Latent variable modelling

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Latent variable models are statistical models that do not only contain observed variables but also latent (unobserved) variables. We study various of such models

  • Multilevel models are used for data that have a multilevel structure, such as pupils nested in classrooms in schools and repeated measures nested within subjects.
  • Structural equation models are used to evaluate structural relationships between measured and latent variables. Examples are confirmatory factor analysis, latent growth models and mediation models.
  • Item Response Theory models relate latent traits (e.g. knowledge) to observed variables (e.g. test scores). Such models are used for the construction of tests and questionnaires, and for the purpose of ability assessment.
  • Other type of latent variable models, such as latent class and mixture models, latent profile analysis and neural network models.

An example is a school-based smoking prevention and cessation study. Randomization is done at the school level so that all subjects within a school receive the same treatment. The data have a multilevel structure with pupils nested within classes within schools. Outcome variables such as smoking behavior may be latent and measured using multiple items. The effect of treatment condition on the outcome may be mediated by variables such as intention. Data from such an intervention study should be analyzed by a model that allows for latent variables, multiple levels of nesting and mediation effects, that is a multilevel structural equation model.

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Our topics for research into such models include statistical power analysis, small sample solutions, longitudinal research, multiple imputation, and measurement invariance. We also study Bayesian estimation methods for such models and Bayesian and AIC-related methods for the evaluation of informative hypotheses.

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