Efficient analysis of mixed hierarchical and cross-classified random structures using a multilevel model

Authors
Goldstein, H. and Rasbash, J.
Year
1994
Journal
Journal of Educational and Behavioral Statistics, 22:3, 364-375
DOI
10.3102/10769986019004337
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.

Number of levels
2
Model data structure
Response types
Multivariate response model?
Yes
Longitudinal data?
Yes
Substantive discipline
Impact

Sets out algorithm for general use.

Paper submitted by
Harvey Goldstein, Graduate School of Education, University of Bristol, h.goldstein@bristol.ac.uk
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