Are Attitude Items Monotone Or Single Peaked An Analysis Using Bayesian Methods

This model has item response functions that are single-peaked. Depending on the item parameters, the peak of the item response function can be at plus or minus infinity which corresponds to a monotone increasing or decreasing item response function. That is, the new model contains a model with monotone item response functions as a special case. This implies that testing whether the item response function of a statement is monotone, boils down to evaluating the goodness-of-fit of a restricted model relative to a more general (unrestricted) model. The goodness-of-fit of the restricted model is evaluated with a posterior-predictive
check. It is found that the power of the traditional posterior-predictive check is unsatisfactory. This problem is solved by computing the posterior-predictive p-value using the posterior distribution of the nuisance parameters under the unrestricted instead of the restricted model. The methodology is applied to a real data set.