Factor Analysis of Ordinal Variables with Full Information Maximum Likelihood

The basic idea of factor analysis is the following. For a given set of manifest variables x1, . . . , xp one wants to find a set of latent variables ξ1, . . . , ξk, fewer in number than the manifest variables, that contain essentially the same information. The latent variables are supposed to account for the dependencies among the manifest variables in the sense that if the latent variables are held fixed, the manifest variables would be independent. Classical factor analysis assumes that both the manifest and the latent variables are continuous variables and is usually carried out by factor analyzing the sample covariance or correlation matrix of the manifest variables. There is a long history of methods for fitting factor models to a correlation or covariance matrix, see e.g., Jöreskog (2006)