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
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.
Other publications
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