Re: Residuals

From: lewis@c255.ucsf.EDU (LSheiner) Subject: Re: Residuals Date: Tue, 6 Oct 1998 12:36:20 -0700 Which 'residuals' are your referring to? 1. Within-individual 'epsilons'? These are estimated from observation minus IPRED - individual prediction; i.e., prediction made with eta set to individual specific estimate. But IPRED is a Bayes estimate and is biased. So the IPREDs within an individual will not have mean zero. Pooling all of them, one might be able to see if their distribution is normal-like, but why be concerned with this? ELS is a least-squares type method, and enjoys reasonable asymptotic properties without the assumption of normality. 2. Between-individual residuals? These are the post-hoc etas. Their mean should be near zero. There are usually too few to check normality, and again, normality is not an essential assumption. 3. RES (that is DV-PRED) - these are peculiar creatures and no assumption about their distribution is made. In sum, there are no essential assumptions made about the distribution of any of the possible residuals, and the estimates of the various residuals will not necessarily well reflect the distribution of the "true" residuals. Residuals are very useful for model-building, to check whether the model descibes the data adequately. But checking the distributional shape is not a particularly helpful procedure for this purpose... LBS.