Random Slope model Flashcards
How does the random slope differ from the random intercept model?
Equation
How does the random slope differ from the random intercept model?
visually
we allow the slopes to vary:
Random Slope model in Stata
How to check/test whether RS is better than RI model?
Log likelihood ratio test for whether the RS model fits better
-> quite common statistical testing to see whether a random slope pays off
Variance components of RI vs RS model
How to calculate slope variance?
What does Intercept-slope covariance tell us?
If the covariance is positive, then a higher intercept value is associated with a higher slope.
If negative, a higher intercept value is associated with a lower slope.
If near-zero, there is minimal/no relationship between the intercept and slope values.
Why do random slopes vary less than fixed slopes?
Random slopes are subject to shrinkage, which is a statistical technique that pulls estimates towards a common value, typically the overall mean. Shrinkage helps to stabilize the estimates and reduces the influence of extreme or noisy observations. As a result, the estimated random slopes tend to be less variable compared to fixed slopes, which do not undergo shrinkage.
Practical advice: Random slopes
- Do not include random slopes without random intercepts (possible but doesn’t make a lot sense)
- Many random slopes make the model unstable (limit number of random slopes)
- Include random slopes only if strongly suggested by theory (Rabe-Hesketh & Skrondal 2012)
- For correct statistical inference, include a random slope for all lower-level variables involved in cross-level interactions (Heisig & Schaeffer 2019) → not intuitive
Why does centering matter?
In random intercept models, Level-2 variance is constant. In random slope models, Level-2 variance is a function of the random slope.
You can center at different levels but depending on where you center your intercept, the variance will vary - you have to be aware
Level-2 variance function of RS models
Cross-level interactions
Typical setup
- Theory suggests slope variance
- Model finds slope variance
- We have measures of L2 factors explaining slope variance
a) What is the estimated slope of ESCS for private schools?
b) How much of ESCS slope variance is associated with school type?
a) 26 (main + interaction effect)
b) Bild
Which effect/estimator is b1?
What is the mixed meaning of RE?
Level-1 & Level-2 hypothesis of ESCS on math score?
Level-1 & Level-2 mechanism of ESCS on math score?
Separating within and between theoretically:
ESCS on mscore
Separating within and between statistically:
ESCS on mscore
Interpret the RE, FE & BE estimator
Interpret the cross-level interaction
