Factor model for ordinal categorical data with latent factors explained by auxiliary variables applied to the major depression inventory

In behavioral and social research, questionnaires are an important assessment tool, through which individuals can be categorized according to how they classify themselves in respect to a personal trait. One example is the Major Depression Inventory (MDI), which is widely used for the assessment of depression. It can also be used as a depression severity scale, with scores ranging from 0 to 50 constructed considering the same weight for each item in the MDI. However, the dependence among the items of the questionnaire suggests that a score with better properties could be obtained through factor models, which besides allowing to reduce the dimensionality of multivariate data, provides the estimation of common factors and factor loadings that often have an interesting theoretical interpretation. Additionally, auxiliary information could be available and, the effect of these variables in the latent factor could be estimated and provide interesting results. Thus, the main aim of this paper is to propose a factor model for ordered categorical data which incorporates auxiliary variables to explain the latent factors. The proposed model provides an alternative score to MDI based on the estimated latent factors that takes the uncertainty in the data and auxiliary information into account.