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Testing for interaction in two-way random and mixed effects models: the fully nonparametric approach.

Trent Gaugler¹, Michael G Akritas

¹Department of Statistics, Penn State University, University Park, Pennsylvania 16802, USA. tgaugler@stat.psu.edu

|March 16, 2011

Summary

This study introduces a new nonparametric test for interaction effects in random effects designs, outperforming standard methods in non-normal and heteroscedastic conditions. The test maintains Type I error rates and handles missing data effectively.

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Area of Science:

Statistics
Statistical Modeling
Nonparametric Statistics

Background:

Traditional statistical models often assume normality and homoscedasticity, limiting their application in real-world data.
Testing for interaction effects in random effects designs presents unique challenges, especially when standard assumptions are violated.

Purpose of the Study:

To extend nonparametric modeling for testing interaction effects in random effects designs.
To develop a robust test procedure that accommodates dependence, heteroscedasticity, and non-normality.
To address missing data at random (MAR) within the proposed framework.

Main Methods:

Development of new nonparametric models for random effects designs.
Introduction of a test procedure for interaction effects applicable to factors with many levels.
Incorporation of methods to handle heteroscedasticity, dependence, and missing data.
Simulation studies to evaluate the performance of the proposed test against standard procedures.

Main Results:

The proposed test procedure maintains nominal Type I error rates across various simulation settings, including those with missing data.
Standard procedures (e.g., SAS PROC GLM, PROC MIXED, exact F-test) are found to be overly liberal in heteroscedastic settings.
Under homoscedasticity and normality, the proposed test performs comparably to standard methods.
The limiting distribution of the test statistic is normal, facilitating its application.

Conclusions:

The developed nonparametric test offers a robust alternative for detecting interaction effects in random effects designs, particularly when assumptions are violated.
The procedure's ability to handle heteroscedasticity, dependence, and missing data makes it broadly applicable.
The findings challenge the reliability of traditional methods under non-ideal conditions and highlight the utility of nonparametric approaches.