Been there / done that:
• Stata
• Logistic regression (……)
• Conjoint analysis
Coming up:
• Multi-level analyses
Advanced Methods and Models in Behavioral Research – 2014
AMMBR course design
CONTENT
Y is
0/1
conjoint
analysis
METHOD
logistic
regression
multi-level
methods
Advanced Methods and Models in Behavioral Research – 2014
• Intro: multi-level analysis
• Logistic regression: finale (?)
Advanced Methods and Models in Behavioral Research – 2014
MULTI – LEVEL ANALYSIS
Advanced Methods and Models in Behavioral Research – 2014
In with the (multi-level) statistics...
Y = student grade
X = introversion
Y = manager grade
X = age
Advanced Methods and Models in Behavioral Research – 2014
Multi-level models or ...
•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
dealing with clustered data.
One solution: the variance component model
Advanced Methods and Models in Behavioral Research – 2014
Clustered data -> multi-level models
• Pupils within schools
(within regions within countries)
• Firms within regions (or sectors)
• Vignettes within persons
• Employees within stores (our fastfood.dta example)
Advanced Methods and Models in Behavioral Research – 2014
Two issues with clustered data
• Your estimates will (in all likelihood) be too precise:
you find effects that do not exist in the population
[make sure you get that]
• You will want to distinguish between effects within
clusters and effects between clusters
[see next two slides]
Advanced Methods and Models in Behavioral Research – 2014
On individual vs aggregate data
For instance:
X = introversion
Y = student grade(s)
X = age of McDonald’s employee
Y = like the manager
Advanced Methods and Models in Behavioral Research – 2014
Had we only known, that the data are clustered!
Using the
school example:
lines represent
schools. And
within schools
the effect of
being introvert
is positive!
So the effect of an X within clusters can be different
from the effect between clusters!
Advanced Methods and Models in Behavioral Research – 2014
Advanced Methods and Models in Behavioral Research – 2014
MAIN MESSAGES
Be able to recognize clustered data and deal
with it appropriately (how to do that will
follow)
Distinguish two kinds of effects: those at the
"micro-level" (within clusters) vs those at the
aggregate level (between clusters). They
need not be the same!
(and ... do not test a micro-hypothesis with
aggregate data)
Advanced Methods and Models in Behavioral Research – 2014
Multi-level analysis:
variance at different levels
Advanced Methods and Models in Behavioral Research – 2014
A toy example – two schools, two pupils
Two schools each with two pupils. We first calculate the means.
(taken from Rasbash)
exam score
3
2
-1
Overall mean(0)
-4
School 1
School 2
Overall mean= (3+2+(-1)+(-4))/4=0
Advanced Methods and Models in Behavioral Research – 2014
Now the variance
exam score
3
2
-1
Overall mean(0)
-4
School 1
School 2
The total variance is the sum of the squares of the departures of the
observations around the mean, divided by the sample size (4) =
(9+4+1+16)/4=7.5
Advanced Methods and Models in Behavioral Research – 2014
The variance of the school means
around the overall mean
exam score
3
2
2.5
Overall mean(0)
-1
-2.5
-4
School 1
School 2
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 – 2014
The variance of the pupils scores
around their school’s mean
exam score
3
2
2.5
-1
-2.5
-4
School 1
School 2
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 – 2014
-> So you can partition the total variance
in individual level variance and school level variance
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 the
differences are at the
school level more than
the pupil level
Advanced Methods and Models in Behavioral Research – 2014

In a multi-level analysis,
we would like to have an estimate
of the amount of variance at the
aggregate level vs at the individual level
Advanced Methods and Models in Behavioral Research – 2014
Advanced Methods and Models in Behavioral Research – 2014
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 and cannot
distinguish between effects at the
cluster vs at the school level
Possible solution (but not so good)
You can aggregate within clusters,
and then run a multiple regression
on the aggregate data. Two
problems: no individual level
testing possible + you get much
less data points.
So what can we do?
Advanced Methods and Models in Behavioral Research – 2014
Multi-level models
The standard 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 – 2014
Solution 1: add dummy-variables per cluster
• Try 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 differences are (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 – 2014
Solution 2: split your micro-level X-vars
Say you have:
Make sure that you
understand what
is happening here,
and why it is of use.
then create:
and add both as predictors (instead of x1)
Advanced Methods and Models in Behavioral Research – 2014
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 – 2014
• NB solution 1 en 3 gaan niet samen
Advanced Methods and Models in Behavioral Research – 2014
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 commands
xtset and xtreg
bys <varA>: egen <meanvarB> = mean(<varB>)
gen dvarB = <varB> - <meanvarB>
convenience commands
tab <var>, gen()
order
edit
drop
des
sum
Advanced Methods and Models in Behavioral Research – 2014
Up next
• How do we run the "Solution 1”, "Solution 2”, and “Solution 3”
analysis and compare which works best? What about
assumption checking?
• Random intercept we now saw, but how about random slopes?
Advanced Methods and Models in Behavioral Research – 2014
Non-response
Advanced Methods and Models in Behavioral Research – 2014
Non-response analysis
• Not all of the ones invited are going to participate
• Think about selective non-response: some (kinds of)
individuals might be less likely to participate.
How might that influence the results?
sample
Non-response scenarios: things to try
• Compare sample with population on several
characteristics …
• … for instance by trying to ask questions to your
whole sampling frame
• Compare earlier response with later response
Advanced Methods and Models in Behavioral Research – 2014
What is still missing from
these logit do files?
Advanced Methods and Models in Behavioral Research – 2014
What is still missing from
these logit do files?
• Try all the available tools: outliers, transformations,
interactions, dummy-variables, analyze subsets,
assumption checking …
• Add more comments (in general) + add
interpretation of the findings
• In the end: conclude. A “final model” or …
• … and that can also be a sequence of models
Advanced Methods and Models in Behavioral Research – 2014
Check out:
My logistic regression run on auto.dta
(Not easy to explain /
thinking out loud /
there is more than one correct answer)
Advanced Methods and Models in Behavioral Research – 2014
This Friday latest:
• Deliver: per data file: one do-file
• Make sure that it is complete. Questions / stuck?
Ask!
Advanced Methods and Models in Behavioral Research – 2014