Information Matrices and Standard Errors for MLEs of Item Parameters in IRT

The paper clarifies the relationship among several information matrices for the maximum likelihood estimates (MLEs) of item parameters. It shows that the process of calculating the observed information matrix also generates a related matrix that is the middle piece of a sandwich-type covariance matrix. Monte Carlo results indicate that standard errors (SEs) based on the observed information matrix are robust to many, but not all, conditions of model/distribution misspecifications. SEs based on the sandwich-type covariance matrix perform most consistently across conditions. Results also suggest that SEs based on other matrices are either not consistent or perform not as robust as those based on the sandwich-type covariance matrix or the observed information matrix.