A Logistic Model For Time Limit Tests

The likelihood of this model, however, resists simplification towards a form appropriate for calculations, in
particular it does not yield the attractive result of Dubey if more than one item is involved. The main obstacle is an interdependence of conditional times spend on the items, given that on items are finished in the allotted time. Therefore, an approximate pseudolikelihood function is proposed that is proven to be asymptotically equal to a pseudolikelihood. Using a result from Arnold and Strauss (1988), maximization of this function yields consistent estimates of the model parameters. The pseudolikelihood circumvents the interdependence, and the approximation returns Dubeys result. With this function the derivation is straightforward and
presents no difficulties. Available programs for the estimation and testing of item and person parameters in logistic models are applicable. The estimation of the subject parameters is evaluated for realistic testing situations by a series of simulations.