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I am using the sjPlot package to estimate my multilevel model and I am loving it. However, I am a bit confused by the output of the random intercept.

Background: My dependent variable is on a scale from 0-100. I fitted a model with lmer with some individual level variables that are all group-mean centered and a random intercept on the country level (12 countries). When I visualize the random effects (just the intercept in my case) like this:

sjp.lmer(mymodel3, type="re",
         sort.est = "sort.all",
         y.offset = .4)

I get this plot:

Question: This confuses me a bit. My dependent variable only has values from 0 to 100, so how are there negative values for some countries? What does that mean? And what do the numbers tell me exactly? I was under the impression that having group-mean centered my variables, the intercepts should give me values on the dependent variable scale for a respondent with average predictors (average income, average education etc.) but of course this doesn't make sense with negative values.

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See ranef(mymodel3), fixef(mymodel3), and coef(mymodel3). The random effects are the deviation from "global average" (i.e. the fixed effects), so when you sum up ranef + fixef you get coef.

Here's an example:

library(lme4)
fm1 <- lmer(Reaction ~ Days + (1 + Days | Subject), sleepstudy)

ranef(fm1)
#> $Subject
#>     (Intercept)        Days
#> 308   2.2585654   9.1989719
#> 309 -40.3985770  -8.6197032
#> 310 -38.9602459  -5.4488799
#> 330  23.6904985  -4.8143313
# ... truncated

fixef(fm1)
#> (Intercept)        Days 
#>   251.40510    10.46729

coef(fm1)
#> $Subject
#>     (Intercept)       Days
#> 308    253.6637 19.6662579
#> 309    211.0065  1.8475828
#> 310    212.4449  5.0184061
#> 330    275.0956  5.6529547
# ... truncatated

E.g. Subject 310: -40.3985770 (ranef) + 251.40510 (fixef) = 212.4449 (coef).

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