Lecture 10 Flashcards
What is added in the new, more complex multilevel model of random intercept?
add a group-level predictor
What is the formula for the random intercept model with group predictor?
Yij = γ00 + γ10Xij + γ01Zj + u0j + εij
WHERE:
β0j = γ00 + γ01Zj + u0j (random intercept)
β1 = γ10 (fixed slope)
What is the first thing you do when you want to use a multilevel model?
- run the null model
- calculate the ICC to see whether the group-level is important
What effects are present in the random intercept null model?
- one fixed (γ00)
- one random
- one residual
What do you look at to determine whether the fit of your multilevel, random intercept model has improved form the null?
- 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
Where do you put binary variables when conducting a multilevel model?
- 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)
What effects are present in the random intercept model with group predictor?
- X fixed effects, X = predictors + 1 (Y00 and fixed slope for each predictor)
- one random (variance uoj)
- one residual (variance eij)
What is the equation for the random slope model?
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)
What is special about the random slope model?
individual-level predictor is both a fixed and random effect
What effects are present in the random slope model?
- X fixed effects, X = predictors + 1 (Y00 intercept and slope for each predictor)
- 2 random
- 1 residual
What do you look at in the output for random slope?
- 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
What is the more complex random slope model?
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)
What is the key to the random slope model with the group level predictors?
- 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
What calculations should you do to interpret results?
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
What are the 4 issues with MLM?
- centring
- assumptions
- estimation
- covariance structures
What type of variables do you put into “covariates” rather than “factor”?
- continuous variables
- can also put binary variables, coded 0/1 in this box
- “factor” for categorical
What does random slopes MLM assume about the slopes?
that they are normally distributed around a mean value
Why do we use “variance components” as the covariance type in SPSS for MLMs? What can you use to get around this?
- 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”
What are the types of centring? What is the point of this?
- 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)
What are the assumptions of MLM?
- regression assumptions
- EXCEPT: not independent errors, the reason we are doing MLM is because of dependency
- also: random effects normally distribution!
What is the issue with estimation in MLM?
- we used restricted ML
- usually won’t make much difference
- use ML for model fit estimates to compare accross models
What is the issue of covariance structures in MLM?
- 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
Why do the uoj and eij terms “go away” when we write out the equation at the end?
- 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
What does it mean if the intercept variance is still significant after you’ve added in your predictors?
- there is still more b/w groups variance to remove
- you can reduce this more with more predictors, but might want a simpler model??
What does a sig. + or -ve interaction term mean in the complex random slope model?
- +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)
