GLLAMM
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
References
RabeHesketh, Skrondal and Pickles (2004). Generalized
multilevel structural equation modelling. Psychometrika,
69 (2), 167190 Local.
Skrondal, A. and RabeHesketh, S. (2004).
Generalized latent variable modeling:
Multilevel, longitudinal and structural equation models.
Boca Raton, FL: Chapman & Hall/ CRC Press.
Other publications
