1 / 26

# Moderation: Assumptions - PowerPoint PPT Presentation

Moderation: Assumptions. David A. Kenny. What Are They?. Causality Linearity Homogeneity of Variance No Measurement Error. Causality. X and M must both cause Y.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Moderation: Assumptions' - hasana

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

David A. Kenny

Causality

Linearity

Homogeneity of Variance

No Measurement Error

• X and M must both cause Y.

• Ideally both X and M are manipulated variables and measured before Y. Of course, some moderators cannot be manipulated (e.g., gender).

• Need to know causal direction of the X to Y relationship.

• As pointed out by Irving Kirsch, direction makes a difference!

• Judd & Kenny (2010, Handbook of Social Psychology), pp. 121-2 (see Table 4.1).

• A dichotomous moderator with categories A and B

• The X  Y effect can be stronger for the A’s than the B’s.

• The Y  X effect can be stronger for the B’s than the A’s.

• In some cases, causality is unclear or the two variables may not even be a direct causal relationship.

• Should not conduct a moderated regression analysis.

• Tests for differences in variances in X and Y, and if no difference, test for differences in correlation.

• Assume that either X  Y or Y  X.

• Given parsimony, moderator effects should be relatively weak.

• Pick the causal direction by the one with fewer moderator effects.

• Say we find that Gender moderates the X  Y relationship.

• Is it gender or something correlated with gender: height, social roles, power, or some other variable.

• Moderators can suggest possible mediators.

• Helpful to look for violations of linearity and homogeneity of variance assumptions.

• M is categorical.

• Display the points for M in a scatterplot by different symbols.

• See if the gap between M categories change in a nonlinear way.

• Using a product term implies a linear relationship between M and X to Y relationship: linear moderation.

• The effect of X on Y changes by a constant amount as M increases or decreases.

• It is also assumed that the X  Y effect is linear: linear effect of X.

• Threshold model: For X to cause Y, M must be greater (lesser) than a particular value.

• The value of M at which the effect of X on Ychanges might be empirically determined by adapting an approach described by Hamaker, Grasman, and Kamphuis (2010).

Second Alternative to Linear Moderation

• Curvilinear model: As M increases (decreases), the effect of X on Y increases but when M gets to a particular value the effect reverses.

• Add M2 and XM2 to the regression equation.

• Test the XM2 coefficient.

• If positive, the X  Y effect accelerates as M increases.

• If negative, then the X  Y effect de-accelerates as M increases.

• If significant, consider a transformation of M.

• Graph the data and look for nonlinearities.

• Add X2 and X2M to the regression equation.

• Test the X2 and X2M coefficients.

• If significant, consider a transformation of X.

• Consider a dichotomous moderator in which not much overlap with X (X and M highly correlated).

• Can be difficult to disentangle moderation and nonlinearity effects of X.

Y

X

Moderation

Y

X

• Variance in Moderation Analysis

• X

• Y (actually the errors in Y)

• Not a problem if regression coefficients are computed.

• Would be a problem if the correlation between X and Y were computed.

• Correlations tend to be stronger when more variance.

• A key assumption of moderated regression.

• Visual examination

• Plot residuals against the predicted values and against X and Y

• Rarely tested

• Categorical moderator

• Bartlett’s test

• Continuous moderator

• not so clear how to test

• The category with the smaller variance will have too weak a slope and the category with the larger variance will too strong a slope.

• Separately compute slopes for each of the groups, possibly using a multiple groups structural equation model.

• No statistical solution that I am aware of.

• Try to transform X or M to create homogeneous variances.

Variance Differences as Moderatora Form of Moderation

• Sometimes what a moderator does is not so much affect the X to Y relationship but rather alters the variances of X and Y.

• A moderator may reduce or increase the variance in X.

• Stress  Mood varies by work versus home; perhaps effects the same, but much more variance in stress at work than home.

Measurement Error Moderator

• Product Reliability (X and M have a normal distribution)

• Reliability of a product: rxrm(1 + rxm2)

• Low reliability of the product

• Weaker effects and less power

• Bias in XM Due to Measurement Error in X and M

• Bias Due to Differential X Variance for Different Levels of M

Differential Reliability Moderator

• categorical moderator

• differential variances in X

• If measurement error in X, then reliability of X varies, biasing the two slopes differentially.

• Multiple groups SEM model should be considered