GLLAMM Models (original) (raw)
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
- Links and families for the following response types:
- 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.