Collections > Electronic Theses and Dissertations > Generalized fiducial inference for graded response models

Generalized fiducial inference (GFI) has been proposed as an alternative inferential framework in the statistical literature. Inferences of various sorts, such as confidence regions for (possibly transformed) model parameters, making prediction about future observations, and goodness of fit evaluation, can be constructed from a fiducial distribution defined on the parameter space in a fashion similar to those used with a Bayesian posterior. However, no prior distribution needs to be specified. In this work, the general recipe of GFI is applied to the graded response models, which are widely used in psychological and educational studies for analyzing ordered categorical survey questionnaire data. Asymptotic optimality of GFI is established (Chapter 2), and a Markov chain Monte Carlo algorithm is developed for sampling from the resulting fiducial distribution (Chapter 3). The comparative performance of GFI, maximum likelihood and Bayesian approaches is evaluated via Monte Carlo simulations (Chapter 4). The use of GFI as a convenient and powerful tool to quantify sampling variability in various inferential procedures is illustrated by an empirical data analysis using the patient-reported emotional distress data (Chapter 5).