Advanced Methods and Models in Behavioral Research – 2009/2010 AMMBR course design CONTENT METHOD...
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Transcript of Advanced Methods and Models in Behavioral Research – 2009/2010 AMMBR course design CONTENT METHOD...
Advanced Methods and Models in Behavioral Research – 2009/2010
AMMBR course design
CONTENT METHOD
Y is 0/1
conjoint analysis
logistic regression
multi-level methodsour own
survey
Advanced Methods and Models in Behavioral Research – 2009/2010
DATA COLLECTION
Advanced Methods and Models in Behavioral Research – 2009/2010
Data collection
• surveys not ready to roll – some technical issues unsolved
• please wait until you get the green light to send your invitations
• If you have not done so yet – send your list of respondents (it’s mandatory)
Advanced Methods and Models in Behavioral Research – 2009/2010
MULTI – LEVEL ANALYSIS
Advanced Methods and Models in Behavioral Research – 2009/2010
Multi-level models or ...
dealing with clustered data.One solution: the variance component model
•Bayesian hierarchical models •mixed models (in SPSS)•hierarchical linear models •random effects models •random coefficient models •subject specific models •variance component models •variance heterogeneity models
Advanced Methods and Models in Behavioral Research – 2009/2010
Clustered data / multi-level models
• Pupils within schools (within regions within countries)
• Firms within regions (or sectors)
• Vignettes within persons
[copy to blackboard]
Advanced Methods and Models in Behavioral Research – 2009/2010
Two issues with clustered data
• Your estimates will (in all likelihood) be too precise: you find effects that do not exist in the population
[further explanation on blackboard]
• You will want to distinguish between effects within clusters and effects between clusters
[see next two slides]
Advanced Methods and Models in Behavioral Research – 2009/2010
On individual vs aggregate data
For instance: X = introvert X = age of McDonald’s employee Y = school results Y = like the manager
Advanced Methods and Models in Behavioral Research – 2009/2010
Had we only known, that the data are clustered!
So the effect of X within clusters can be different from the effect between clusters!
Using the school example: lines represent schools. And within schools the effect of being introvert is positive!
Advanced Methods and Models in Behavioral Research – 2009/2010
MAIN MESSAGES
Be able to recognize clustered data and deal with it appropriately (how you do that will follow)
Distinguish two kinds of effects: those at the "micro-level" vs those at the aggregate level
(and do not test a micro-hypothesis with aggregate data)
Advanced Methods and Models in Behavioral Research – 2009/2010
A toy example – two schools, two pupils
Overall mean(0)
Two schools each with two pupils. We first calculate the means.
Overall mean= (3+2+(-1)+(-4))/4=0
3
2
-1
-4
exam
sco
re
School 2School 1
(taken from Rasbash)
Advanced Methods and Models in Behavioral Research – 2009/2010
Now the variance
Overall mean(0)
3
2
-1
-4
exam
sco
re
School 2School 1
The total variance is the sum of the squares of the departures of the observations around mean divided by the sample size (4) =
(9+4+1+16)/4=7.5
Advanced Methods and Models in Behavioral Research – 2009/2010
The variance of the school means around the overall mean
3
2
-1
-4
exam
sco
re
School 2School 1
Overall mean(0)
2.5
-2.5
The variance of the school means around the overall mean=
(2.52+(-2.5)2)/2=6.25 (total variance was 7.5)
Advanced Methods and Models in Behavioral Research – 2009/2010
The variance of the pupils scores around their school’s mean
3
2
-1
-4
exam
sco
re
School 2School 1
2.5
-2.5
The variance of the pupils scores around their school’s mean=
((3-2.5)2 + (2-2.5)2 + (-1-(-2.5))2 + (-4-(-2.5))2 )/4 =1.25
Advanced Methods and Models in Behavioral Research – 2009/2010
-> So you can partition the variance in individual level and school level
How much of the variability in pupil attainment is attributable to factors at the school and how much to factors at the pupil level?
In terms of our toy example we can now say
6.25/7.5= 82% of the total variation of pupils attainment is attributable to school level factors
1.25/7.5= 18% of the total variation of pupils attainment is attributable to pupil level factors
And this is important; we want to know how
to explain (in this example)
school attainment,and appararently thedifferences are at theschool level more than
the pupil level
Advanced Methods and Models in Behavioral Research – 2009/2010
Standard multiple regression won't do
Y D1 D2 D3 D4 D5 id …
+4 -1 -1 0 1 0 1
-3 1 1 1 0 -1 1
+2 0 0 1 0 -1 2
0 1 0 -1 1 0 2
+1 … … … … … 3
+2 … … … … … 3
-3 … … … … … 4
+4 … … … … … 4
… … … … … … …
So:
You can use all the data and just run a multiple regression, but then you disregard the clustering effect, which gives uncorrect confidence intervals
You can aggregate within clusters, and then run a multiple regression on the aggregate data. Two problems: no individual level testing possible + you get less data points.
So what can we do?
Advanced Methods and Models in Behavioral Research – 2009/2010
Multi-level models
The usual multiple regression model assumes
... with the subscript "i" defined at the case-level.
... and the epsilons independently distributed with covariance matrix I.
With clustered data, you know these assumptions are not met.
Advanced Methods and Models in Behavioral Research – 2009/2010
Solution 1: add dummy-variables per cluster
• So just multiple regression, but with as many dummy variables as you have clusters (minus 1)
... where, in this example, there are j+1 clusters.
IF the clustering is (largely) due to differences in the intercept between persons, this might work.
BUT if there are only a handful of cases per person, this necessitates a huge number of extra variables
Advanced Methods and Models in Behavioral Research – 2009/2010
Solution 2: split your micro-level X-vars
Say you have:
then create:
and add both as predictors (instead of x1)
Make sure that you understand what
is happening here,and why it is of use.
Advanced Methods and Models in Behavioral Research – 2009/2010
Solution 3: the variance component model
In the variance component model, we split the randomness
in a "personal part" and a "rest part"
Advanced Methods and Models in Behavioral Research – 2009/2010
Now: how do you do this in Stata?
<See Stata demo> [note to CS: use age and schooling as examples to split at restaurant level]
relevant commandsxtset and xtregbys <varA>: egen <meanvarB> = mean(<varB>)gen dvarB = <varB> - <meanvarB>
convenience commandstab <var>, gen() droporder desedit sum
Advanced Methods and Models in Behavioral Research – 2009/2010
Up next
• How do we run the "Solution 1" and "Solution 2" analysis?
• Random intercept we now saw, but how about random slopes?
Advanced Methods and Models in Behavioral Research – 2009/2010
When you have multi-level data (2 levels)
1. If applicable: consider whether using separate dummies per group might help (use only when this does not create a lot of dummies)
2. Run an empty mixed model (i.e., just the constant included) in Stata. Look at the level on which most of the variance resides.
3. If applicable: divide micro-variables in "group mean" variables and "difference from group mean" variables.
4. Re-run your mixed model with these variables included (as you would a multiple regression analysis)
Advanced Methods and Models in Behavioral Research – 2009/2010
To Do
• Put your respondent list only if you have not done so yet.
• Check the material online (as of tomorrow morning)
• Check in Stata: how do I create:– dummies per cluster– the mean of a variable within a cluster– the deviation from the mean within a cluster
• Next time: bring your laptop. We’ll have a full session of practicing only