Regression models for retention and graduation rates at University of California-Berkeley.

Our Markov chain model (see Fig 1) requires specification of the parameters λ4G, λ5G, λ6G, and ρ, which are related, respectively, to the four-year graduation, five-year graduation, six-year graduation, and first-year retention rates. These rates must be specified for each year and for each racial/ethnic group. We assess the fit of linear, log-linear, and optimal Box-Cox models on historical data. We choose the preferred model, specified in the table above, and use it to forecast future values. Fig 3 shows various models for four-year graduation rates, corresponding to the top section of the table above. The column labeled Λ is an exponent used in the Box-Cox transformation, and thus is relevant only to those fits.本研究的马尔可夫链模型（Markov chain model，见图1）需对参数λ₄G、λ₅G、λ₆G以及ρ进行设定，上述参数分别对应四年毕业率、五年毕业率、六年毕业率与一年级学生留存率。上述指标需针对每一年度以及每一个种族/族裔群体分别设定。我们基于历史数据，对线性模型、对数线性模型以及最优Box-Cox模型的拟合表现进行评估。我们选取上表中指定的优选模型，并利用该模型开展未来数值预测工作。图3展示了对应上表上半部分的各类四年毕业率模型。标注为Λ的列是Box-Cox变换中使用的指数，因此仅与上述拟合结果相关。