Odds ratio and confidence intervals from glmer output

Question

I have made a model that looks at a number of variables and the effect that has on pregnancy outcome. The outcome is a grouped binary. A mob of animals will have 34 pregnant and 3 empty, the next will have 20 pregnant and 4 empty and so on.

I have modelled this data using the glmer function where y is the pregnancy outcome (pregnant or empty).

mclus5 <- glmer(y~adg + breed + bw_start + year + (1|farm),
                data=dat, family=binomial)

I get all the usual output with coefficients etc. but for interpretation I would like to transform this into odds ratios and confidence intervals for each of the coefficients.

In past logistic regression models I have used the following code

round(exp(cbind(OR=coef(mclus5),confint(mclus5))),3)

This would very nicely provide what I want, but it does not seem to work with the model I have run.

Does anyone know a way that I can get this output for my model through R?

Answer 1

The only real difference is that you have to use fixef() rather than coef() to extract the fixed-effect coefficients (coef() gives you the estimated coefficients for each group).

I'll illustrate with a built-in example from the lme4 package.

library("lme4")
gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
               data = cbpp, family = binomial)

Fixed-effect coefficients and confidence intervals, log-odds scale:

cc <- confint(gm1,parm="beta_")  ## slow (~ 11 seconds)
ctab <- cbind(est=fixef(gm1),cc)

(If you want faster-but-less-accurate Wald confidence intervals you can use confint(gm1,parm="beta_",method="Wald") instead; this will be equivalent to @Gorka's answer but marginally more convenient.)

Exponentiate to get odds ratios:

rtab <- exp(ctab)
print(rtab,digits=3)
##               est 2.5 % 97.5 %
## (Intercept) 0.247 0.149  0.388
## period2     0.371 0.199  0.665
## period3     0.324 0.165  0.600
## period4     0.206 0.082  0.449

A marginally simpler/more general solution:

library(broom.mixed)
tidy(gm1,conf.int=TRUE,exponentiate=TRUE,effects="fixed")

for Wald intervals, or add conf.method="profile" for profile confidence intervals.

Answer 2

I believe there is another, much faster way (if you are OK with a less accurate result).

From: http://www.ats.ucla.edu/stat/r/dae/melogit.htm

First we get the confidence intervals for the Estimates

se <- sqrt(diag(vcov(mclus5)))
# table of estimates with 95% CI
tab <- cbind(Est = fixef(mclus5), LL = fixef(mclus5) - 1.96 * se, UL = fixef(mclus5) + 1.96 * se)

Then the odds ratios with 95% CI

print(exp(tab), digits=3)