There is a lot of stuff online about eliciting p-values for lme4 linear mixed-effects regression model coefficients (just google it). I opted for MCMCglmm because I like MCMC , and because lme4 has deprecated its own MCMC implementation. [Here][1]'s the MCMCglmm quick start guide. The main idea is simulating the regression model and seeing how much of the posterior density lies in regions beyond a certain value (typically 0). This is the Bayesian version of what p-values are supposed to be doing anyway. The expression we use to form a model is a bit different from lme4. prettyprint model <- lmer(score ~ nstates_amp_and_freq_n + (nstates_amp_and_freq_n | id) + condition:phase, data=all, REML=F)  prettyprint mc <- MCMCglmm(score ~ nstates_amp_and_freq_n + condition:phase, random=~us(nstates_amp_and_freq_n):id, data=all, nitt = 50000, thin=100, pr=TRUE)  where  pr = TRUE indicates we want to keep samples of random effects as well. The samples can be accessed using mc\$Sol and summary(mc) produces a summary that includes p-values. [1]: https://cran.r-project.org/web/packages/MCMCglmm/vignettes/Overview.pdf
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