Evaluation Of Response Probabilities Along Studied Latent Dimensions: A Polytomous Item Extension

A readily and widely applicable procedure is discussed that can be used to point and interval estimate the probabilities of particular responses on polytomous items at pre-specified points along underlying latent continua. The items are assumed thereby to be part of unidimensional multi-component measuring instruments that may contain also binary and/or other polytomous items as well as following the popular graded response model, possibly within hybrid item response models. The approach generalizes extant research on estimation of the probability for a specific response on a binary or binary scored item at latent locations to the polytomous item case. The method can be used for answering theoretically and empirically relevant questions concerning given response probabilities on pre-specified items, such as Likert-type questions within surveys or questionnaires, at certain distances from the latent population mean. The discussed procedure is directly employed with widely circulated statistical software and is illustrated using an empirical example.