Ordinal Data: Inference and Simulation

Jillian Jinelle Morrison

In many applications, including medicine, social science, and surveys, ordinal data is collected. Some common methods for analyzing ordinal data include ordinal logit regression, ordinal probit regression, Likert Scale analysis and ordinary least squares regression. The motivating example for this dissertation is data collected from upper level high school students in Belize about their level of intent to pursue higher education. The dataset includes students' demographic and socio$-$economic background information. The factors that are relevant for predicting students’ intention to pursue higher education are age, gender, family size and make$-$up, residence, and job preference. Males and females give different reasons for not intending to pursue higher education. Ordinal logit and probit as well as ordinary least square (OLS) were used for estimation. The inferential results were very similar notwithstanding the method of analysis. In OLS, ethnic group (Maya) came up as a relevant factor, unlike logit and probit. To compare these models for power, type-1 error and predictive accuracy, a simulation study is done. The results show that the methods to analyze the simulated data have similar power, though the ordinal logit had less power in identifying predefined effects. This explains why similar significant effects were identified in the applied study. For predictive accuracy, we find the results to be low over all the methods, though the ordinary least squares regression is lowest. However, the gap between predictive accuracy for OLS versus logit and probit (similar predictive accuracy) decreases as the sample size increases. All the methods preserve the nominal type-1 error. Another issue addressed in this dissertation is the lack of a multiple comparison procedure to compare student intent by the district in which students live using other covariates. A Wald type multiple comparison procedure that compares parameter sets to a reference parameter set is developed. With this procedure, intent of students from Cayo, Stann Creek and Toledo districts are compared to students from the Belize district. A difference between parameter sets of the Toledo district and Belize district was found. A power comparison, via a simulation study, is made between the Wald-type procedure and Likelihood Ratio type procedure.

Ordinal Data: Inference and Simulation

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