Multilevel time series models with applications to repeated measures data

A time series model is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals and it is shown how the autcorrelation parameters can themselves be structured in terms of further explanatory variables.

Abstract

The analysis of repeated measures data can be conducted efficiently using a two-level random coefficients model. A standard assumption is that the within-individual (level 1) residuals are uncorrelated. In some cases, especially where measurements are made close together in time, this may not be reasonable and this additional correlation structure should also be modelled. A time series model for such data is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals. First- and second-order autoregressive models are considered in detail, together with a seasonal component. Both discrete and continuous time are considered and it is shown how the autocorrelation parameters can themselves be structured in terms of further explanatory variables. The models are fitted to a data set consisting of repeated height measurements on children.