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(This article was first published on <strong><a href="http://www.datasurg.net/2018/01/13/p-values-from-random-effects-linear-regression-models/"> DataSurg » R</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p><pre>lme4::lmer</pre>
<p> is a useful frequentist approach to hierarchical/multilevel linear regression modelling. For good reason, the model output only includes <em>t</em>-values and doesn’t include <em>p</em>-values (partly due to the difficulty in estimating the degrees of freedom, as discussed <a rel="nofollow" href="https://stats.stackexchange.com/questions/146988/getting-degrees-of-freedom-from-lmer" target="_blank">here</a>).</p>
<p>Yes, <em>p</em>-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 <em>p</em>-values on the fixed effects coefficients. Interpret with caution.</p>
<pre>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$t&lt;0, 2, mean))*2,
  (1-apply(boot.out$t>0, 2, mean))*2)
apply(p, 2, min)

# Alternative &quot;pipe&quot; syntax
library(magrittr)

lmer(angle ~ recipe + temp + (1|recipe:replicate), cake) %>% 
  bootMer(fixef, nsim=100) %$% 
  rbind(
  (1-apply(t&lt;0, 2, mean))*2,
  (1-apply(t>0, 2, mean))*2) %>% 
  apply(2, min)</pre>
<p> </p>
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