VanLeeuwen et al. 1996

VanLeeuwen, D. M., L. W. Murray, and N. S. Urquhart. 1996. A mixed model with both fixed and random trend components across time. Journal of Agricultural, Biological, and Environmental Statistics 1(4):435-453.

The use of longitudinal data is common in environmental and agricultural applications where interest lies in trends in a response variable through time.  Various methodologies have been applied in the analysis of such data.  Although many methods allow for correlation among the repeated measurements taken on the same experimental unit, nearly all assume independence of those units.  Additionally, in mixed model settings, where trends are random, interest has often focused on Best Linear Unbiased Predictors (BLUPs), rather than variance components, and on techniques for large unbalanced data sets rather than relatively small balanced data sets.  We present a model that incorporates random trends through time and also allows correlations to exist among observations taken at the same time from the different units.  The analysis (for the balanced case) focuses on variance components and an overall fiixed trend through time, and is based on intuitively reasonable sums of squares that, under the usual normality assumptions, can be shown to possess desireable distributional properties.