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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