Using Item response models to investigate attitudes towards divorce

Abstract

Item Response Theory (IRT) is a form of latent structure analysis that is used to analyze binary or ordinal response data. IRT models are used to evaluate the relationships between the latent trait of interest and the items measuring the trait. Several IRT models will be fitted to assess the factors that lead to divorce in the Maltese Islands. The 1-PL and 2-PL logistic Rasch models are used for dichotomous responses, whereas the 1-PL rating scale and 1-PL partial-credit models are used for polytomous responses. All the models are fitted using the generalized linear latent and mixed modeling (GLLAMM) framework. The gllamm directive estimates parameters by maximum likelihood using adaptive quadrature (Rabe-Hesketh, Skrondal, and Pickles 2002; 2005). In the 1-PL Rasch model, the probability that a person agrees with a divorce-related item is modeled as a function of subject ability and item difficulty parameters. The major weakness of this model is that the items have the same discrimination parameter. In the 2-PL Birnbaum model, an item-specific weight is added so that the slope of the item response function varies between the items. The 1-PL rating scale model specifies that the items share the same rating scale structure, while the 1-PL partial credit model specifies a distinct rating scale structure for each item.