SEM of another flavour: Two new applications of the supplemented EM algorithm

The supplemented EM (SEM) algorithm is applied to address two goodness‐of‐fit testing problems in psychometrics. The first problem involves computing the information matrix for item parameters in item response theory models. This matrix is important for limited‐information goodness‐of‐fit testing and it is also used to compute standard errors for the item parameter estimates. For the second problem, it is shown that the SEM algorithm provides a convenient computational procedure that leads to an asymptotically chi‐squared goodness‐of‐fit statistic for the ‘two‐stage EM’ procedure of fitting covariance structure models in the presence of missing data. Both simulated and real data are used to illustrate the proposed procedures.