TL03: A Review of Modeling Distributions for Student GPA

Music City Center 

The normality assumption, which was generally made for modeling student GPA outcomes, is untenable in real-life scenarios. Unlike the normal distribution, the distribution of grades is usually bounded, oftentimes with a certain degree of skewness and possibilities of multimodality. Therefore, it is well-recognized that cumulative logistic regression or the partial proportional odds model should be the go-to model for the GPA score, which is ordinal and categorical by nature. However, the proportional odds assumption made for all variables in the cumulative logit model and some of the variables in the partial proportional odds model is usually determined by likelihood ratio tests, rendering most partial proportional odds model post-hoc models and increasing the risk of overfitting. The heavy demand on sample size for parameter estimation is another downside for these two types of models. Other distributional assumptions, as the beta distribution for skewness, zero-inflated model or hurdle model for zero-inflation, and Tobit model for data censoring and boundedness, are included in this study for a more comprehensive discussion on distributional assumptions for modeling student GPA.

GPA

beta distribution

cumulative logistic regression

zero-inflation

partial proportional odds model 

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