Many measures found in educational research are ordered categorical response variables that are empirical realizations of an underlying normally distributed variate. These ordered categorical variables are commonly referred to as Likert or rating scale data. Regression models are commonly fit using these ordered categorical variables as the criterion (i.e., dependent or response) variable; however, a common recommendation in the methodological literature is that researchers make use of ordinal logistic regression when they have these ordered categorical response variables. An advantage of ordinal logistic regression is that it provides a pseudo R-squared measure of fit so that researchers may find this regression model familiar and hence appealing. This study investigated how the pseudo R-squared fit statistic in ordinal logistic regression operates under a variety of conditions over a varying number of Likert scale points and skewness of the Likert data. The study also demonstrates how the regular ordinary least-squares R-squared statistic operates in the same conditions as the Likert data. The pseudo R-squared fit statistic operates well in a majority of conditions, and so it is recommended that educational researchers begin to explore the use of ordinal logistic regression in their modeling practice with ordered categorical data. Using the pseudo R-squared index will ease the transition to ordinal logistic regression because it provides a sense of familiarity to the researcher. (Contains 4 figures, 11 tables, and 6 references.) (Author/SLD)