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1989) ML2: Software for Two-Level Analysis. London: Institute of Education, University of London. , and Prosser, B. 0. Bristol, UK: Centre for Multilevel Modeling. W. (1988) ‘Education Applications of Hierarchical Linear Models: A Review’, Journal of Educational Statistics, 12: 85–116. W. S. (1986) ‘A Hierarchical Model for Studying School Effects’, Sociology of Education, 59: 1–17. A. O. (2001) ‘Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves’, Biometrics, 57: 253–9. , and Brumback, B.

5), it is surprising to some that this is an automatic consequence. 5). In this formulation, the covariates on the random effects are represented by zs rather than xs in order to distinguish the two. This structure can be written (in matrix form) for group j as y j = X j β + Z j u j + ε j . Here, y j is the vector of observations, X j is the fixed effects design matrix, and Z j is a the random effects design matrix for group j. tex” — 2013/7/25 — 11:25 — page 9 10 THE MULTILEVEL MODEL FRAMEWORK by a distributional assumption.

This chapter merges ideas from latent growth curve modeling (Jones and Nagin, 2007) and model-based clustering (Banfield and Raftery, 1993) to form a coherent framework for more realistic longitudinal data modeling. tex” — 2013/7/25 — 10:38 — page xxx 4 THE DESIGN AND GOALS OF THIS BOOK Having established both the general framework and extensions of multilevel models, Part III of the Handbook covers model fitting and specification issues. , replacing normal distributions with tor Cauchy distributions).

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