Bayesian estimation of a flexible bifactor generalized partial credit model to survey data

Item response theory (IRT) models provide an important contribution in the analysis of polytomous items, such as Likert scale items in survey data. We propose a bifactor generalized partial credit model (bifac-GPC model) with flexible link functions - probit, logit and complementary log-log - for use in analysis of ordered polytomous item scale data. In order to estimate the parameters of the proposed model, we use a Bayesian approach through the NUTS algorithm and show the advantages of implementing IRT models through the Stan language. We present an application to marketing scale data. Specifically, we apply the model to a dataset of non-users of a mobile banking service in order to highlight the advantages of this model. The results show important managerial implications resulting from consumer perceptions. We provide a discussion of the methodology for this type of data and extensions. Codes are available for practitioners and researchers to replicate the application.