Information Matrices in Latent-Variable Models

The Fisher, or expected, information matrix for the parameters in a latent-variable model is bounded from above by the information that would be obtained if the values of the latent variables could also be observed. The difference between this upper bound and the information in the observed data is the “missing information.” This paper explicates the structure of the expected information matrix and related information matrices, and characterizes the degree to which missing information can be recovered by exploiting collateral variables for respondents. The results are illustrated in the context of item response theory models, and practical implications are discussed.