Generalized Linear Latent And Mixed Models (GLLAMMs) are a class of multilevel latent variable models, where

a latent variable is a factor
  or a random effect
    (intercept or coefficient)
  or a disturbance/residual

Main Features of GLLAMMs

  • Response Model: conditional on the latent variables, the response model is a generalized linear model with:
    • Links and families for the following response types:
      • continuous
      • dichotomous
      • ordinal
      • unordered categorical/ discrete choice
      • rankings
      • counts
      • durations
      • mixed responses
    • Heteroscedastic error terms
    • Latent variables in the linear predictor:
      • interpretable as factors with factor loadings
      • interpretable as random effects
      • varying at (any number of) different levels of a hierarchical or multilevel dataset
  • Structural Model: structural equations for the latent variables:
    • Regressions of latent variables on other latent variables
    • Regressions of latent variables on observed variables
  • Distribution of the latent variables:
    • Multivariate normal
    • Discrete
      • Latent classes or finite mixtures
      • Nonparametric maximum likelihood (NPML)

Important special cases of GLLAMMs

  • Generalized Linear Mixed Models
  • Multilevel Regression Models
  • Factor Models
  • Item Response Models
  • Structural Equation Models
  • Latent Class Models


Rabe-Hesketh, Skrondal and Pickles (2004). Generalized multilevel structural equation modelling. Psychometrika, 69 (2), 167-190 Local.

Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal and structural equation models. Boca Raton, FL: Chapman & Hall/ CRC Press.

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