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On the estimation of the polychoric correlation coefficient via Markov Chain Monte Carlo methods Olvera Astivia, Oscar Lorenzo

Abstract

Bayesian statistics is an alternative approach to traditional frequentist statistics that is rapidly gaining adherents across different scientific fields. Although initially only accessible to statisticians or mathematically-sophisticated data analysts, advances in modern computational power are helping to make this new paradigm approachable to the everyday researcher and this dissemination is helping open doors to problems that have remained unsolvable or whose solution was extremely complicated through the use of classical statistics. In spite of this, many researchers in the behavioural or educational sciences are either unaware of this new approach or just vaguely familiar with some of its basic tenets. The primary purpose of this thesis is to take a well-known problem in psychometrics, the estimation of the polychoric correlation coefficient, and solve it using Bayesian statistics through the method developed by Albert (1992). Through the use of computer simulations this method is compared to traditional maximum likelihood estimation across various sample sizes, skewness levels and numbers of discretisation points for the latent variable, highlighting the cases where the Bayesian approach is superior, inferior or equally effective to the maximum likelihood approach. Another issue that is investigated is a sensitivity analysis of sorts of the prior probability distributions where a skewed (bivariate log-normal) and symmetric (bivariate normal) priors are used to calculate the polychoric correlation coefficient when feeding them data with varying degrees of skewness, helping demonstrate to the reader how does changing the prior distribution for certain kinds of data helps or hinders the estimation process. The most important results of these studies are discussed as well as future implications for the use of Bayesian statistics in psychometrics

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Attribution 3.0 Unported

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