Chapter 10. Moderation, mediation and more regression
Moderation: the combined effect of two variables on another. In statistical terms
called an interaction effect.
A moderator variable is one that affects the relationship between two others
Statistically we are predicting the outcome from the predictor variable, the
moderator and the interaction between the two. it is the interaction effect that
tells us whether moderation has occurred, but the predictor and moderator must
be included as well for the interaction term to be valid.
A model that test for moderation looks as following
y=(b0 +b 1 a 1+ b2 a2+ b3 ab1 )+ e1
When an interaction term is included in the model the b parameters have a
specific meaning: for the individual predictors they represent the regression of
the outcome on that predictor when the other predictor is zero. Sometimes there
are situations where it makes no sense for a predictor to have a score of zero. In
these cases the presence of the interaction term makes the bs for the main
predictors uninterpretable in many situations. For this reason it is common to
transform the predictors using grand mean centring.
Centring: the process of transforming a variable into deviations around a fixed
point, typically the grand mean.
Grand mean centring: the transformation of a variable by taking each score and
subtracting the mean of all scores from it.
‘highest-order’ and ‘lower-order’: this refers to how many variables are involved
Centring is particularly important when your model contains an interaction term
because it makes the bs for lower-order effects interpretable. With centred
variables the bs for individual predictors have two interpretations:
- They are the effect of that predictor at the mean value of the sample
- They are the average effect of that predictor across the range of scores for
the other predictors
Creating interaction variables
Interaction is mathematically peaking the combined effect of two variables
multiplied together. So an interaction variable would be the scores of one variable
multiplied with the scores of another variable. Interaction = variable 1 x variable
2
Following up an interaction effect If the interaction is significant then we know
that there is moderation, but we don’t know the nature on the effect. Simple
slopes analysis is done to find out the relationship between the two variables
• Low values: mean – 1 standard deviation
• Mean values: mean
• High values: mean + 1 standard deviatio
Cramming sam’s tips – moderation:
- Moderation occurs when the relationship between two variables changes
as a function of a third variable.
- Moderation is tested using a regression in which the outcome is predicted
from a predictor, the moderator and the interaction of these variables
, - Predictors should be centred before the analysis
- The interaction of two variables is simply the scores on the two variables
multiplied together
- If the interaction is significant then moderation is present
- If moderation is found, follow up the analysis with simple slopes analysis.
Mediation: a situation when the relationship between a predictor variable and an
outcome variable can be explained by their relation to a third variable.
Mediator: a variable that reduces the size and/or direction of the relationship
between a predictor variable and an outcome variable and is associated statically
with both.
Mediation is said to have occurred if the strength of the relationship between the
predictor and the outcome is reduced by including the mediator. Perfect mediator
occurs when c’ is zero, which means that the relationship between the predictor
and outcome is completely wiped out by including the mediator in the model.
A and b are unstandardized regression coefficients for the relationships between
variables denoted by the path
Direct effect: the effect of a predictor on an outcome variable when a mediator is
present in the model
Indirect effect: the effect of a predictor variable on an outcome variable through a
mediator
The statistical model is the same as the conceptual model. There are four
conditions necessary to demonstrate mediation:
- The predictor variable must significantly predict the outcome variable
- The predictor variable must significantly predict the mediator
- The mediator must significantly predict the outcome variable
- The predictor variable must predict the outcome variable less strongly in
model 3 than in model 1
These conditions have some limitations. Especially the fourth condition. Perfect
mediation is shown when the relation between the predictor and the outcome is
reduced to zero in model 3, but this usually doesn’t happen.so how much of a
reduction in model 3 is needed to conclude mediation?
Mediation would occur if the relationship between the predictor and the outcome
was significant (p < .05_ when looked at in isolation (model 1) but not significant
when the mediator is included too model 3.
This approach is all-or-nothing thinking and not always the ideal way. Because the
b-values can change a lot, although not significant.
An alternative to this approach is to estimate the indirect effect and its
significance. The indirect effect is the combined paths of a and b. the Sobel test
can be used to measure this effect. If the Sobel test is significant it means that
the predictor significantly affects the outcome variable via the mediator. Thus
significant mediation.
Best method is to compute confidence intervals for the indirect effect using
bootstrap methods.
ab
Indirect effect (standardized) = ×S predictor
S outcome
Also called the index of mediation. This measure is useful in that it can be
compared across different mediation models.
Moderation: the combined effect of two variables on another. In statistical terms
called an interaction effect.
A moderator variable is one that affects the relationship between two others
Statistically we are predicting the outcome from the predictor variable, the
moderator and the interaction between the two. it is the interaction effect that
tells us whether moderation has occurred, but the predictor and moderator must
be included as well for the interaction term to be valid.
A model that test for moderation looks as following
y=(b0 +b 1 a 1+ b2 a2+ b3 ab1 )+ e1
When an interaction term is included in the model the b parameters have a
specific meaning: for the individual predictors they represent the regression of
the outcome on that predictor when the other predictor is zero. Sometimes there
are situations where it makes no sense for a predictor to have a score of zero. In
these cases the presence of the interaction term makes the bs for the main
predictors uninterpretable in many situations. For this reason it is common to
transform the predictors using grand mean centring.
Centring: the process of transforming a variable into deviations around a fixed
point, typically the grand mean.
Grand mean centring: the transformation of a variable by taking each score and
subtracting the mean of all scores from it.
‘highest-order’ and ‘lower-order’: this refers to how many variables are involved
Centring is particularly important when your model contains an interaction term
because it makes the bs for lower-order effects interpretable. With centred
variables the bs for individual predictors have two interpretations:
- They are the effect of that predictor at the mean value of the sample
- They are the average effect of that predictor across the range of scores for
the other predictors
Creating interaction variables
Interaction is mathematically peaking the combined effect of two variables
multiplied together. So an interaction variable would be the scores of one variable
multiplied with the scores of another variable. Interaction = variable 1 x variable
2
Following up an interaction effect If the interaction is significant then we know
that there is moderation, but we don’t know the nature on the effect. Simple
slopes analysis is done to find out the relationship between the two variables
• Low values: mean – 1 standard deviation
• Mean values: mean
• High values: mean + 1 standard deviatio
Cramming sam’s tips – moderation:
- Moderation occurs when the relationship between two variables changes
as a function of a third variable.
- Moderation is tested using a regression in which the outcome is predicted
from a predictor, the moderator and the interaction of these variables
, - Predictors should be centred before the analysis
- The interaction of two variables is simply the scores on the two variables
multiplied together
- If the interaction is significant then moderation is present
- If moderation is found, follow up the analysis with simple slopes analysis.
Mediation: a situation when the relationship between a predictor variable and an
outcome variable can be explained by their relation to a third variable.
Mediator: a variable that reduces the size and/or direction of the relationship
between a predictor variable and an outcome variable and is associated statically
with both.
Mediation is said to have occurred if the strength of the relationship between the
predictor and the outcome is reduced by including the mediator. Perfect mediator
occurs when c’ is zero, which means that the relationship between the predictor
and outcome is completely wiped out by including the mediator in the model.
A and b are unstandardized regression coefficients for the relationships between
variables denoted by the path
Direct effect: the effect of a predictor on an outcome variable when a mediator is
present in the model
Indirect effect: the effect of a predictor variable on an outcome variable through a
mediator
The statistical model is the same as the conceptual model. There are four
conditions necessary to demonstrate mediation:
- The predictor variable must significantly predict the outcome variable
- The predictor variable must significantly predict the mediator
- The mediator must significantly predict the outcome variable
- The predictor variable must predict the outcome variable less strongly in
model 3 than in model 1
These conditions have some limitations. Especially the fourth condition. Perfect
mediation is shown when the relation between the predictor and the outcome is
reduced to zero in model 3, but this usually doesn’t happen.so how much of a
reduction in model 3 is needed to conclude mediation?
Mediation would occur if the relationship between the predictor and the outcome
was significant (p < .05_ when looked at in isolation (model 1) but not significant
when the mediator is included too model 3.
This approach is all-or-nothing thinking and not always the ideal way. Because the
b-values can change a lot, although not significant.
An alternative to this approach is to estimate the indirect effect and its
significance. The indirect effect is the combined paths of a and b. the Sobel test
can be used to measure this effect. If the Sobel test is significant it means that
the predictor significantly affects the outcome variable via the mediator. Thus
significant mediation.
Best method is to compute confidence intervals for the indirect effect using
bootstrap methods.
ab
Indirect effect (standardized) = ×S predictor
S outcome
Also called the index of mediation. This measure is useful in that it can be
compared across different mediation models.
