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Solutions for Determining the Significance Region Using the Johnson-Neyman Type Procedure in Generalized Linear (Mixed) Models

Author

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  • Ann A. Lazar

    (University of California, San Francisco)

  • Gary O. Zerbe

    (University of Colorado, Denver)

Abstract

Researchers often compare the relationship between an outcome and covariate for two or more groups by evaluating whether the fitted regression curves differ significantly. When they do, researchers need to determine the “significance region,†or the values of the covariate where the curves significantly differ. In analysis of covariance (ANCOVA), the Johnson-Neyman procedure can be used to determine the significance region; for the hierarchical linear model (HLM), the Miyazaki and Maier (M-M) procedure has been suggested. However, neither procedure can assume nonnormally distributed data. Furthermore, the M-M procedure produces biased (downward) results because it uses the Wald test, does not control the inflated Type I error rate due to multiple testing, and requires implementing multiple software packages to determine the significance region. In this article, we address these limitations by proposing solutions for determining the significance region suitable for generalized linear (mixed) model (GLM or GLMM). These proposed solutions incorporate test statistics that resolve the biased results, control the Type I error rate using Scheffé’s method, and uses a single statistical software package to determine the significance region.

Suggested Citation

  • Ann A. Lazar & Gary O. Zerbe, 2011. "Solutions for Determining the Significance Region Using the Johnson-Neyman Type Procedure in Generalized Linear (Mixed) Models," Journal of Educational and Behavioral Statistics, , vol. 36(6), pages 699-719, December.
    • Handle: RePEc:sae:jedbes:v:36:y:2011:i:6:p:699-719
    DOI: 10.3102/1076998610396889
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    References listed on IDEAS

    as
    1. Richard Potthoff, 1964. "On the Johnson-Neyman technique and some extensions thereof," Psychometrika, Springer;The Psychometric Society, vol. 29(3), pages 241-256, September.
    2. Palmer Johnson & Leo Fay, 1950. "The Johnson-Neyman technique, its theory and application," Psychometrika, Springer;The Psychometric Society, vol. 15(4), pages 349-367, December.
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