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An overview is given of modeling of longitudinal and multilevel data using a latent variable framework. Particular emphasis is placed on growth modeling. A latent variable model is presented for three-level data, where the modeling of the longitudinal part of the data imposes both a covariance and a mean structure. Examples are discussed where repeated observations are made on students sampled within classrooms and schools.

This article gives an introduction to some new techniques for multilevel covariance structure modeling with latent variables. Although these techniques only incorporate a subset of models that are relevant to multilevel data, the techniques do provide a large set of new analysis possibilities and have the advantage that they only require conventional structural equation modeling software. The presentation draws on methodology presented in earlier works by the author.

This article discusses how a factor model with continuous latent variables can be used to analyze a set of strongly skewed dichotomous items and how such a model can be used for classification of subjects. The suitability of the specification of normally distributed latent variables, as is assumed with the use of tetrachoric correlations, is investigated. Both exploratory and confirmatory analyses, including multiple groups with mean structures, are illustrated. Substantive findings include support for unidimensionality of the items used in the DSM-III diagnosis of depression and a large degree of invariance in factor structure for the Baltimore and Durham sites.

This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a random mode of variation. Both maximum likelihood and Bayesian analyses are applied. A survey of close to 50,000 subjects in 26 countries is used as an illustration. In addition, the two methods are studied by Monte Carlo simulations. A list of considerations for choosing between the two methods is presented.