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.