Lecture 9 Flashcards
What is multilevel modelling?
- models that permit constructs at more than one level
- micro and macro
- predict individual outcomes from other individual variables, as well as group-level variables, taking into account group structure
What is interesting about multilevel modelling in terms of independence?
- grouping (macro) structure = dependence among observations
but don’t we usually want independent observations??
»_space;> dependence here is the interesting phenomenon
What are the formulas for the micro and macro relations/propositions?
- micro prop: x > y
- macro prop: Z > Y
- macro-mirco relations: Z > y, Z/x > y, Z/x > y
- micro-macro proposition: x > Z
- casual chain: W > x > y > Z
What is aggregation vs. disaggregation?
- aggregation: at MACRO level, go up, take mean from micros and apply to macro
- disaggregation: at MICRO level, apply macro level down
What are the 5 main issues with aggregation?
- shift of meaning: from individual scores to average scores
- ecological fallacy: cannot infer macro level applies to micro
- aggregation bias: inflated stat effects is these means are interpreted as relating to individuals
- neglecting original data structure
- prevents examination of cross-level interactions
What are the 4 main issues with disaggregation?
- macro-level variable is considered micro
- miraculous multiplication of the number of units
- risk of Type 1 errors
- doesn’t take into account that observations within a macro-unit could be correlated
What is the difference between fixed and random factors?
- fixed: sample from all groups, only make inferences about those groups
- random: when you only sample a subset of groups in the population (subset of macro-units), generalise
What is the random effects ANOVA equation?
Yij = Y00 + uj + eij
- adding in this u value adds in group level variation
What are the assumptions of the terms in the random effects ANOVA?
- uj = normal, mean 0, variation t2
- eij = normal, mean 0, variance sigma2
- total variance = t2 + sigma2
- sigma2 = residual variance
- t2 = variance due to group structure
What types of effects are present in a random effects ANOVA?
- one fixed (Y00 intercept)
- one random (variance of uj)
- one residual (individual level)
What things can you get directly from the output to put into the equation?
the fixed effects > check they are sig.
What is the ICC?
intra class correlation
- we use ICC1 (there are many diff ones)
- proportion of variance explained by the group structure
- also the correlation b/w two randomly drawn individuals in one randomly drawn group
How do you calculate the ICC?
var(uj) / [(var(uj) + var (eij)]
i. e. intercept estimate/ (intercept + residual variance estimate)
- gives you a %
How do you interpret the ICC?
- if >5%, then you can say that the group structure is important to explaining the DV
- > 5%: need MLM
What are the 2 stages in multilevel models?
- level 1: rships b/w level 1 variables estimated separately for each higher level (level 2) units
- these rships are then used as outcome variables for the variables at level 2
