lme4::lmer

is a useful frequentist approach to hierarchical/multilevel linear regression modelling. For good reason, the model output only includes *t*-values and doesn’t include *p*-values (partly due to the difficulty in estimating the degrees of freedom, as discussed here).

Yes, *p*-values are evil and we should continue to try and expunge them from our analyses. But I keep getting asked about this. So here is a simple bootstrap method to generate two-sided parametric *p*-values on the fixed effects coefficients. Interpret with caution.

library(lme4)
# Run model with lme4 example data
fit = lmer(angle ~ recipe + temp + (1|recipe:replicate), cake)
# Model summary
summary(fit)
# lme4 profile method confidence intervals
confint(fit)
# Bootstrapped parametric p-values
boot.out = bootMer(fit, fixef, nsim=1000) #nsim determines p-value decimal places
p = rbind(
(1-apply(boot.out$t<0, 2, mean))*2,
(1-apply(boot.out$t>0, 2, mean))*2)
apply(p, 2, min)
# Alternative "pipe" syntax
library(magrittr)
lmer(angle ~ recipe + temp + (1|recipe:replicate), cake) %>%
bootMer(fixef, nsim=100) %$%
rbind(
(1-apply(t<0, 2, mean))*2,
(1-apply(t>0, 2, mean))*2) %>%
apply(2, min)

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