Efficiency comparison of methods for estimation in longitudinal regression models

Estimation of the mean response in a longitudinal regression model can be based on a model which relates the response variable to a set of covariates. Often, for reasons of cost, time, and practicality, a larger set of covariates may be available at the model development stage than in later applications of the model. There are two different approaches to dealing with covariates which will not be available in later applications. Clearly, one can, even at the model development stage, simply ignore covariates which will not be collected later. Alternatively, one may apply the approach of simultaneous equations or the approach of handling missing data, where the covariates which will be unavailable are estimated or imputed from the available covariates. When data are not longitudinal, these two approaches produce the same result. When data are longitudinal, however, they are different, although both of them provide almost unbiased estimates and predictions. The purpose of this study is to compare the relative efficiency of these two methods when data are longitudinal. We find that when the unavailable covariates are in fact not related to the response variable, the two methods have the same performance in terms of asymptotic efficiency; otherwise neither method is uniformly better than the other. In specific situations, asymptotic relative efficiency between the two methods can be estimated so that the better method can be selected.