Huber M-estimator for Cumulative Odds Model with Application to the Measurement of Students' Final Exam Grades

Abstract

The Huber M-estimator is proposed in this study as a robust method for estimating the parameters of the cumulative odds model, which includes a logistic link function and polytomous explanatory variables. With the help of an intensive Monte Carlo simulation study carried out using the statistical software R, this study evaluates the performance of the maximum likelihood estimator (MLE) and the robust technique developed. Bias, RMSE, and the Lipsitz Statistic are used to measure comparisons. When conducting the simulation study, different sample sizes, contamination proportions, and error standard deviations are considered. Preliminary findings indicate that the M-estimator with Huber weight estimates produces the best results for parameter estimation and overall model fitting compared to the MLE. As an illustration, the procedure is applied to real-world data of students' final exam grades as measured by two different estimators.