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Pairwise Regression Weight Contrasts: Models for Allocating Psychological Resources

Author

Listed:
  • Mark L. Davison
  • Hao Jia
  • Ernest C. Davenport

    (University of Minnesota)

Abstract

Researchers examine contrasts between analysis of variance (ANOVA) effects but seldom contrasts between regression coefficients even though such coefficients are an ANOVA generalization. Regression weight contrasts can be analyzed by reparameterizing the linear model. Two pairwise contrast models are developed for the study of qualitative differences among predictors. One leads to tests of null hypotheses that the regression weight for a reference predictor equals each of the other weights. The second involves ordered predictors and null hypotheses that the weight for a predictor equals that for the variables just above or below in the ordering. As illustration, qualitative differences in high school math course content are related to math achievement. The models facilitate the study of qualitative differences among predictors and the allocation of resources. They also readily generalize to moderated, hierarchical, and generalized linear forms.

Suggested Citation

  • Mark L. Davison & Hao Jia & Ernest C. Davenport, 2024. "Pairwise Regression Weight Contrasts: Models for Allocating Psychological Resources," Journal of Educational and Behavioral Statistics, , vol. 49(4), pages 533-564, August.
    • Handle: RePEc:sae:jedbes:v:49:y:2024:i:4:p:533-564
    DOI: 10.3102/10769986231200155
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    References listed on IDEAS

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    1. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
    2. Jan F. Kiviet, 1986. "On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 241-261.
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