I've conducted an experiment in which we have registered a physiological measure (FR) of 30 participants in two different conditions. In each condition, I registered the measure in 20 time points, equally spaced in time.
To analyze the data, I'have fitted a multilevel model in R, using the nlme package. I've considered the condition as fixed factor, while time is a random factor (nested in subjects). My interest is to check whether there is an effect of condition on FR.
The first model (model 1) I fitted shows that condition is a significant predictor of the outcome. Then, as measures in each time point seem to be correlated and this correlation is weaker as time gets further apart, I included an autoregressive covariance structure in the model (corAR1), and this second model (model 2) fits better, although condition is no longer significant.
My questions are:
How can I check the homoskedasticity of the models? and the independence of residuals?
If both models show heteroskedasticity, what can I do to correct it?
If only one of them is homoskedastic and residuals are not correlated, should I interpret that the model is right, and that the covariance structure applied to the other model is wrong?
Thank you for your help!!