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Understanding and Analyzing Significant Interactions in Statistical Models

This guide explores the concepts of interaction and moderation in statistical analysis, focusing on how variables (X, Y, Z) work together to predict outcomes. It discusses the methodologies for graphing interactions, including dichotomous and continuous variables, and delves into the limitations of the traditional pick-a-point approach. The Johnson-Neyman technique is highlighted for assessing regions of significance in interactions. Illustrative empirical examples illustrate the negative relationship between antisocial behavior and math ability, moderated by hyperactivity, providing practical insights for researchers in design and statistical analysis.

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Understanding and Analyzing Significant Interactions in Statistical Models

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  1. You found an interaction! Now what? A practical guide to graphing & probing significant interactions Design and Statistical Analysis Lab Colloquium Laura J. Sherman umdconsulting@gmail.com

  2. Bauer & Curran (2005)

  3. Interaction/Moderation • X and Z interact to predict Y • The effect of X on Y is moderated by Z • I have a theory... X Y (Antisocial Behavior) (Math Ability) Z (Hyperactivity)

  4. Interaction/Moderation • X and Z interact to predict Y • The effect of X on Y is moderated by Z • I have a theory... X * Z Y (Antisocial x Hyperactivity) (Math Ability) Y = b0 + b1X+ b2Z+ b3 (X*Z)

  5. Remember Slopes? b = 5 Positive relationship between X and Y b = 0 No relationship between X and Y Math Ability b = -5 Negative relationship between X and Y Antisocial Behavior

  6. Types of Interactions • Dichotomous x Dichotomous • Antisocial (yes/no) x Hyperactivity (yes/no) • Variables were actually measured dichotomously • Continuous x Dichotomous • Antisocial (range: -5 to 5) x Hyperactivity (yes/no) • Continuous x Continuous • Antisocial (range: -5 to 5) x Hyperactivity (range: -5 to 5)

  7. Dichotomous x Dichotomous Hyperactivity

  8. SPSS walk-through

  9. Dichotomous x Continuous

  10. Continuous x Continuous • “Pick-a-point” approach (Rogosa, 1980) • Plotting and testing the conditional effect of X at designated levels of Z Hyperactivity (Z)

  11. Problems with pick-a-point approach • Values selected arbitrarily • May even be outside range of observed sample data • Sample dependent • You designated a continuous variable, but you are only testing its effect at a few values

  12. Johnson-Neyman Technique • Computation of regions of significance • Indicates over what range of the moderator the effect of X is significantly positive, nonsignificant, or significantly negative • Plotting of confidence bands for the conditional effect • APA task force: confidence intervals are much more informative than null hypothesis tests • In the case of conditional effects, both the effect estimate and its standard error vary as a function of M. Cannot plot just one confidence interval, must plot bands over full range of M.

  13. Empirical Example • Child math ability, antisocial, & hyperactivity • Hypothesis: There would be a negative relation between antisocial behavior and math ability that would be moderated by the presence of child hyperactive behavior. • Stated alternatively, antisocial behavior and hyperactive behavior interact to predict math ability (assessment of the Children of the National Longitudinal Survey of Youth, 1990)

  14. Prepping Variables Mean center X and Z Calculate X * Z variable (do not center that)

  15. Empirical Example • Regression results Now what?

  16. Empirical Example: Pick-a-point Y = 38.07 + .0373(A) - .799(H) - .397(A x H) +/- 1 SD Hyperactivity: Low (-1.54), Medium (0), High (1.54) *Prior to running regression, mean center or standardize predictors involved in interactions

  17. Empirical Example: Pick-a-point *

  18. Problems with pick-a-point approach • Values selected arbitrarily • May even be outside range of observed sample data • Sample dependent • You designated a continuous variable, but you are only testing its effect at a few values

  19. Empirical Example: J-N Technique • Regression Results

  20. *

  21. 1.49

  22. Empirical Example Regression Results

  23. http://www.quantpsy.org

  24. 38.07 .0373 -.799 -.397 -1.54 0.00 1.54 .1039 .0719 .0461 .0204 -5 5 952 -.0003 -.0124

  25. Region of Significance =========================== Z at lower bound of region = -2.3285 Z at upper bound of region = 1.4948 (simple slopes are significant *outside* this region.)

  26. Summary • Major points: • When probing interactions, use information from your ANOVA/Regression equation • Pick-a-point is a limited, out-dated approach to testing and displaying Continuous x Continuous interactions • www.quantpsy.org

  27. Which variable is the moderator? Theory-driven, no statistical test Mean centering Covariates 3-way interactions Simple slopes difference testing Non-linear Additional comments/next steps

  28. umdconsulting@gmail.com Thank you!

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