factor	[ angry | fearf | happy | peacef | tender | sad ]

covox (Voice Preferences)

This is a selection of the Covox dataset (Bruder et al., 2024). The data comes from a rating experiment, where 60 raters (column rater), assessed 330 items (column item) in total which respect to liking (column score).

The items were short monophonic audio excerpts by 22 singers which rendered 3 different melodies (column melody) in 5 different styles (column style), three singing styles (opera, pop, and lullaby) and two speech styles (infant directed ID and adult directed AD, see also column speech).

Further, all participants rated all items on two different occasions (column time).

Variable	Type	Values
singer	factor	[ singer01 | singer02 | singer03 | singer04 | ... ]
rater	character	[ r01 | r02 | r03 | r04 &vert& ... ]
style	factor	[ AD | ID | lullaby | opera | pop ]
melody	factor	[ CH | MS | NN ]
time	factor	[ T1 | T2 ]
score	integer	1–9
item	factor	[ singer01_CH_AD | singer01_CH_ID | singer01_CH_lullaby | singer01_CH_opera | ... ]
speech	logical	[TRUE | FALSE]

kid_beats (Development of Synchronisation Abilities in Children)

This is a subset of the raw data from Will et al. 2024. In this experiment, 188 participants from five different age groups (column age_group), had to tap to a beat in two different settings and for two different tempos. Precision (precision) was measured as the negative logarithm of the standard deviation (column log_sd_ioi) of the produced inter-beat intervals (the higher, the better). Furthermore, beat perception (beat_perc) and production (beat_prod) skills were assessed with a different test battery.

Variable	Type	Values
p_id	factor	[ i_e_05_02 | i_e_06_02 | i_e_07_02 | i_e_09_02 | ... ]
age_group	factor	[ 5yo | 6yo | 7yo | 8yo | adults ]
setting	factor	[ metronome | social ]
experimenter	factor	[ i | l | w ]
tempo	factor	[ fast | slow ]
beat_perc	numeric
beat_prod	numeric
log_sd_ioi	numeric
beat_ability	numeric
precision	numeric

scenario2 (Simulated data with measurement error)

This is simulated data with heteroscedastic and measurement error from a study by Müllensiefen & Frieler (in preparation). Outcome is y, with two predictors x and z. True coefficients are intercept = 1, beta_x = .4, and beta_z = .2. The original values, before applying measurement errors xe, ye, and ze', are in columns xt, ytandzt'. The level of measurement error can be high or low.

Variable	Type	Values
y	numeric
x	numeric
xe	numeric
xt	numeric
zt	numeric
ze	numeric
z	numeric
p_id	integer	1–50
me	character	[ low | vert ]