Categorical and Limited Dependent Variable Modeling in Higher Education

Higher education researchers have applied increasingly sophisticated regression techniques to the study of many important issues. Historically, the statistical workhorse of this work has been linear regression, which has several desirable properties for analyzing continuous outcomes, and under certain assumptions yields unbiased coefficient estimates. However, several outcomes of interest to higher education scholars are categorical or limited in the values they assume, and using linear regression to study them may violate important assumptions. Herein we provide an overview of regression techniques often employed when studying categorical or limited dependent variables. We begin by discussing the modeling of binary outcomes, which are often studied using linear probability, logistic, or probit models. We then consider dependent variables with multiple categories, modeled using ordinal and multinomial regression methods. We also discuss the use of models for other limited dependent variables, including counts, fractions, and censored or truncated outcomes. Throughout the chapter, we apply these techniques to the study of students’ college choice using a relatively new data set available from the National Center for Education Statistics.