Today’s program

1. Today’s program • Herwart / Axel: Kiva intro (the Galak et al. paper) • Follow-up questions • Non-response (and respondent list) • Multi-level models in Stata

2. Your follow-up questions See Galak_etal_follow_ups.rtf Advanced Methods and Models in Behavioral Research – 2012

3. Issues • Consider doable in short vs long term • Consider doable with the same or similar data, and on the same or another site • Consider topic (it should not be Kiva) • Not just ... “this might also be interesting” Advanced Methods and Models in Behavioral Research – 2012

4. Typical paper follow-ups • Paper is wrong • There is an alternative explanation for the analytical results • Paper’s conclusion might be dependent on design/measurement/analysis. Redo with different kind of design/measurement/analysis • Paper is right, but conclusions limited to a given time or place or context • Paper argues that X’s of a given kind are important  you check several other X’s of that kind, or  you check several X’s of a different kind • Relative importance of (kinds of) X’s • A connection XY is given with a “theory” behind it. You check that theory behind it in more detail (typically with another kind of design/measurement/analysis).

5. Finding other papers on the topic • Look at the references in the original paper • Search for Kiva related papers (either in Google scholar or directly in Web of Science / Scopus ...) • Search for more general key-words: “micro-financing” & “decision-making” • Other literature: try “matching” (e.g. Literature on online dating), other sites with similar setup (e.g. eBay), persuasion and trust, charitable giving ...

6. New analysis/paper: conjoint experiment • Tests importance of stimuli directly (allows comparison of importance of different stimuli + choice of stimuli) (also note the analysis on magnitude of donation in Galak et al., and their complicated analysis of the similarity argument) • Population consists largely of non-donors • No real money involved • ...

7. 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

8. Back to the (multi-level) statistics... Advanced Methods and Models in Behavioral Research – 2012

9. MULTI – LEVEL ANALYSIS Advanced Methods and Models in Behavioral Research – 2012

10. 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 – 2012

11. Clustered data / multi-level models • Pupils within schools (within regions within countries) • Firms within regions (or sectors) • Vignettes within persons Advanced Methods and Models in Behavioral Research – 2012

12. 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 – 2012

13. 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 – 2012

14. 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! Advanced Methods and Models in Behavioral Research – 2012

15. 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" (within clusters) vs those at the aggregate level (between clusters) (and ... do not test a micro-hypothesis with aggregate data) Advanced Methods and Models in Behavioral Research – 2012

16. 3 2 exam score Overall mean(0) -1 -4 School 1 School 2 A toy example – two schools, two pupils Two schools each with two pupils. We first calculate the means. (taken from Rasbash) Overall mean= (3+2+(-1)+(-4))/4=0 Advanced Methods and Models in Behavioral Research – 2012

17. 3 2 exam score Overall mean(0) -1 -4 School 1 School 2 Now the variance 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 – 2012

18. 3 2.5 2 exam score Overall mean(0) -1 -2.5 -4 School 1 School 2 The variance of the school means around the overall mean 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 – 2012

19. 3 2.5 2 exam score -1 -2.5 -4 School 1 School 2 The variance of the pupils scores around their school’s mean 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 – 2012

20. -> 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 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 1.25/7.5= 18% of the total variation of pupils attainment is attributable to pupil level factors Advanced Methods and Models in Behavioral Research – 2012

21. Standard multiple regression won't do 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 less data points. So what can we do? Advanced Methods and Models in Behavioral Research – 2012

22. 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 – 2012

23. 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 – 2012

24. 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 – 2012

25. 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 – 2012

26. 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() drop order des edit sum Advanced Methods and Models in Behavioral Research – 2012

27. 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 – 2012

28. When you have multi-level data (2 levels) • If applicable: consider whether using separate dummies per group might help (use only when this does not create a lot of dummies) • Run an empty mixed model (i.e., just the constant included) in Stata. Look at the level on which most of the variance resides. • If applicable: divide micro-variables in "group mean" variables and "difference from group mean" variables. • Re-run your mixed model with these variables included (as you would a multiple regression analysis) • (and note: use regression diagnostics secretly, to find outliers and such) Advanced Methods and Models in Behavioral Research – 2012

29. To Do • Make an invitation list using the Excel template that I will send to you later this week (don’t invite anyone just yet!) • Make sure you understand the multi-level concept with random intercepts (that is: c0 varies per cluster), and know how to do it in Stata • Try the assignment on the website. Next week we will work on that data in class. Check out the practice data “motoroccasion8March2012.dta” on the website as well. It’s practice data. Advanced Methods and Models in Behavioral Research – 2012

30. Data: TVSFP on influencing behavior Advanced Methods and Models in Behavioral Research – 2012

31. Online already (though not visible) motoroccasion8March2012.dta Advanced Methods and Models in Behavioral Research – 2012