Moderation and simple slopes Flashcards
Define
Moderation
conditions where the effect or relationship of a predictor with the outcome depends upon another variables
Define
Simple slope analysis
the regression of the outcome y on the predictor x at a specific value of the moderator m
Define
Enhancing moderator
Moderators that strengthen the association
Define
Buffering moderator
Moderators that reduce the association
Define
Antagonistic moderator
Moderators that flip the direction of the association
Define
Centering
The process where we take a variable and change its location so that it has a new center
Definition
conditions where the effect or relationship of a predictor with the outcome depends upon another variables
Moderation
Definition
the regression of the outcome y on the predictor x at a specific value of the moderator m
Simple slope analysis
Definition
Moderators that strengthen the association
Enhancing moderator
Definition
Moderators that reduce the association
Buffering moderator
Definition
Moderators that flip the direction of the association
Antagonistic moderator
Definition
The process where we take a variable and change its location so that it has a new center
Centering
What is the difference between a main effect and an interaction?
A main effect is the effect of one factor (IV) on its own.
An interaction examines two or more factors at the same time – that is, their combined effect, which may not be predictable based on the effects of either factor on their own.
What type of moderator is sex in this example?
What is the difference between moderation and interaction?
Moderation and interaction are used interchangeably. Generally, we use interaction for factors in ANOVAs and moderation to describe a second IV in a regression that moderates another IV
In both cases, an interaction between two variables means that the association between one IV and the DV depends on (i.e., is moderated by) the other IV.
What are the three types of moderators?
Enhancing
Buffering
Antagonistic
What is moderation?
Moderation refers to conditions where the effect or relationship of a predictor with the outcome depends upon another variable
Moderation implies that the relationship between two variables is not the same for everyone
In this example what is the moderator?
Stress predicts more negative affect, but responses to stress depend on coping strategies
Coping strategies
How is moderation statistically measured?
Through interactions between two or more variables
What types of variables can interactions be measured for?
In regression, interactions can be between two categorical variables, two continuous variables, or a categorical and a continuous variable
Interactions between more than two variables work similarly, but interpretation becomes more challenging
In regression, interactions are added as additional variables
If the regression equation is: SWLS = b0+ (b1 * Age )+ (b2 * Stress), what would the equation be if an interaction between age and stress was added?
SWLS = b0+ (b1 * Age) + (b2 * Stress) + (b3 * Age_x_Stress)
Rearrange this equation to pull out age
SWLS = b0+ (b1 * Age) + (b2 * Stress) + (b3 * Age_x_Stress)
SWLS = b0+ b1 * Age + b2 * Stress + b3 * (Age * Stress)
SWLS = b0+ b1 * Age + b3 * (Age * Stress) + b2 * Stress
SWLS = b0+ (b1+ b3 * Stress) * Age + b2 * Stress
For the following equation, what happens when stress = 0, 5 and 10?
SWLS = 4 + 1.2 * Age + 2 * Stress + 0.5 * (Age * Stress)
The slope and intercept increases as stress increases
When Stress = 0:
SWLS = 4 + (1.2 + 0.5 * 0) * Age + 2 * 0
SWLS = 4 + 1.2 * Age + 0
SWLS = 4 + 1.2 * Age
When Stress = 5:
SWLS = 4 + (1.2 + 0.5 * 5) * Age + 2 * 5
SWLS = 4 + 3.7 * Age + 10
SWLS = 14 + 3.7 * Age
When Stress = 10
SWLS = 4 + (1.2 + 0.5 * 10) * Age + 2 * 10
SWLS= 4 + 6.2 * Age + 20
SWLS = 24 + 6.2 * Age
What does b3 represent in this equation?
SWLS = b0+ b1 * Age + b2 * Stress + b3 * (Age * Stress)
b3 = estimated difference in b1 slope when Stress changes 1-unit OR difference in b2 slope when Age changes 1-unit
How do we typically calculate high and low values for a moderator?
A common way to define ‘high’ and ‘low’ for the moderator to calculate simple slopes is Mean +/- 1 SD
Suppose Mean Age = 55, SD = 9
Low Age = 55 – 9 = 46
High Age = 55 + 9 = 64
What is b4 and b5 in this equation?
SWLS = b0+ b1 * D_SomeUni + b2 * D_Grad + b3 * Stress + b4 * D_SomeUni x Stress + b5 * D_Grad x Stress
b4 = estimated difference in slope / mean difference for ‘SomeUni’ Education or for a one unit change in Stress
b5 = estimated difference in slope / mean difference for ‘Grad’ Education for a one unit change in Stress
Why would we want to seen if a continuous variable interacts with itself?
To see if the relationship is truly linear.
If the relationship is linear, there will be no difference in slopes
Why do we center values in calculating interactions?
When interactions are in a model, the default simple slopes estimated are for when the variables involved in the interaction are equal to zero
If the range of outcomes does not include zero, the default simple slopes are meaningless and not easy to interpret
Therefore we select a centre value and subtract all of out data by that values
i.e. Stress20 = Stress - 20
What are the assumptions of interactions and simple slope calculations?
DV (Y) is continuous
One IV (the X) is continuous (if both X and moderator (M) are categorical, you want to do a factorial ANOVA)
Independence of observations
No multicollinearity
No significant outliers
CAUTION: Causality – moderators can suggest possible mechanisms/mediators
Linearity (X and Y)
Homogeneity of variance
