Lecture 10

Question 1

What is added in the new, more complex multilevel model of random intercept?

Answer 1

add a group-level predictor

Question 2

What is the formula for the random intercept model with group predictor?

Answer 2

Yij = γ00 + γ10Xij + γ01Zj + u0j + εij

WHERE:
β0j = γ00 + γ01Zj + u0j (random intercept)

β1 = γ10 (fixed slope)

Question 3

What is the first thing you do when you want to use a multilevel model?

Answer 3

• run the null model

- calculate the ICC to see whether the group-level is important

Question 4

What effects are present in the random intercept null model?

Answer 4

• one fixed (γ00)
• one random
• one residual

Question 5

What do you look at to determine whether the fit of your multilevel, random intercept model has improved form the null?

Answer 5

• Reduction in intercept variance. How much (%) LEVEL 2, BETWEEN GROUPS VARIANCE, ALL predictors account for
• Reduction in residual variance. How much (%) LEVEL 1, WITHIN GROUPS VARIANCE, only INDIVIDUAL level predictor accounts for

Question 6

Where do you put binary variables when conducting a multilevel model?

Answer 6

• if only 2 categories and labelled 0 and 1, you can just put it in covariates like all the others
• of more than 2 or not labelled 0/1 then it need to go into factors (this is much more complex)

Question 7

What effects are present in the random intercept model with group predictor?

Answer 7

• X fixed effects, X = predictors + 1 (Y00 and fixed slope for each predictor)
• one random (variance uoj)
• one residual (variance eij)

Question 8

What is the equation for the random slope model?

Answer 8

Yij = (γ00 + γ01Zj + u0j )+ (γ10 + u1jXij + εij

Yij = γ00 + γ10Xij + γ01Zj + u0j + u1jXij + εij

WHERE:
β0j = γ00 + γ01Zj + u0j (random intercept)

β1j = γ10 + u1j (random slope)

Question 9

What is special about the random slope model?

Answer 9

individual-level predictor is both a fixed and random effect

Question 10

What effects are present in the random slope model?

Answer 10

• X fixed effects, X = predictors + 1 (Y00 intercept and slope for each predictor)
• 2 random
• 1 residual

Question 11

What do you look at in the output for random slope?

Answer 11

• check sig. of L1-predictor in random effects > this is the slope, see how much it varies
• sig. variance of u1j indicates that slopes vary across groups

Question 12

What is the more complex random slope model?

Answer 12

Yij = (γ00 + γ0Zj + u0j)+ (γ10 + γ11Zj + u1jXij + εij

Yij = γ00 + γ10Xij + γ01Zj + γ11ZjXij u0j + u1jXij + εij

WHERE:
β0j = γ00 + γ01Zj + u0j (random intercept)

β1j = γ10 + γ11Zj + u1j (random slope)

Question 13

What is the key to the random slope model with the group level predictors?

Answer 13

• the interaction term!
• cross-level interaction b/w the group level and individual level predictors
• need to look at the sig of each of the fixed effects, take out the non-sig. interactions to make it more parsimonious

Question 14

What calculations should you do to interpret results?

Answer 14

HOLDING ALL CONSTANT:

• compare lowest and highest group predictor
• compare lowest and highest on other predictors
• can compare lowest and highest on group predictor with and without binary variable

Question 15

What are the 4 issues with MLM?

Answer 15

• centring
• assumptions
• estimation
• covariance structures

Question 16

What type of variables do you put into “covariates” rather than “factor”?

Answer 16

• continuous variables
• can also put binary variables, coded 0/1 in this box
• “factor” for categorical

Question 17

What does random slopes MLM assume about the slopes?

Answer 17

that they are normally distributed around a mean value

Question 18

Why do we use “variance components” as the covariance type in SPSS for MLMs? What can you use to get around this?

Answer 18

• VC assumes that slopes and intercepts are not correlated (assumes diagonal)
• thus, does not include a parameter for the correlation
• if you want to see if they are correlated, use “unstructured”

Question 19

What are the types of centring? What is the point of this?

Answer 19

• grand mean: subtract grand mean from all, get mean of 0 at end
• group mean: subtract group mean from all

aim is to make interpretation easier, because you know the mean is 0 (it is like standardising it)

Question 20

What are the assumptions of MLM?

Answer 20

• regression assumptions
• EXCEPT: not independent errors, the reason we are doing MLM is because of dependency
• also: random effects normally distribution!

Question 21

What is the issue with estimation in MLM?

Answer 21

• we used restricted ML
• usually won’t make much difference
• use ML for model fit estimates to compare accross models

Question 22

What is the issue of covariance structures in MLM?

Answer 22

• we didn’t really look at this
• we used VC which assumes uncorrelated slopes and intercepts, but there are many other types you can do
• in real life, look at this though

Question 23

Why do the uoj and eij terms “go away” when we write out the equation at the end?

Answer 23

• they are assumed to be normally distributed with a mean of 0
• thus, we can assume that they are 0
• also, we only get estimates of the variances for these

Question 24

What does it mean if the intercept variance is still significant after you’ve added in your predictors?

Answer 24

• there is still more b/w groups variance to remove

- you can reduce this more with more predictors, but might want a simpler model??

Question 25

What does a sig. + or -ve interaction term mean in the complex random slope model?

Answer 25

• +ve: boost to people who are high on both (more positive, steeper slope)
• -ve: lower for people who are high on both (reduces slope steepness)