Latent variable models are where the hiddent variable explains a collection of manifest variables. Factor analysis is the classic latent variable modeling technique. The important thing about factor analysis is that the manifest variables are continuous variables and so are the hidden(latent) variables. So this introduces some additional types of models called latent profile analysis, latent trait model, and latent class model, depending on the type of latent variable and the manifest variable.
(latent variable, manifest variable) - Analysis to be used
(continuous, continuous) - Factor analysis - read more about it here.
(continuous, discrete) - Latent profile analysis (LPA)/mixture model - read more about it here.
(discrete, continuous) - Latent trait analysis (LTA)/item response models/Rasch - read more about it here.
(discrete, discrete) - Latent class analysis (LCA)/multinomial model - read more about this here.
Some important reading material about using SAS in this category of models.
(1) www2.sas.com/proceedings/forum2007/192-2007.pdf - LCA related
Some more references to come ...
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