Mathematical Modeling of Student Flows for a Large Residential University

Abstract

The research in the literature on the problematic effects of attrition in higher education has been well documented in the past. Obviously, the nature and purpose of the colleges/universities involved have a significant impact on the dropout problem, and there may be many factors that post-secondary institutions can control in order to curb attrition. The attempt to delineate those factors require models to be generated to provide additional information on the interruption of student flow toward degree completion, in order to produce forecasting tools. Since most of the attrition appears to be during the first year of college attendance, the spatial distributions of incoming freshmen students coming to Eastern Kentucky University, a large residential university, were inspected to determine if detectable patterns of enrollment trends existed. The University has a regional mission, thus spatial characterization of student flows are important to determine stability of enrollment in its service area and surrounding counties. Student flow models were created and statistically tested for enrollment data from 1979 through 1982, inclusively, as well as change in enrollment from 1981 to 1982, based on data obtained from 117 counties in Kentucky. Three-dimensional modeling techniques as well as hypotheses testing and model comparisons of polynomial trend surfaces were utilized in modeling the spatial distributions of incoming freshmen students. Powerful and statistically significant predictive models of student flow were generated and graphically portrayed for the years studied. The best fit surfaces accounted for a low of 56.32 to a high of 61.61 percent of explained variance in predicting student flows as a function of geographic distribution in Kentucky. However, no such relationship was found to be significant for student change from one year to the next, as evident from the analysis of the change in 1981/1982.