Moderation & Mediation

Moderation & Mediation …but mostly moderation

Moderation vs. Mediation • Generally we ask a question like “Does X predict or cause Y?” • We clearly have to move beyond these simple questions • Moderators address “when” or “for whom” X causes Y • Mediators address “how” or “why” X causes Y

Moderators • A moderator is a variable that alters the direction or strength of the relationship between a predictor and an outcome • Really, it is just an interaction – the effect of one variable depends on the level of another • E.g. Interested not only on the effect of social support on depression levels, but whether this differs if the person is male or female

Mediators • A mediator variable explains the relationship between a predictor and an outcome • E.g. Interested in whether or not males and females have differing levels of depression because of differing levels of social support

Moderator OR Mediator • Consider the effect of gender on depression • Social support could be considered either a moderator OR a mediator • It depends on the theory being tested • Gender as a Moderator • The effect of social support on depression varies depending on gender • Gender as a Mediator • Social support has an effect on depression mainly because of an underlying difference between social support levels of males and females

Moderator Effects • We use multiple regression to examine moderator effects • This protects the ‘continuous’ nature of the predictor (explanatory) variables • Avoid ‘grouping’ continuous data so that you can do an ANOVA • Unfortunately, this is a very common practice

Example • Predictor – Unhelpful Social Support • Outcome – Depression • Moderator – Gender • Hypothesis • Because relationships are more important to women than men (Cross & Madson, 1997), the relation between social support and depression may be stronger for women than for men • So positive relation between support and depression • The effect is larger for females than men

Designing the Experiment

Designing a test of Moderator Effects • It is important that potential moderator effects are selected apriori • In particular, the type of interaction effect should be hypothesised • Types of interaction • Enhancing • Buffering • Antagonistic

Types of Interactions • Enhancing • Increasing moderator further increases the effect of predictor • Buffering • Increasing moderator decreases the effect of predictor (i.e. lessens the size of the effect) • Antagonistic • Increasing moderator reverses the effect of predictor (e.g. high support makes counselling bad)

Detecting Interactions • In nonexperimental situations generally only 20-34% power • To maximise this, • equate sample size between groups • Reliable measures (e.g. from 1 to .8 halves power) • Outcome variable can’t be too coarse (predictor and moderator variables each have 5-point likert measures, then outcome variable should be 25-point)

Simulated Data Good reliability coefficients for social support and depression measures (i.e. alpha coefficients of 0.8) Support measure was on a 5-point Likert scale Outcome measure (of depression) was on a 10-point Likert scale Equal numbers of males and females

Analysing the Data

Coding Categorical Variables • If we have categorical variables then we need to represent this as ‘code’ variables • The number of code variables we need is the number of levels of the categorical variable minus one • Gender has 2 levels • So we need 1 code variable

Code Variables • Type of coding based on question • Dummy coding • Comparisons with base or control group • Female = 1 and Male = 0 • Effects coding • Comparisons with grand mean • Female = 1 and Male = -1 • Contrast coding

Let’s Look at this • Open XYZ.sav • How is the Gender variable coded? • Which sort of coding is this? • How could we change it to be Dummy coding?

Centering Continuous Variables • In multiple regression all sorts of problems are related to having explanatory variables which are highly correlated • Interaction terms are often highly correlated with the terms from which they are created • To decrease the correlation we use centred or standardised variables

Let’s do this • Our moderator variable, Unhelpful Social Support, is a continuous variable • Let’s standardise it • To do this • Get the mean of support variable • Get the standard deviation of support variable • Create a new variable std_support which is equal to ( Actual Score – Mean Score ) / SD Score • std_support is our standardised version of support • Look at the values in this column. Any ideas on what they mean?

Create Product Term • Create a new variable by multiplying together the predictor variable and the moderator variable • For example, to get an ‘interaction’ or ‘product’ term we multiply together gender variable and standardised social support variable

Let’s do this • Create a new variable interact which is equal to std_support* gender • Now we have all that we need to see whether or not gender has a moderating effect on the effect of unhelpful social support on depression

Entering variables into Regression • First enter the predictor and moderator variables • Then enter the ‘interaction’ variables • Example • First enter the gender variable and the social support variable • Then enter the newly-created product variable

Let’s do this • Do a regression with std_support and gender as the explanatory variables and depression as the response variable • Now do another regression which is the same as the first regression, but includes our newly-created interact variable

Interpreting the Results

Three Steps • Interpret the effects of predictor and moderator variables • Test the significance of moderator effect • Plot significant moderator effect

Predictor/Moderator Effects • Regression coefficients are representative of the effect of that variable when all other variables are set at 0 • For categorical variables what 0 means will depend on the coding used • For continuous variables that are centred, 0 represents the average of that variable. • In this case regression coefficients represent the effect of one variable at the average level of the other variable • Only interpret the regression coefficients AFTER interaction term is added

Our Predictor/Moderator effects • Let’s look at the ‘full’ model • What is the regression coefficient for Gender? • What does this mean? • What is the regression coefficient for Social Support? • What does this mean?

Significance of Interaction • We want to look at whether adding the interaction lead to a significant improvement in how well the regression is performing • R2 tells us how much variance in depression scores our regression model is explaining • If the interaction is improving the regression, then we expect R2 to increase • This increase should be significant

The F test where f is the number of parameters in the full model (i.e. with interaction effects), r is the number of parameters in the reduced model (i.e. without interaction effects) and N is sample size

We can do this • Change in R2 due to the addition of interaction term = .046 (from .105) • F(1,316)=17.12, p < .001 • So interaction term is significant

Interpreting Moderator Effects • If the interaction is significant then we can look at the effect of our predictor variable at representative levels of the moderator variable • For example, we could look at the relationship between gender and depression at ‘low’, ‘medium’ and ‘high’ levels of social support

Interpret Interaction • We could get some predicted values and plot them • For example, we could calculate Depression for -1,0 and 1 sd from the average Support scores for both males and females • If we wanted Depression Score for average Support Score for males we would have Depression = 5.09 - 0.08*(-1) + 0.27*0 + 0.19*(-1*0) = 5.17 • Depression score for Support Score -1 sd from mean and for females we would have Depression = 5.09 – 0.08*(1) + 0.27*(-1) + 0.19*(-1*1)=4.55

Interaction plot • If we got all six values and plotted them what would we get? • The six values are

Interpret Interaction • This process reveals the ‘simple’ regressions • In other words, when gender = -1 (male) then the regression equation is • When gender = 1 (female) then we have • Note that the regression coefficient for males is smaller, but the intercept is higher • What does this mean?

Mediator Effects briefly

Mediator Effects • Social support as a mediator of the effect of gender on depression • This means that social support is the underlying cause for the relationship between gender and depression • Males and females have different levels of social support and this causes the difference in depression levels

Mediator in Regression • We observe a relationship between gender and depression • e.g.males show higher levels of depression • We can use regression to see this relationship

Mediator in Regression • We also observe that there is a significant relationship between social support and gender • e.g. males have lower levels of social support • And that social support and depression levels are also related • e.g. higher social support have lower depression

Mediator in Regression • If social support is a mediator then including both variables in the one regression will greatly reduce the relationship between gender and depression

Mediator in Regression • Firstly • Males have higher depression levels • But • Males have lower support • Lower support means higher depression • When we use both gender and support to explain depression levels the effect of gender disappears (or is greatly reduced)

Confounding variables • Look suspiciously like mediator variables • The key difference is that if we have a confound variable then there is no way that the predictor variable (gender) could have caused changes in mediator/confounding (social support). • If introducing social support removes the relationship between gender and depression, but it is not possible that gender could cause differences in social support then social support is a confounding variable.

Real Example • Relationship between type of tobacco use and cancer mortality rate • Found those that used pipe or cigar had higher death rates (35.5%) than those who smoked cigarettes (20.5%) • Are there differences between individuals who smoke pipes or cigars to those who smoke cigarettes? • AGE – average ages were 70 and 51 • Tobacco type doesn’t cause age changes • So Tobacco type is a confound

Moderation & Mediation