5nd meeting: Multilevel modeling: Summary & Extra’s Subjects for today:  How to do multilevel analysis: a 5-step-approach  Interaction, cross-level interactions, mean centering  Influential cases in multilevel modeling  New developments I: generalized multilevel models in SPSS 19  New developments II: Missing data substitution

During this course we discussed several steps in multilevel modeling. Here is a summary that may be followed: 1)Calculate the higher level variances (often level 2), the intra class correlation and test whether it is significant (in linear models use difference in -2 loglikelihood, in logistic models use t-test). 2)When there is level 2 variance, include relevant level 1 variables to test hypotheses on indidual level, but also to take into account compositional effects (notable as a change in the level 2 variance, which in many cases will decrease). 3)After including all relevant level 1 indicators you may include relevant level 2 variables (preferably not all at once but one by one or cluster by cluster). _____________________ 4)When you are after crosslevel interactions (you may think that level 1 effects are conditional upon level 2 variables or that level 2 effects are conditional upon level 1 variables), first set relevant level 1 variables random. 2

4)You may be are after crosslevel interactions. You may think/hypothesize that level 1 effects are conditional upon level 2 variables or that level 2 effects are conditional upon level 1 variables. First set relevant level 1 variables random. 5)Even when you find no random variantion I advice to test the cross-level interaction because random variance may be quite low and non-significant while a test on an interaction may very well be significant. So, include the interaction between X on level 1 and X on level 2 and test whether the interaction is significant (use level 2 df) For the interpretation of interaction mean centering may come in handy (also may prove benificial when model does not converge (see later slides). NEXT SLIDE: an example of a Table with steps

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5 Interactions once more! DATA: again fake and stored in TOPGEAR.sav Why interactions? Because we like to test whether effects DIFFER ACROSS GROUPS or CATEGORIES Suppose we estimated the effect of education on watching Top Gear. This tv-show is about fast cars. Top Gear therefore might just be more interesting for men than for women. This eventually means that it might not be a very good idea to model the educational effect equal for men and women. So the regression model: Top Gear = a + b1 * education + e might be wrong here. Even Top Gear = a + b1 * education + b2 * gender + e is wrong because we only added to the model that women might differ in viewing Top Gear but the educational effect still is the same.

6 First solution: just split the file: sort cases by gender. split file by gender. REGRESSION /DEPENDENT topgear /METHOD=ENTER educat. split file off.

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8 Second solution: just estimate one model so we can statistically test whether the educational effects differs between men and women: Top Gear = a + b1 * education + b2 * gender + b3 * gender * education Now for females (coded 0 on gender) the model can be re-written: Top Gear = a + b1 * education + b2 * 0 + b3 * 0 * education Top Gear = a + b1 * education For males (coded 1) we get: Top Gear = a + b1 * education + b2 * 1 + b3 * 1 * education Top Gear = a + b1 * education + b2 + b3 * education Top Gear = (a + b2) + ((b1 + b3) * education) So b2 is the increase of the intercept in case you are a man B3 is the ADDITIONAL effect for education when you are a man, which can be tested with a t-test

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11 In multilevel we can incorporate interactions as well. Whenm they are on the same level then there is no difference with the previous slides If the interaction is between variables from different levels there something extra. Let us go back to the Math test and the relation with homework:

12 It helps when interpreting the main effects in an interaction model. Suppose you have homework * % black on a school.Then you get someting like this: Homework:.10 % blacks: -.20 Interaction homework * % blacks =.01. What does it say: 1) When % blacks = 0, the effect of homework is.10 2) When Homework = 0, the effect of % blacks is ) When % blacks =1, the effect of homework is.11 4) When homework =1, the effect of % blacks is -.19 So as % blacks increases in a classroom, the effect of homework becomes stronger As the hours spent on homework increase, the effect of % blacks is less strong

13 We know that the co-variance is at x=0 (the intercept) but if we mean center the variable homework the co-variance changes (let us substract 2 we get: 0 So the co-variance dependents upon where you put intercept! Is this important, well yes. 1) It helps in the estimation procedure (interation proces, converging problems

The problem of influential cases at higher levels (more at: at: % volunteers % church attendees 60 landen With the 3 datapoints (Uganda, Tanzania & Zimbabwe) correlation.43, Without these 3 countries it is.2!

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Be aware of non-linear relations: The correlation is -.6, BUT it is far from being linear. When we log transform both variables we get

17 New developments I: generalized multilevel models in SPSS 19 * Since SPSS 19 there are multiple ways to link the dependent variable with x-variables in mixed models. New developments II: Missing data substitution * In MLwiN there is an additional add on called REAL COM to do miising data substition, a short manual is provided on this web site.