What question did this study set out to answer?

This research aims to estimate parameters for hierarchical regression models effectively when outliers are present.

June 3, 20260 citationsOpen Access

A Robust Cubic Spline Approach for Hierarchical Regression Models with Outliers

HTHayder TalibUniversity of Wasit SASARAH SABAH AKRAM AKRAMThi Qar University NFNOOR ABDUL-KAREEM FAYYADH FAYYADHThi Qar University

Key Points

This research aims to estimate parameters for hierarchical regression models effectively when outliers are present.
Conducted Monte Carlo simulation experiments with sample sizes of 15, 25, 40, and 60.
Tested at outlier rates of 1%, 3%, and 5%.
Evaluated performance using absolute deviation error (ADE) and coefficient of determination (R2).
The robust cubic spline method outperformed maximum likelihood estimation in handling outliers.
Performance was measured through absolute deviation error and R2, showing the robustness of the cubic spline.

Abstract

This study is based on parameter estimation for hierarchical regression models in the presence of outliers. The robust cubic spline and the maximum likelihood estimation are compared. In order to test the efficiency of the two methods, Monte Carlo simulation experiments were conducted on sample sizes 15, 25, 40, and 60 at three different percentages of outliers 1%, 3%, and 5%. The assessment of performance was done by the absolute deviation error (ADE) and the coefficient of determination (R2). The outcome of this study showed that the robust cubic spline performed better than maximum likelihood estimation.

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