L7 - Mixed-effects models

Question 1

Common reasons for clustered data? (multilevel data)

Answer 1

• Repeated measurement of the same person
• clustered sampling

Question 2

Why worry about clustered data?

Answer 2

• If data points are not independent of each other this violates the assumption of independent residuals.

Question 3

What happens if the assumption of independent residuals is violated?

Answer 3

Estimated standard errors are too small, inflated Type I error (we reject H0 too quickly).

Question 4

What is ecological fallacy?

Answer 4

Incorrectly generalize the pattern on the aggregate level to the individual level.
- spurious patterns
- hidden patterns

Question 5

Multi-level problem visualized

Answer 5

Question 6

Intraclass correlation (ICC)

Answer 6

Ratio of variance between groups and variance within groups

Question 7

When do you have a high ICC?

Answer 7

Question 8

When do you have a low ICC?

Answer 8

Question 9

Are mixed-effects models, hierarchical models, and multilevel linear models the same?

Answer 9

yes

Question 10

What is fixed effects?

Answer 10

Population-level average effects (main effect or interaction)

Question 11

What is random effects?

Answer 11

Random variability of lower-level units (subjects, items) around a fixed effect.

Question 12

Write down the formula for a mixed-effects model

Answer 12

Question 13

How does the co-variance matrix look like of random effects?

Answer 13

Question 14

What is an example of the by-subject random intercept?

Answer 14

here we measure how the individual participants deviate from the aggregate measure.

Question 15

How to decide between a mixed-effects model and an intercept-only model?

Answer 15

In the context of your lecture slides, the Intraclass Correlation Coefficient (ICC) of .54 provides evidence of dependence between observations within a group. An ICC value close to 1 indicates strong dependence, while an ICC value close to 0 indicates weak dependence. In this case, the ICC value of .54 suggests that there is moderate dependence between observations within a group, making it appropriate to use a mixed-effects model.

Question 16

What is partial pooling?

Answer 16

Due to the hierarchical structure of the mixed-effects model, the individual parameters (random effects) are informed by the group-level parameter (fixed effects)

Question 17

What is shrinkage?

Answer 17

Extreme values are pulled towards the mean of the distribution because they are more likely to be unreliable. Shrinkage is stronger when there is little data on the individual level.

Question 18

Is the variability of random effects in mixed-effects models smaller than the variability of individual parameters in non-hierarchical regression?

Answer 18

Yes

Question 19

Two criteria for model fit

Answer 19

• Likelihood ratio test
• Information criteria

Question 20

What are two information criteria?

Answer 20

• Akaike information criterion (AIC)
• Bayesian information criterion (BIC)

Question 21

What do AIC and BIC tell you

Answer 21

How well the model trades off complexity and model fit

Question 22

Do random slopes increase model complexity?

Answer 22

Yes

Question 23

Is a higher AIC and BIC better?

Answer 23

no it is worse

Question 24

What does the fixed intercept in a mixed-effects model refer to?

Answer 24

Mean of the search efforts across people

Question 25

What does the fixed slope tell you in the mixed-effects model?

Answer 25

e.g. .09 –> By increasing the IV by 1 we get .09 more search effort = DV

Question 26

How do you conduct a statistical evaluation for regression coefficients?

Answer 26

t = b/SEb
b is the estimated regression coefficient

Question 27

What is the problem of computing degrees of freedom in mixed-effects models?

Answer 27

You need N df = N -2

The question is what is N in the mixed-effects model. Number of observations? Number of subjects?

Question 28

Why is calculating df a problem for the p-value?

Answer 28

You need df for the t-value of the regression coefficient. There is ambiguity about what the correct p value is.

Question 29

What do the Satterthwaite and Kenward-Roger approximation do?

Answer 29

They approximate the degrees of freedom

Question 30

What canbe used for model comparison?

Answer 30

• likelihood ratio test
• parametric bootstrap

Question 31

what is t-as-z approach?

Answer 31

if t>2 it is significant

Question 32

can you use mixed-effects logitstic regression

Answer 32

yes

Question 33

How many levels should the random-effects grouping factor (participants, items) have to reliable estimation of random effects?

Answer 33

at least 6 levels (# people)

Question 34

What can you do if you have fewer than 6 levels?

Answer 34

One might consider running a regular multiple regression with the grouping factors as a dummy-coded covariate