Testing the difficulty theory of the SON-R 5(1/2)-17, a non-verbal test of intelligence.

Fischer's (1973) linear logistic test model can be used to test hypotheses regarding the effect of covariates on item difficulty and to predict the difficulty of newly constructed test items. However, its assumptions of equal discriminatory power across items and a perfect prediction of item difficulty are never absolutely met. The amount of misfit in an application of a Bayesian version of the model to two subtests of the SON-R 5(1/2)-17 is investigated by means of item fit statistics in the framework of posterior predictive checks and by means of a comparison with a model that allows for residual (co)variance in the item parameters. The effect of the degree of residual (co)variance on the robustness of inferences is investigated in a simulation study.

Analysis of longitudinal randomized clinical trials using item response models.

Patient-relevant outcomes, such as impairments, disability and health-related quality of life, are becoming increasingly popular as outcome measures in clinical research. These outcomes are generally assessed using questionnaires. In a longitudinal randomized clinical trial where the outcome is measured by a questionnaire or some other instrument consisting of a set of discretely scored items, treatment effects can be analyzed using item response theory. The problem addressed is how to take the estimation error in the estimates of the latent outcome variables into account in the estimation of the treatment effects. Three approaches are compared: plausible value imputation (PVI), concurrent marginal maximum likelihood (MML) estimation and a limited information two-step marginal maximum likelihood method. The results show that the power of the former two methods to detect small and moderate effect sizes is considerably larger than the power of the latter approach. An additional advantage of the PVI method as compared to MML is that the treatment effects can be estimated with standard software. An example using data from a longitudinal randomized clinical trial illustrates the use of the methods in a practical setting. It is shown that even when responses on different sets of items for different groups of patients are used for the data analysis, the power to detect the experimental effects is comparable to the power obtained when responses to all items for all patients are used in the analysis. This creates considerable flexibility in the design and use of measures in experiments.