Multiple matrix sampling is a psychometric procedure in which a set of test items is subdivided randomly into subtests of items with each subtest administered to different subgroups of examinees selected at random from the examinee population. Although each examinee receives only a proportion of the complete set of items, the statistical model…

Multiple matrix sampling (MMS) theory indicates how data may be gathered to most efficiently convey information about levels of attainment in a population, but standard analyses of these data require random sampling of items from a fixed pool of items. This assumption proscribes the retirement of flawed or obsolete items from the pool as well as…

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…