Interval Estimation of Item Response Probabilities Along Studied Latent Dimensions

An interval estimation procedure is discussed that can be used to evaluate the probability of a particular response for a binary or binary scored item at a pre-specified point along an underlying latent continuum. The item is assumed to: (a) be part of a unidimensional multi-component measuring instrument that may contain also polytomous items, and (b) to follow a one-parameter or two-parameter logistic model. The approach is developed within the framework of latent variable modeling, and can be used in answering theoretically and empirically relevant questions concerning specific response probabilities at certain distances from the latent population mean. The method is readily and widely applicable with popular statistical software, and is illustrated using an empirical example.