When should I allow level 1 errors to be autocorrelated?
Generally, you would allow level 1 error terms to be correlated when the observations are close together in time so that you would expect that an observation will be similar to the previous observation (the phenomenon known as ‘autocorrelation’). When the observations are further apart in time so that you expect that, after you have taken the mean response for the individual into account, there is no relationship between an observation and the one before it, the observations are not autocorrelated and you do not need to allow the level 1 error terms to be correlated. What counts as ‘close together in time’ and what counts as ‘further apart in time’ depends on exactly what you are measuring. Sometimes it is hard to decide before modelling whether the level 1 error terms should be correlated or not. In that case it is a good idea to fit a model which allows the level 1 error terms to be correlated and compare that model with one which does not allow the level 1 error terms to be correlat
