An Application of Latent Trait Mental Test Theory

Solutions were sought for problems in applying the Birnbaum three‐parameter logistic mental test model through Bayesian tailored testing. Both empirical and Monte Carlo data were utilized. The general conclusions were: (1) Although conventional tests are not generally good for tailored testing, some individual items are excellent. (2) It may be possible to develop methods of graphic parameter estimation to the point where expensive maximum‐likelihood methods can be by‐passed. (3) An item bank for tailored testing must have a sufficiently large number of items whose difficulties are uniformly distributed and whose discriminatory powers are high. (4) The use of prior information in Bayesian tailored testing does not lead to a substantial reduction in the number of items needed, unless prior information is unrealistically accurate. (5) The standard error of the estimate of ability has certain characteristics which may have important consequences for tailored testing under certain conditions.