Multiple Regression and Correlation Techniques: Recent Controversies and Best Practices

  • Hoyt W
  • Imel Z
  • Chan F
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Abstract

Objective: This article presumes familiarity with the basics of multiple regression and correlation (MRC) methods and addresses recent controversies and emerging innovations. Areas of emphasis include linking analyses to theory-driven hypotheses, treatment of covariates in hierarchical regression models, recent debates about the testing of mediator and moderator hypotheses, and incorporating confidence intervals into reports of findings using MRC. Conclusions: Two important conceptual innovations (linking analyses closely to theory-derived hypotheses; focusing interpretations on effect sizes and confidence intervals rather than p values) can increase the scientific yield for researchers making use of MRC methods in rehabilitation psychology. Multiple regression and correlation (MRC) analyses provide a flexible data-analytic framework for addressing a wide variety of questions of interest to rehabilitation psychologists. Regression models can accommodate multiple correlated predictor variables, including nominal (categorical) variables, and can be used to test sophisticated models involving mediation or moderation (statisti-cal interactions). They can be used to statistically control for confounding variables and to examine the predictive power of sets of predictor variables as well as the unique association of a single predictor with the dependent variable (DV). Regression methods have been popular with rehabilitation re-searchers. Examination of approximately 200 articles published in Rehabilitation Psychology between February 2004 and February 2008 revealed that more than one third of these studies used some form of regression analysis. An additional reason why familiarity with regression methods is valuable is that these techniques form the foundation for multivariate methods such as factor analysis, structural equation modeling, and multilevel modeling. Familiarity with analysis and interpretation issues in MRC is therefore impor-tant for consumers and users of these more sophisticated methods. One of the authors of the present article recently collaborated on an introduction to MRC directed at researchers in rehabilitation counseling and rehabilitation psychology (Hoyt, Leierer, & Mill-ington, 2006). That article defined basic terms and notational conventions and offered guidance about fundamental issues such as the choice between standardized and unstandardized regression coefficients, interpretation of partial regression coefficients (i.e., regression coefficients for a given predictor variable when other predictors are also in the regression equation), power analysis, and factors affecting the magnitude of correlation and regression co-efficients. The goal of the present article is to build on this foundation, reviewing guidelines for addressing more sophisti-cated research hypotheses (such as those involving mediation or moderation) and providing illustrative examples for reporting and interpreting findings. We review recent controversies regarding definitions and analytical methods and provide recommendations to assist both authors and readers with design, analysis, and inter-pretation using MRC.

Author-supplied keywords

  • confidence intervals
  • data analysis
  • mediation
  • multiple regression
  • research methods

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Authors

  • William T Hoyt

  • Zac E Imel

  • Fong Chan

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