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
What is the formula for the random intercept model?
Yij = Yoo + Y10Xij + uoj + eij
Boj = Yoo + uoj B1 = Y10
What is the random intercept null model? What does this allow for?
set Y10 to zero
- this makes the RANDOM EFFECTS ANOVA (as before)
- can check the ICC and see if you should be using a mutlilevel model
What effects are involved in a random intercept model?
- 2 fixed effects (fixed Yoo intercept and fixed slope for IV)
- 1 random effect (variance uj)
- 1 residual effect (variance eij)
How do you work out how much variation X accounts for?
BETWEEN GROUPS VARIATION:
- change in intercept
- (old-new) / old
WITHIN-GROUPS VARIATION
- change in residual
- (old-new) / old
When is aggregation okay?
- if you are ONLY interested in macro-level propositions
What is the equation for a one-way ANOVA?
Yij = B0 + Bj + eij
What do the i and j represent in the MLM equations?
- i: ith person
- j: jth group
- if neither, it is FIXED
When do you look at the fit tests for random effects ANOVA?
- when you are comparing b/w two models
- we didn’t focus on this
What do you need for the ICC to be sig.?
the intercept variance to be sig.
What is the assumption of the random intercept MLM?
the intercepts are normally distributed around a mean value
What do uj and t2 actually mean for the intercept?
- intercept varies across all groups by amount uj for group j
- jth group intercept: Yoo + uj
- variance of intercept term across all groups is t2
What did Snijders & Bosker say about aggregation, disaggregation and MLM?
- if macro-units have any meaningful relation with the
phenomenon under study, analysing only aggregated or
disaggregated data is apt to lead to misleading and
erroneous conclusions. - a multi-level approach, in which within-group and between-group relations are combined, is more difficult but much more productive
What are the standard regression and multiple regression equations in MLM terms?
standard regression: Yi = B0 + B1Xi + ei
multiple regression: Yi = B0 + EBkXki + ei
