Lecture 3 Flashcards
Why is theory of error important?
- need a theory of error to find the truth
- OR to determine if the observation supports our theory
- statistical provides a theory of error
What is GLM? What is important about this?
adding up variables using a weighted sum - there is no variation though!
So add the error term to allow for variation > can then use the same equation for everyone, just change the error term and you can always get it to fit
What is a theory of error?
- error term that requires statistical techniques
- eg. residuals (estimates of error), normal distribution
- usually assume that the error is normally distributed
What are the assumptions of regression?
- residuals are normal
- mean of 0 for residuals
- independent residuals
- homoscedasticity
- look at P-P plot, histogram and scatterplot
What is mediation? What is the simplest mediation model?
- one variable acts on another through an intervening (mediating) variable
- simplest: X > M > Y
What do a, b and c’ represent in mediation?
- a = effect of X on M
- b = effect of M on Y
- c’ = effect of X on Y (if it is 0, then there is complete mediation)
What are the indirect, direct and total effects in mediation?
- a*b = indirect effect
- c’ = direct effect
- a*b + c’ = total effect
- c = total effect too (c = c’ + a*b)
What is the Sobel test?
- null = indirect effect is 0 (a*b=0)
- if p less than 0.05, then indirect effect is sig.
What are the issues with the Sobel test?
- not always effective
- bc. of low power
- bc. of non-normality in distribution of mediated effects
What is a bootstrap CI? Why is it good?
- bootstrap takes many samples of your sample to get a sampling distribution
- without any assumptions of normality
- is CI includes 0 = significant indirect effect (sig. mediation)
How to you tell if partial or complete mediation from the PROCESS output?
- if direct effect not sig., but indirect sig. then there is complete mediation
- if direct effect sig. and indirect sig., then partial mediation
What do you look at in the PROCESS script output for mediation?
- look at X, Y and M to see which variables are being used
- check sig. of predicting the diff variables
- sig. of direct effect
- look at indirect effect CI (don’t want to include 0)
- look at ‘normal theory tests’ = Sobel test. Want p less than .05
What are the 4 requirements for mediation?
- IV directly predicts DV (c significant)
- IV directly predicts MV (a significant)
- MV directly predicts DV (b significant)
- crucial step: IV and MV both predict DV (IV either eliminated or partially reduced)»_space;> same as saying c’ is sig. smaller than c (reduction) OR c’ is not sig./0 (elimination)
What is the mediation regression equation?
Y = b3 + c’X + bM + e3
What is moderation?
- 1 variable moderates the association b/w 2 variables when the association differs depending on the value of the moderating variable
- INTERACTION b/w M and X
What is the moderation regression equation? How can it be rearranged?
Y = b0 + b1X + b2M + b3XM + e
Y = (b0 + b2M) + (b1 + b3M)X + e
- if b3 is sig > there is moderation occurring
What depends on M? Which terms represent this?
BOTH slope and intercept
- mediated intercept: b0 + b2M
- mediated slope: b1 + b3M
What do you look at in the PROCESS output for moderation?
- interaction p value (want less than 0.05 for sig.)
- diff ‘effects’ (slopes) for diff values of moderator > how the slope changes, can change direction and strength
- look at where the sig. moderation stops being sig.
- look at “Johnson and Newman” output to determine where the moderator stops being sig. (look at p values and CI)
How do you graph moderation?
- save PROCESS output called “data for visualizing conditional effect of X on Y”
- make scatterplot of yhat vs. IV (set markers by M)
- look at slopes/intercepts and how they differ for diff values of M
- can also plot effect, LLCI and ULCI to see where the association stops being sig.
- where it includes 0, the moderator is so strong that association b/w Y and X is no longer significant
How can you tell how many dimensions a line is in?
- how many things there are in the equation (not error though)
- # IVs + constant(1)
What are the 3 mediation equations according to Baron and Kenney?
Y = B + cX + e M = B + aX + e Y = B + c'X + bM + e
Why do only test whether the indirect effect is sig. in mediation?
Because ab = c - c’
This is the critical criteria
What do you do Sobel and bootstrap do not agree?
Use bootstrap, it is better
What happens is error is random?
- it should cancel out across all subjects in the sample
- this is good!
What does modern mediation say?
- a*b sig.
- c also sig.
- just test a*b
What is moderation based on? What way can you do this other than PROCESS?
- all about simple slope and the standard error of it
- can test with t-test of (b1 + b3M)/SE(slope)
- df: N - k - 1 (N = sample size, k = no. predictors in interaction term)
