Final Flashcards
(19 cards)
Hausman test
Tests the random effects assumption that u_j is uncorrelated with the fixed effects (null hypothesis is that random and fixed effects target the same betas)
Likelihood ratio test null hypothesis
Simpler model is adequate
How do you test whether state intercepts and slopes are correlated?
Test the level 2 covariance term using its standard error
When do you need a complex level 1?
When the variance term AND/OR the covariance term for the level 1 random slope
Interpretation of complex level 1 intercepts and slopes
e_0ij: within-cluster variance conditional on the predictor
e_1ij: describes how within-cluster variance changes as an x function of the predictor
3 sources of variation
Sampling
Stochastic
Variation in parameters/relationships
Types of ecological effects
Cross-level effect modification
Direct ecological effect
Indirect ecological effect
Why might adding a level 1 predictor increase level 2 variance?
If contextual effects were being masked without the predictor
What are the weights used in the random effects grand mean?
Ratio of between-group parameter variance to total variance
Assumption of random vs fixed effects
Random: exchangeability between clusters
Fixed: no overall model
Why might a random slopes model show less shrinkage?
Because the slope could provide “evidence” supporting the mean
When would a fixed effects model be preferred?
If we are concerned about ecological confounders correlated with the fixed part of the model
What should we do to facilitate interpretation of covariance terms?
Mean-center the predictors
Why should we model complex heterogeneity at level 1?
Otherwise might have apparent complex level 2 results that are actually complex level 1
What do you NOT have if you use separate coding in the random part?
No constant at level 2
Difference between environmental and integral/global variable
Environmental usually has a level 1 analog (which may or may not be measured)
How can we deal with collinearity between individual and group-level variables?
Use group mean centering (correlation greater than about 0.2)
How do we perform group mean centering?
Group mean goes in the model as a fixed effect
Add fixed effect for individual difference from group mean
Contextual effect is now Beta_1 - Beta_2
How to deal with measurement error in higher-level variables?
Use modeled precision-weighted group means
