Been there / done that: Stata Logistic regression (……) Conjoint analysis Coming up:

Advanced Methods and Models in Behavioral Research – 2014

Been there / done that:• Stata• Logistic regression (……)• Conjoint analysis

Coming up:• Multi-level analyses


AMMBR course design CONTENT METHOD

Y is 0/1

conjoint analysis

logistic regression

multi-level methods

• Intro: multi-level analysis

• Logistic regression: finale (?)



MULTI – LEVEL ANALYSIS

In with the (multi-level) statistics...


Y = student gradeX = introversion

Y = manager gradeX = age


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


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)


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]


On individual vs aggregate data

For instance: X = introversion X = age of McDonald’s employee Y = student grade(s) Y = like the manager


Had we only known, that the data are clustered!

So the effect of an 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!



MAIN MESSAGESBe 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)

Multi-level analysis:

variance at different levels



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

32

-1

-4

exam

scor

e

School 2School 1

(taken from Rasbash)


Now the variance

Overall mean(0)

32

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exam

scor

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School 2School 1

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


The variance of the school means around the overall mean

32

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exam

scor

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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)


The variance of the pupils scores around their school’s mean

32

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exam

scor

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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


-> 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 thedifferences are at theschool level more than

the pupil level

In a multi-level analysis,

we would like to have an estimateof the amount of variance at the

aggregate level vs at the individual level




Standard multiple regression won't doY 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 20 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?


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.


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


Solution 2: split your micro-level X-varsSay 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.


Solution 3: the variance component model

In the variance component model, we split the randomness

in a "personal part" and a "rest part"

• NB solution 1 en 3 gaan niet samen



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


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?


Non-response

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


What is still missing from these logit do files?


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


Check out:My logistic regression run on auto.dta

(Not easy to explain / thinking out loud /

there is more than one correct answer)

This Friday latest:

• Deliver: per data file: one do-file

• Make sure that it is complete. Questions / stuck? Ask!


Been there / done that: Stata Logistic regression (……) Conjoint analysis Coming up:

Documents

behavioral research

ageadvanced methods

slides8advanced methods

rasbash14advanced methods

aggregate level

multilevel statistics

multi level analysis4in

total variance