I'm attempting to fit a linear mixed model to my dataset.  This data is the measure of stimulus-evoked power as a function of time.  We have 32 subjects from two populations (broken down by genotype).  The stimulus-evoked power is sampled at a high rate (one data-point every 5 msec) and reflects the "longitudinal" or "within-subjects" measure in my study.

Right now I've defined the model as:

power ~ genotype * time + (1|subject_id)

I understand that one must also test additional models such as:

power ~ genotype * time + (time|subject_id)
power ~ genotype * time + (1|subject_id) + (0+time|subject_id)

However, power is not a linear function of time (i.e. it is non-monotonic).  Power rapidly increases over a few hundred milliseconds to a peak value then gradually declines afterwards.  In this situation, would it be inappropriate to use time for determining a slope for the random effect?

I'm actually not even sure whether a linear mixed model is appropriate for this type of data (considering the power response is non-monotonic with respect to time).  However, this is how the original analysis was set up by a predecessor and I am currently trying to determine the validity of this approach.

Thanks,
Brad

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