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mixed-effects model with partially nested fixed effects

2 messages · Yuqi Liu, Jake Westfall

Original
Yuqi Liu
# 
Hi R-experts,

  I am analyzing data from 3 experiments using linear mixed model. Each experiment had 2 fixed effects, movement type and motor effort. Movement type is shared by all experiments, motor effort varied but partially shared across experiments. The data looks like this:


  Subject              experiment        movement_type              motor_effort     DV

  1                           1                              synchronous                      normal
  2                           1                              asynchronous                    normal
   .
   .
   .

  101                       2                              synchronous                      normal
  102                       2                              asynchronous                    normal
  103                       2                              synchronous                      medium
  104                       2                              asynchronous                    medium
   .
   .
   .
  201                       3                              synchronous                      normal
  202                       3                              asynchronous                    normal
  203                       3                              synchronous                      hard
  204                       3                              asynchronous                    hard
   .
   .
   .
  I want to test if the effect of movement type differed across experiments and motor effort, but I am a little confused of how the model should be constructed in this case.

  My current model is :   model <- lmer(DV ~ movement_type * experiment/motor_effort + (1|subject), data). Is that correct in terms of my purpose?

  I am also wondering how to center independent variables in this case. For movement_type, I could code "synchronous" as "0.5" and "asynchronous" as "-0.5". For motor_effort, should I center them for each experiment separately, or across all experiment?

Thank you for your help!
Yuqi
Jake Westfall
# 
Hi Yuqi,

Because each subject has only a single row, you don't need random effects
for subjects. You do have observations nested in experiments, so you
probably want some sort of experiment effects. Right now you have fixed
experiment effects, but random effects probably make more sense.

The maximal model
<http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.703.657&rep=rep1&type=pdf>
w/
random experiment effects would be like:
lmer(DV ~ movement_type*motor_effort + (movement_type*motor_effort|
experiment))

In case of convergence problems, you can probably drop the random
movement_type*motor_effort
interaction, but usually it's best to decide what to drop by eyeballing the
nonconverged results to see which random effects seem extraneous (due to
either 0 estimated variance or perfect estimated correlations with other
random effects).

As for how to center, it depends on what you're interested in. A good
reference here is Enders & Tofighi
<http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.928.9848&rep=rep1&type=pdf>
.

Jake
On Mon, Oct 9, 2017 at 9:20 AM, Yuqi Liu <yliu at psych.udel.edu> wrote: