Latent variable models with fixed effects

We discuss latent variable models that allow for fixed effect covariates, as well as covariates affecting the latent variable directly. Restricted maximum likelihood and maximum likelihood are used to estimate model parameters. A generalized likelihood ratio test can be used to test significance of the covariates effecting the latent outcomes. Special cases of the proposed model correspond to factor analysis, mixed models, random effects models, and simultaneous equations. The model is applied to birth defects data, where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls.