A review of two different approaches for the analysis of growth data using longitudinal mixed linear models: Comparing hierarchical linear regression (ML3, HLM) and repeated measures designs with structured covariance matrices (BMDP5V)

Abstract

In this paper we review two approaches for the analysis of growth data by means of longitudinal mixed linear models. In these models the individual growth parameters, (most often) specifying polynomial growth curves, may vary randomly across individuals. This variation may in turn be accounted for by explaining variables. The first approach we discuss, is a type of multilevel model in which growth data are treated as having a hierarchical structure: measurements are ‘nested’ within individuals. The second is a version of a MANOVA repeated measures model employing a structured (error)covariance matrix. Of both approaches we examine the underlying statistical models and their interrelations. Apart from this theoretical comparison we review software by which they can be applied for real data analysis: two multilevel programs, ML3 and HLM, and one repeated measures program, BMDP5V. The programs are described and discussed with respect to several more general criteria, such as data setup and handling, implemented numerical routines and user friendliness, and, in particular, with respect to their application in longitudinal situations, i.e. their capabilities for the analysis of data on growth. Two data sets are used to compare the results of analyses performed by the three programs. Although both ways of specifying growth curve models show some shortcomings, each appears to be a fruitful method to handle growth data, theoretically, as well as in a practical sense. For the most part, shortcomings are induced by the accompanying software, developed within different scientific traditions. Applied to comparable problems, the three programs produce equivalent results.