I have some doubts about the covariance structure in a multilevel model fitted in R (using the
nlme package). I'm not an expert (just starting to learn statistics...), so I apologize if some of my questions seem evident. I've checked the previous posts and haven't found an answer.
I have data from an experiment in which we have registered physiological data from 30 subjects in 2 conditions (with 30 trials in each condition). These 30 trials are close in time, and we expected a higher correlation between closer trials, with the correlation decreasing as trials are further apart from each other. We are interested in the effect of condition, not in time effects. I think that the right way to analyze these data is to fit a multilevel model, in which TRIAL is a level 1 variable, SUBJECT is a level 2 variable, CONDITION is a fixed factor, and the DV is the physiological response (FR). The R command I'm using is:
lme(fixed= FR ~ CONDITION, data=mydata, random= ~ TIME | SUBJECT)
My (many) questions are both theoretical and practical:
Which covariance structure
lmedoes use by default? Is it a problem not to use the most appropriate covariance structure?
I've read that an autoregressive covariance structure (AR1) refers to a constant variance at each time point and a weaker correlation as time points get further apart. My data only meets the second criterion. How can I know which covariance structure is right for my data? How important is it to the validity of the results?
I'm only interested in the CONDITION effect, which is significant when I'm not including TIME in the model. I'm not interesting in TIME effects, nor I want to use the model to make a prediction, but only to check the significance of the CONDITION effects. Is it correct if I drop out TIME and fit a model only with CONDITION?
Thank you for your help!