A Weibull-Link Response Model for Measuring Unipolar-Skewed Constructs With Continuous Responses
Authors
Abstract
In certain noncognitive applications attempts are made to measure unipolar traits expected to have positively skewed distributions in the target populations, two conditions that clash head-on with the bipolarity and normality assumptions on which most standard IRT models are based. Unipolar-skewed models are an alternative to be used in these conditions, and we propose here a model intended for double-bounded continuous response items in which: (a) the link function or item response function is a cumulative Weibull curve, and (b) the initial latent distribution is lognormal. The model is simple, has desirable psychometric properties, and, conceptually, provides a plausible account of the response functioning. We propose a full development which has been also implemented in a free R program. Moreover, an empirical study is included, and its results show that the model behaves appropriately when used with real data, delivering the anticipated accuracy and external validity outcomes.