Lecture 14: Assumptions / mediation & moderation

Question 1

Assumptions

Question 2

Assumption 1 - Linearity

Answer 2

Check visually based on scatterplot
- If the assumption is met, the residuals will be plotted evenly on each side of the horizontal line, getting more concentrated towards the middle.

Question 3

Assumption 2 - Random sampling

Answer 3

We minimize residuals in order to estimate betas for a specific sample, but the sample should reflect the population distribution (and it will, if it was randomly selected from the population)

This is not something you can measure, but something you need to know about your data.

Question 4

Assumption 3 - No perfect collinearity (aka ‘no multicollinarity)

Answer 4

Violation can happen if you include variables that are measured differently. That could for example be age in terms of years and age in terms of month.

You cannot put both of them into the same regression equation and therefore if you have a survey where you have respondents who have answered both in terms of month and years you need to recode the variables before estimating the regression model.

Question 5

Assumption 4 - zero conditional mean of error

Answer 5

The durbin-watson statistics can be used to measure autocorrelation of errors.

This test is dependent on the number of predicted values and the number of observations.

The number should be in between 1-3 in order to meet the assumption.

Question 6

Assumption 5 - Homoscedacticity

Answer 6

The residuals in the scatterplot should be placed in a band/ribbon from around the x-axis and not as a funnel

Question 7

Assumption 6 - Multicollinearity

Answer 7

When different IV’s are strongly correlated

• This increases the variance in the coefficients
• Makes out coefficients less precise

Rule of thump: Under four –> Very good (the assumption is met)
Above 10 –> serious multicollinarity

Question 8

Assumption 7 - Normality of errors

Answer 8

Looking at the histogram
- Want to see a symmetrical and build shaped histogram. If not, look at the normal probability plot of regression standardized residuals.

Regression standardized residuals
- If the actual distribution is normal the points for the cases fall along the diagonal running from the lower left to the upper right with only some minor deviations. If not, look at the bootstrap confidence intervals

bootstrap confidence intervals
- We don’t want the coefficients to have a possibility of a value of zero in the bootstrap confidence interval. If we have no zeros in there we can conclude that we have significant betas.

Question 9

Moderation/Mediation

Aguinis et. al. (2016)

Question 10

What is moderation?

Answer 10

• Moderation happens when the effect of an IV on the DV is conditional on another IT which is the moderator
• This means that the moderator either makes the relationship between the IV and DV stronger or weaker.
• Moderating variables is consciously understood based on literature review
• Moderating variables is usually explicitly stated as part of the hypothesis.

Question 11

What is mediation?

Answer 11

• Mediation is used to determine whether there only is a direct effect of the IV on the DV.
• Or whether the IV affect the DV through another variable which is called the mediator effect
• You choose which variable is the mediator

Question 12

What is a full mediation?

Answer 12

• One in which the effect of the IV on the DV become insignificant or disappears
• The IV only affect the DV though a mediator

Question 13

What is a partial mediation

Answer 13

• Exists when there is both a direct effect on IV on the DV and an effect on the DV going through a mediator