Topic 5: Interaction & Mediation Flashcards
interaction effect
the extent to which the effect of one factor depends on the level of the other factor
when is an intreaction present?
when the effect of one factor on the DV changes at different levels of the other factor
interpreting cell mean plots
- if the slopes are the same, there is no interaction
- if the slopes are different (& the lines eventually intersect), there is an interaction
interactions in linear regression
a change in one predictor’s relationship with the DV when another predictor changes
three types of interactions in linear regression
- interaction b/n two continous predictors
- interaction b/n nominal & continuous predictors
- interaction b/n nominal predictors (two-way ANOVA)
interaction between two continuous predictors formula
Ŷ = a + B1X1 + B2X2 + B3X1X2
a (interaction b/n two continuous predictors formula)
average in y when x1 = x2 = 0
b1 (interaction b/n two continuous predictors formula)
effect of x1 when x2 = 0
b2 (interaction b/n two continuous predictors formula)
effect of x2 when x1 = 0
b3 (interaction b/n two continuous predictors formula)
change in the effect of x1 on average as x2 increases by 1 unit
H0 (interaction b/n two continuous predictors formula)
B3 = 0 (no interaction b/n x1 & x2)
H1 (interaction b/n two continuous predictors formula)
B3 ≠ 0 (x1 & x2 interact)
interaction b/n binary & continuous predictors formula
we use the same regression equation as for two continuous predictors
interaction b/n multicategorical & continuous predictors formula
Ŷ = a + B1X1 + B2D1 + B3D2 + B4X1D1 + B5X1D2
a (interaction b/n multicategorical & continuous predictors)
average for y for group 3 (baseline) when x1 = 0
b1 (interaction b/n multicategorical & continuous predictors)
effect of x1 on y for group 3
b2 (interaction b/n multicategorical & continuous predictors)
effect of D1 on y when x1 = 0
b3 (interaction b/n multicategorical & continuous predictors)
effect of D2 on y when x1 = 0
b4 (interaction b/n multicategorical & continuous predictors)
differences in slopes for x1 b/n groups 1 & 3
b5 (interaction b/n multicategorical & continuous predictors)
differences in slopes for x1 b/n groups 2 & 3
hierarchical principle
- if we include an interaction term in a model, we should also include the main effects, even if they’re not statistically significant
- ex. x1x2 is normally correlated with x1 & x2
mean-centring
- mean-centring x1 & x2 gives us a meaningful way of interpreting their regression coefficients
- the means of centred x1 & x2 = 0
- B1 indicates the effect of x1 on y among those average on x2 & vice versa
3 types of effects in mediation
direct, indirect, and total
mediation analysis in linear regression
used to quantify pathways of influence or the process by which an IV can influence a DV
direct effect
the influence of one variable on another that isn’t mediated by any other vairable
indirect effect
the influence of a variable mediated by at least one intervening variable
total effect
direct effect + indirecteffect
simple mediation model
- total effect of x1 on y
- direct & indirect effects of x1
simple mediation model with covariates
all of the interpretations of total, direct, and indirect effects remain the same, but with the addition of holding x3 & x4 constant
inference about indirect effect
testing the statistical significance of unstandardized indirect effects with a single mediator
two tests of unstandardized indirect effects with a single mediator
bootstrap CI, Monte Carlo Ci
