Statistical modeling study demonstrates order-restricted estimation of grade point averages, indicating improved predictive accuracy for incoming freshmen.
The problem of interest is to estimate a two-way table of means of grade point averages (GPAs) of University of Iowa freshmen grouped by levels of ACT scores and high school percentiles. Suppose one believes a priori that the table means satisfy a specific partial order. The use of two different classes of prior distributions is considered in modeling this prior information. The use of simulation and, in particular, the Gibbs sampler are outlined to summarize various posterior distributions of interest. The posterior distribution is used to predict the grade point averages of future Iowa freshmen.
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James H. Albert (1994) studied this question.
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