P-values from random effects linear regression models

(This article was first published on DataSurg » R, and kindly contributed to R-bloggers)

`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\$t0, 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(t0, 2, mean))*2) %>%
apply(2, min)```