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I am struggling to address a specific research question within a MLM-framework. I have got a large dataset (N > 75,000) and three levels. Let's just assume I got individuals nested in gender, and gender nested in schools. The dataset contains 50 schools, gender (women/men), and my dependent variable is happiness. How can I test whether happiness differs unsystematically between gender across schools? For example, in school 1 women might be statistically significant more happy than men, and vice versa in school 2, whereas in school 3 there are no significant gender differences. I thought the crucial test might be comparing a mixed model in which individuals and schools are random but gender is fixed with a model in which the slope of gender is also random. Does this make sense? If so, how can I specify this in R, for example within lme4 or nlme?

Thank you

EDIT: I was also playing around with interactions (not sure if it makes sense, thought), but a comparison revealed exactly the same model fit (p = 1): 

fm.null <- lmer(Happi~ 1 + (1|gender) + (1|school), df1, na.action=na.omit)
fm2 <- lmer(Happi ~ 1 + (1|gender) * (1|school), df1, na.action=na.omit)
anova(fm.null, fm2)
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  • $\begingroup$ Have you looked at the lme4 documentation? cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf. See page 6. Also, I believe nlme only takes 1 level. $\endgroup$
    – Jon
    Commented Oct 10, 2016 at 18:45
  • $\begingroup$ Here is an example: ats.ucla.edu/stat/r/examples/alda/ch4.htm $\endgroup$
    – Jon
    Commented Oct 10, 2016 at 18:46
  • $\begingroup$ Thanks Jon, the lme4 documentation is useful. Unfortunately, I am unable to transfer the example codes to my research question. Also, I am not sure if the analytic approach suggested above makes sense. $\endgroup$
    – user134224
    Commented Oct 11, 2016 at 13:53

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Here an answer to my own question in case someone is having the same problem: Compare a random intercept with a random intercept and random slope model.

h2.null <- lmer(Happi ~ gender+ (1|school), data = df, na.action=na.omit)    
h2 <- lmer(Happi ~ gender+ (gender|school), data = df1, na.action=na.omit)
anova(h2, h2.null)

The code is adapted from Rob Thomas' book "Data analysis with R statistical software: a guidebook for scientists" (p. 94).

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