1. Advanced Methods and Models in Behavioral Research – 2009/2010 AMMBR course design CONTENT METHOD Y is 0/1 conjoint analysis logistic regression multi-level methods our own survey

2. Advanced Methods and Models in Behavioral Research – 2009/2010 DATA COLLECTION

3. 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)

4. Advanced Methods and Models in Behavioral Research – 2009/2010 MULTI – LEVEL ANALYSIS

5. 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

6. 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]

7. 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]

8. Advanced Methods and Models in Behavioral Research – 2009/2010 On individual vs aggregate data For instance: X = introvertX = age of McDonald’s employee Y = school resultsY = like the manager

9. 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!

10. 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)

11. 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 -4 exam score School 2School 1 (taken from Rasbash)

12. Advanced Methods and Models in Behavioral Research – 2009/2010 Now the variance Overall mean(0) 3 2 -4 exam score 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

13. Advanced Methods and Models in Behavioral Research – 2009/2010 The variance of the school means around the overall mean 3 2 -4 exam score School 2School 1 Overall mean(0) 2.5 -2.5 The variance of the school means around the overall mean= (2.5 2 +(-2.5) 2 )/2=6.25 (total variance was 7.5)

14. Advanced Methods and Models in Behavioral Research – 2009/2010 The variance of the pupils scores around their school’s mean 3 2 -4 exam score 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

15. 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 the differences are at the school level more than the pupil level

16. Advanced Methods and Models in Behavioral Research – 2009/2010 Standard multiple regression won't do YD1D2D3D4D5id… +4 0101 -311101 +200102 010 102 +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?

17. 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.

18. 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

19. 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 x 1 ) Make sure that you understand what is happening here, and why it is of use.

20. 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"

21. Advanced Methods and Models in Behavioral Research – 2009/2010 Now: how do you do this in Stata? [note to CS: use age and schooling as examples to split at restaurant level] relevant commands xtset and xtreg bys : egen = mean( ) gen dvarB = - convenience commands tab, gen()drop orderdes editsum

22. 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?

23. 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)

24. 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