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Measuring and detecting associations: methods based on robust regression estimators or smoothers that allow curvature
1Department of Psychology, University of Southern California, Los Angeles, California 90089, USA. rwilcox@usc.edu
The British Journal of Mathematical and Statistical Psychology
|December 22, 2009
Summary
This study introduces robust methods for estimating association strength, even with data curvature. New techniques improve accuracy and address bias issues in statistical modeling.
Area of Science:
- Statistics
- Econometrics
- Data Science
Background:
- Estimating association strength is crucial in statistical analysis.
- Existing methods may struggle with non-linear relationships or data curvature.
- Robust statistical measures are needed for reliable analysis.
Purpose of the Study:
- To develop and evaluate robust methods for estimating overall association strength.
- To address challenges posed by curvature in regression surfaces.
- To provide reliable statistical tools for analyzing complex data.
Main Methods:
- Fitting robust regression lines and smoothers that accommodate curvature.
- Utilizing a robust analogue of explanatory power, eta-squared (η²).
- Comparing the performance of Theil-Sen estimator and generalized kernel estimators.
Main Results:
- Theil-Sen estimator performs well for planar regression surfaces regarding mean squared error and bias.
- Generalized kernel and alternative smoothers show promise for curved surfaces.
- A variation of eta-squared is proposed to mitigate bias when eta-squared is near zero.
Conclusions:
- Robust regression and smoothing techniques offer effective solutions for estimating association strength.
- The proposed methods provide reliable tools for handling curvature and bias in statistical analysis.
- Validated methods for testing hypotheses about association strength are presented, with software available.
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