Bayesian approaches to factor analysis models for cognitive outcomes with multiple nuisance dimensions

Data on cognitive outcomes may come from a variety of specialized tests such as the Mini Mental State Examination or the Boston Naming Test. Alzheimer's researchers are often only interested in the primary latent variable such as memory or executive functioning and would like to ignore multiple nuisance dimensions that are common in cognitive testing. One may consider using variants of item response theory (IRT) and factor analysis models for fitting such data. However, basic IRT models often provide poor fit for cognitive testing data. More complex IRT models, such as multidimensional IRT, require either specifying the latent structure before fitting the model or resorting to model selection procedures. Both practices do not reflect substantive needs of Alzheimer's researchers well. To adequately account for multiple nuisance dimensions or residual correlations in cognitive testing data, we propose to factor out nuisance parameters. We discuss several approaches for implementing this idea in the framework of factor analysis that include Bayesian model averaging and integrated test information curve. We point out advantages these approaches have over more ad-hoc procedures and describe difficulties in implementation and some open problems using cognitive testing data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.