Skip to Main Content
 

Global Search Box

 
 
 
 

ETD Abstract Container

Abstract Header

Latent Variable Models of Categorical Responses in the Bayesian and Frequentist Frameworks

Abstract Details

2014, Master of Arts, Ohio State University, Psychology.
The thesis consists of two self-contained manuscripts. The first manuscript presents a Bayesian multilevel formulation of a cross-classified latent variable model for categorical responses. In the manuscript, we discuss the issue of model non-identifiability and how parameter constraints in the form of item-level regression covariates can aid in model identification. We use the latent regression identification strategy to fit one of two models that we propose to examine the latent structure of emotional distress regarding aspects of anxiety and depression. The models are fit to an empirical dataset consisting of item responses on the Patient-Reported Outcomes Measurement Information System (PROMIS) profile of emotional distress. The second manuscript expands upon methodological issues outlined in Halpin et al. (2014) that involve the problem of identifiability of a two-dimensional CFA model. In the manuscript, we incorporate the nonlinearity brought about by the discreteness of the response variable in the model's specification. The identification of the resulting Categorical Item Factor Analysis (CIFA) model with mixed dichotomous and ordinal responses is examined and some of the results already published in Halpin et al. (2014) regarding identification are re-derived and expanded upon accordingly. We also propose and examine a theoretically informed parameter constraint in which the crossloading parameters are a deterministic function of the anxiety latent variable. The proposed constraint adds a quadratic latent variable in the model rendering the latent space nonlinear. The two types of nonlinearity result in a mixed-response nonlinear categorical item factor analysis model which can be formulated as the conditional distribution of a generalized linear mixed model with the logit link function. The model is then fit to an empirical dataset and a Monte Carlo simulation study is performed.
Paul De Boeck (Advisor)
Bob Cudeck (Committee Member)
Michael Edwards (Committee Member)
142 p.

Recommended Citations

Citations

  • Farouni, T. (2014). Latent Variable Models of Categorical Responses in the Bayesian and Frequentist Frameworks [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1412374136

    APA Style (7th edition)

  • Farouni, Tarek. Latent Variable Models of Categorical Responses in the Bayesian and Frequentist Frameworks. 2014. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1412374136.

    MLA Style (8th edition)

  • Farouni, Tarek. "Latent Variable Models of Categorical Responses in the Bayesian and Frequentist Frameworks." Master's thesis, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1412374136

    Chicago Manual of Style (17th edition)