Computation of Standard Errors

In a previous study (1998), how to evaluate whether adaptive testing data used for online calibration sufficiently fit the item response model used by C. Glas was studied. Three approaches were suggested, based on a Lagrange multiplier (LM) statistic, a Wald statistic, and a cumulative sum (CUMSUM) statistic respectively. For all these methods, the asymptotic variance of the parameter estimates has to be approximated. In the previous study, standard errors were computed using an observed Fisher information matrix. However, when the number of items in each bank becomes very large, manipulating complete information matrices becomes quite difficult. This study investigates the extent to which standard errors can be computed using the diagonal of information matrices only, and how the CUMSUM procedure must be tuned to this alternative approach. Simulation studies showed that the asymptotic standard errors are underestimated by the block-diagonal approach but that the magnitude of the bias in the standard errors was relatively small. It was also shown that the power of the statistical test based on a CUMSUM statistic using these approximated standard errors is well under control. (Author/SLD) Reproductions supplied by EDRS are the best that can be made from the original document.