MMR Learning Objectives Flashcards
(17 cards)
Explain the research questions that can be addressed using moderated multiple regression
The research questions that can be addressed using MMR are those which examine whether the relationship between a predictor and a criterion changes as a function of a second predictor.
Explain what it means to find an interaction in moderated multiple regression
An interaction is where a particular effect or relationship between variables changes as a function of another variable. They add nuance to established effects, by indicating the conditions under which the effect is likely to be stronger, weaker, non-existent, or even reversed. These interactions are tested for by using MMR.
Explain what a moderator is and what it does and explain what it means for a moderator to enhance vs. attenuate an effect
A moderator is the predictor that changes the relationship between the focal predictor and the criterion. The relationship can be enhanced (strengthened), attenuated (weakened), or reversed at different levels of the moderator.
Explain how moderated multiple regression with two predictors and their interaction term is conceptually equivalent to a two-way between-participants ANOVA
MMR with two predictors and their interaction term is conceptually equivalent to a two-way between-participants ANOVA as they both test whether the interaction between two factors/predictors is significant. They also both follow up significant interactions by testing one factor/predictor at each level of the other (simple effects/simple slopes).
Specify the structural model for moderated multiple regression with two predictors and their interaction term
The structural model for MMR is Ŷ = bXX + bWW + bXWXW + a, where X is the focal predictor, W is the moderator, and XW is the interaction.
Describe how moderated multiple regression uses hierarchical multiple regression to test for significant moderation
MMR uses HMR to test for significant moderation by only entering predictors to test their additive ‘direct effects’ - leaving the interaction term out. Then at step two the interaction term is entered to see if it increases the variance accounted for in Y by a significant amount.
Describe how we would mean-centre the predictor variables and explain the rationale for mean-centring them
To mean-centre, the scores from predictors have the mean from each predictor subtracted from each score on that predictor. This is done to reduce multicollinearity between predictors and their interaction term. If this was not done, the resulting interaction term would be highly intercorrelated with the original predictor scores. It also makes all the predictor regression coefficients/slopes more interpretable.
Explain which statistics are changed by mean-centring and which would stay the same
Mean-centring makes all predictor regression coefficients/slopes more interpretable.
Describe how we would calculate the interaction term
After completing step one (mean-centring both predictors, and finding their significance), the interaction term would be created using both predictors, and would be added into step two of the regression.
Explain how we would test the significance of the interaction term, and identify the statistics we would examine to determine whether an interaction is significant
R2change, Fchange, p value.
Identify the tests we would use to follow up (or “decompose”) a significant interaction in moderated multiple regression
Simple slopes would be used to follow up a significant interaction.
Explain what simple slopes are, why we test them, and how we test them
Simple slopes are an analysis which help us interpret significant interactions in regression. They test the relationship between X and Y at low and high levels of the moderator.
Identify the values we typically use to represent “low” and “high” levels of the moderator
Low: -1SD; High: +1SD
Explain how we would re-run the model to test the simple slope of the focal predictor at low and high levels of the moderator
The model would be rerun by creating two new variables representing both low and high levels of the moderator. Then, two new interaction terms representing the XW interaction at both the low level of X and the high level of W. A MMR will then be ran twice, once for at the low level of W, and the other for the high level of W.
Identify the statistics we would need to interpret to determine whether a simple slope is significant
T-test, p value, beta, sr2
Explain what a significant simple slope tells us
A significant simple slope tells us the magnitude and significance of the slopes.
Describe how simple slopes are plotted
Simple regression equations are used to calculate predicted values of Y at low and high levels of X. They are then plotted onto a line graph.
