# P-values from random effects linear regression models

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lme4::lmeris 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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