# Linear Mixed Model with Unbalanced Observational Data

I am doing an observational study that yields very unbalanced data. First, let me describe the experiment and my hypothesis.

Participants performed a task (e.g., reading) with some physiological measure recorded every 5 second (say, pupil size). For half of the people, they were told to press a key whenever they caught themselves distracted during reading (so always a "YES" response). For another half, they were sometimes interrupted by a probe and they responded to the probe whether they were just distracted (can be "YES" or "NO"). My hypothesis is that pupil size would show a different time course shortly before the report, depending on participant's attention. E.g., pupil size keeps increasing before participants indicate "YES", but remains the same for "NO".

My data structure looks like this:

(Data was aggregated at participant-level)

As you can see, people in group A do not have data associated with "NO". For group B, only some people have both YES and NO data (they may be focused all the time - only have data for NO, or distracted all the time, only have data for YES).

I am using Linear Mixed Model (lme4) with a formula like this:

p_size ~ time * distracted + group + (1+time|subject)


The random effect of "distracted" was not included because of the imbalance.

My questions are:

(1) Is my model correctly specified?

(2) Is there a better approach to investigate the same question, and why? (e.g., bootstrapping, perhaps?)

Thank you!

• Specifically, in my model above I am not comfortable with treating "distracted" as if it is a between-subject factor, which would increase Type I error rate. Should I perhaps do an additional analysis using a subset of data where participants have both YES and NO response (i.e., a subset of group B), so that I can model the random effect of "distracted"? – Han Zhang Jun 28 '18 at 21:43