Abstract
In Chap. 13, we discussed analysis of covariance (ANCOVA). With ANCOVA, we enter a continuous predictor into a regression model before adding a categorical one. The presence of the continuous predictor is designed to reduce the error variance, thereby increasing the power of an experimental treatment or grouping variable. ANCOVA is not the only way to combine categorical and continuous predictors in a regression analysis, however. Continuous predictors can also be used to examine the generality of an experimental manipulation by studying their interaction with a categorical variable. Such an analysis is termed moderated regression analysis (or, simply, moderation), because our interest is in whether a continuous predictor moderates the impact of a categorical one.
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Notes
- 1.
When performing these analyses, some textbooks recommend a hierarchical approach, using a different error term to test the significance of the lower-order terms. I disagree. When an interaction is the focus of an investigation, I believe all terms should be tested using the overall MS res with the cross-product term included. Consequently, the order you use to perform these analyses is arbitrary.
- 2.
Equation 9.11 presents an alternative formula for calculating the crossing point with two continuous predictors.
- 3.
See Chap. 9 for a discussion of disordinal vs. ordinal interactions.
- 4.
Later, we will use the highlighted portion of the covariance matrix to create an augmented covariance matrix.
- 5.
I have omitted plotting the predicted value for subjects of average age because the means fall halfway between those that are displayed.
- 6.
- 7.
The boxed values reference the relevant analysis in Table 14.10.
References
Bauer, D. J., & Curran, P. J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40, 373–400.
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Brown, J.D. (2014). Moderation. In: Linear Models in Matrix Form. Springer, Cham. https://doi.org/10.1007/978-3-319-11734-8_14
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