Bayesian Variable Selection in Multilevel Item Response Theory Models with Application in Genomics.

The goal of this paper is to present an implementation of stochastic search variable selection (SSVS) to multilevel model from item response theory (IRT). As experimental settings get more complex and models are required to integrate multiple (and sometimes massive) sources of information, a model that can jointly summarize and select the most relevant characteristics can provide better interpretation and a deeper insight into the problem. A multilevel IRT model recently proposed in the literature for modeling multifactorial diseases is extended to perform variable selection in the presence of thousands of covariates using SSVS. We derive conditional distributions required for such a task as well as an acceptance-rejection step that allows for the SSVS in high dimensional settings using a Markov Chain Monte Carlo algorithm. We validate the variable selection procedure through simulation studies, and illustrate its application on a study with genetic markers associated with the metabolic syndrome.

Using item response theory to model multiple phenotypes and their joint heritability in family data.

Many important complex diseases are composed of a series of phenotypes, which makes the disease diagnosis and its genetic dissection difficult. The standard procedures to determine heritability in such complex diseases are either applied for single phenotype analyses or to compare findings across phenotypes or multidimensional reduction procedures, such as principal components analysis using all phenotypes. However each method has its own problems and the challenges are even more complex for extended family data and categorical phenotypes. In this paper, we propose a methodology to determine a scale for complex outcomes involving multiple categorical phenotypes in extended pedigrees using item response theory (IRT) models that take all categorical phenotypes into account, allowing informative comparison among individuals. An advantage of the IRT framework is that a straightforward joint heritability parameter can be estimated for categorical phenotypes. Furthermore, our methodology allows many possible extensions such as the inclusion of covariates and multiple variance components. We use Markov Chain Monte Carlo algorithm for the parameter estimation and validate our method through simulated data. As an application we consider the metabolic syndrome as the multiple phenotype disease using data from the Baependi Heart Study consisting of 1,696 individuals in 95 families. We adjust IRT models without covariates and include age and age squared as covariates. The results showed that adjusting for covariates yields a higher joint heritability (h2=0.53) than without co variates (h2=0.21) indicating that the covariates absorbed some of the error variance.

Improving psychometric assessment of the Beck Depression Inventory using multidimensional item response theory.

We studied the latent factor structure of the Beck Depression Inventory (BDI) under the light of Multidimensional Item Response Theory models. Under a Bayesian Markov chain Monte Carlo setting, we chose the most adequate model, estimated its parameters and verified its fit to the data. An evaluation of the inventory in terms of the assumed dimensions seems to agree with previous investigations in the factor structure of the BDI present in the literature. Cognitive and somatic-affective latent traits were identified in the analysis making possible the interpretation of symptom evolution along these dimensions, in terms of probability of their appearance.