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Toolkit + “show your skills” AMMBR from xtreg to xtmixed (+checking for normality, and random slopes, and cross-classified models, and then we are almost done in terms of theory) xtreg (with assumption checking) We knew already ... We have the standard regression model (here with only one x): but think that the data are clustered, and that the intercept (c0) might be different for different clusters … where the S-variables are dummies per cluster. Because k can be large, this is not always feasible to estimate. Instead we estimate: … with the delta normally distributed with zero mean and variance to be estimated. And this you can do with xtreg xtset <clustervariable> xtreg y x1 … and by doing this, we are trying to take into account the fact that the errors are otherwise not independent. xtreg: replacing the dummies by a delta • This is only allowed when the dummies themselves follow a normal distribution (and when delta and epsilon do not correlate) CHECK NO 1: • First run your model with all the dummies included (if possible – might not be feasible) • Then check whether the coefs of these dummies follow a normal distribution through the following Stata-code: * Run a regression (with numbered dummies) reg y d2 ... d40 x1 x2 * Write the coefficients to a new variable gen coef = . forvalues i=2/40 { replace coef = _b[d`i’] if _n==`i’ } OR: for num 2/40: replace coef = _b[dX] if _n==X swilk coef // test for normality Note: with all the dummies included, you consider the “within-effects” (the d_ variables) only! CHECK NO 2: • Compare the “dummy-estimates” with the “deltaestimates”: xtset id xtreg y x1 x2, fe estimates store fixed xtreg y x1 x2, re estimates store random hausman fixed random // “fe” for “fixed effects” // store these estimates // “re” for “random effects”* // store these estimates // compare the estimates <show this in Stata> Try it yourselves - The THKS data (Tobacco, Health and Knowledge Scale) • PostTHKS • PreTHKS • CC, TV, CCTV Target variable is PostTHKS xtmixed (random slopes, and >2 levels) What if c1 varies as well? The same argument applies. We already had: … and now make the c1 coefficient dependent on the cluster (“random slopes”) This is not feasible to estimate for large k, so instead we want to model: … with zeta a normally distributed variable with zero mean and variance to be estimated xtreg does not do this (it only does random intercepts) And this you can do with xtmixed xtmixed y x1 || <clustervar>: is just like the xtreg command, but if you want random slopes for x1, you add x1 after the “:” xtmixed y x1 || <clustervar>: x1 Your output then gives you estimates for the variance (or standard deviation) of delta and zeta. The THKS data (Tobacco, Health and Knowledge Scale) • PostTHKS • PreTHKS • CC, TV, CCTV Target variable is PostTHKS xtmixed postthks cc || schoolid: cc xtmixed can deal with nested clusters too! (here: “classes within schools”) Again the same kind of argument applies. We already had: … and we want separate constant terms per class and per school So we estimate instead: … where delta is again a normally distributed variable at the school level with zero mean and variance to be estimated, and tau is a normally distributed variable at the class level with zero mean and variance to be estimated. And this you can do with xtmixed as well xtmixed y x1 || school: || class: Remember to put the bigger cluster on the left! xtmixed postthks || schoolid: || classid: [show this in Stata] (compare empty xtmixed with xtreg) Horrors (first: you now have a wealth of opportunities with clustered data. All effects might depend on any kind of cluster-level.) xtmixed finds its estimates using an iterative process. This can complicate matters: – it might not converge – it might converge but to the wrong values (and you can’t tell) – it might converge to different estimates for different algorithms in the iterative process You have only a couple of weapons against that: – run again using a different algorithm (use option “, mle”) – Allow estimation of correlations as well (use option “, cov(unstr)”) – (run the dummy-variant (with lots of dummies) anyway) I do not know if any of these horrors will happen in the data you get! This is also something you can pre-check yourselves. Splitting up variables (within vs across clusters) Basically this is completely unrelated to the previous. The important thing is that it can be done in clustered data, and can lead to different interpretations (see before) HOWEVER: Note that if you have three or more levels (pupils within classes within schools) then you can average out on each level … There is more... • Multilevel data and Y = binary xtlogit • Multilevel data and levels are not nested “crossclassified” multilevel models xtmixed • The random utility model clogit Exam material, clogit and xtlogit are not Cross-classified multi-level models • You use the xt-commands to “summarize a large set of dummies”, so to speak • … and you have seen this happening – … with the intercept (xtreg) – … with the slope (xtmixed) – … with nested intercepts (xtmixed) • And you can also apply it on non-nested clusters (“cross-classified multilevel models”) And you do this also with xtmixed xtmixed Y X || _all: R.school || _all: R.club In this example, Y is the target variable, predicted with X, using that there are two non-overlapping clusters: school and club. Note: you could try this, for instance, on the motoroccasion.dta data set. (NB you only need to know this basic option, no more complicated ones) Exam approaching ...