A comparative study of the effectiveness of two Bayesian models for predicting the academic successes of selected allied health students enrolled in the comprehensive community college

Because of high enrollment demands, limited instructional spaces, and the high cost of programs, many community colleges have been forced to place stringent admission requirements in the guidance and selection of certain allied health curricula such as Dental Assistant, Mental Health, Nursing, and Radiology. In this guidance-selection environment in which there were more candidates than vacancies, methods and/or procedures must be established that discern the "best" applicants. Since neither the classical statistical models which utilize correlations, regression, discriminate analysis, etc. nor the counselor-selection models have typically utilized all the information regarding a student, the need for more efficient and effective guidance-selection models was indicated. In this context Bayesian-type models have been proposed that can utilize the strengths of both the classical statistical models and the counselor-selection models.

The purpose of the study was to present and evaluate Bayesian-type models for estimating probabilities of program completion and predicting first quarter grade point average (GPA). Bayesian Model 1 Estimating Probabilities of Program Completion was developed from the discrete case of Bayes' formula with counselors' inputs as a priori probabilities and posterior probabilities of graduate status of the discriminant analysis function as likelihoods. The a priori probabilities and likelihood probabilities were combined in Bayes’ Theorem to produce posterior probabilities of successful program completion. Bayesian Model 2 -- Predicting First-Quarter GPA’s which was an application and specialization of the Bayesian linear model developed by Lindley and Smith (1972) involved the assumption of homogeneity of regression coefficients (but not intercepts) across groups. The efficiencies of the Bayesian-type models were compared and evaluated in terms of two counselor selection models and two classical statistical models.

Although inspection by curriculum and by individual students indicated that all three program completion models were appropriate in specific cases, an analysis of ranking efficiencies using the Friedman (1937) test rejected the hypothesis of identical treatments. Further analyses using multiple comparisons aspects proposed by Anderson (1959) indicated that there were statistically significant linear comparison differences among the models with the Bayesian Model 1 ranking as the most efficient model. An analysis of the three GPA models using an analysis of variance test contradicted the hypothesis that the three treatment effects were equal at the .01-level with Tukey's Test for differences of average absolute-errors confirming that the Bayesian Model 2 and the Classical Statistical Model 2 were more efficient than the Counselor Model 2. The results of the study supported several recommendations for further study.