Mathematics and Statistics Vol. 9(4), pp. 566 - 573
DOI: 10.13189/ms.2021.090415
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Robust Estimation for Proportional Odds Model through Monte Carlo Simulation

Faiz Zulkifli ^1,2, Zulkifley Mohamed ^2,*, Nor Afzalina Azmee ², Rozaimah Zainal Abidin ^1
1 Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Perak Branch, Tapah Campus, 35400 Tapah Road, Perak, Malaysia
² Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjong Malim, Perak, Malaysia

ABSTRACT

Ordinal regression is used to model the ordinal response variable as functions of several explanatory variables. The most commonly used model for ordinal regression is the proportional odds model (POM). The classical technique for estimating the unknown parameters of this model is the maximum likelihood (ML) estimator. However, this method is not suitable for solving problems with extreme observations. A robust regression method is needed to handle the problem of extreme points in the data. This study proposes Huber M-estimator as a robust method to estimate the parameters of the POM with a logistic link function and polytomous explanatory variables. This study assesses ML estimator performance and the robust method proposed through an extensive Monte Carlo simulation study conducted using statistical software, R. Measurement for comparisons are bias, RMSE, and Lipsitzs' goodness of fit test. Various sample sizes, percentages of contamination, and residual standard deviations are considered in the simulation study. Preliminary results show that Huber estimates provide the best results for parameter estimation and overall model fitting. Huber's estimator has reached a 50% breakdown point for data containing extreme points that are quite far from most points. In addition, the presence of extreme points that have only a distance of two times far from most points has no major impact on ML estimates. This means that the estimates for ML and Huber may yield the same results if the model's residual values are between -2 and 2. This situation may also occur for data with a percentage of contamination below 5%.

KEYWORDS
Proportional Odds Model, M-Estimation, Ordinal Response Model, Robust Estimator

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Faiz Zulkifli , Zulkifley Mohamed , Nor Afzalina Azmee , Rozaimah Zainal Abidin , "Robust Estimation for Proportional Odds Model through Monte Carlo Simulation," Mathematics and Statistics, Vol. 9, No. 4, pp. 566 - 573, 2021. DOI: 10.13189/ms.2021.090415.

(b). APA Format:
Faiz Zulkifli , Zulkifley Mohamed , Nor Afzalina Azmee , Rozaimah Zainal Abidin (2021). Robust Estimation for Proportional Odds Model through Monte Carlo Simulation. Mathematics and Statistics, 9(4), 566 - 573. DOI: 10.13189/ms.2021.090415.