# comparing fixed effects of a binomial GLMM

I got stuck interpreting the result of a generalised linear mixed model (GLMM). Feedbacks on how to compare two coefficients within a categorical fixed effect would be really helpful!

To be specific, the research question I ask is that are mind-wandering minds more likely to lead to deliberate thought than at-present minds? So the response variable is deliberateness (1 or 0), the predictor variable is attention status (at-present vs. mind-wandering). I also wanted to include Participant ID and the activity (both categorical) as the random effects.

I used the GLMM model because: 1. the response was binary, 2. it was a repeated measure, each participant received this question 18 times. 3. there were random missing values.

I used the GLMM package in R, my code was:

intent_status <- glmm(
deliberate ~ 0 + Status_Q,
random = list(~ 0 + Participant, ~ 0 + activity),
varcomps.names = c("Participant", "activity"),
data = intent_status,
family.glmm = bernoulli.glmm, m = 10^4, debug = TRUE)


The result is:

summary(intent_status)

Call:
glmm(fixed = deliberate ~ 0 + Status_Q, random = list(~0 + Participant,
~0 + Day_Recons), varcomps.names = c("at-present", "mind-wandering"),
data = intent_status, family.glmm = bernoulli.glmm, m = 10^4,
debug = TRUE)

Fixed Effects:
Estimate Std. Error z value Pr(>|z|)
Status_Qat-present       1.1898     0.1215   9.796   <2e-16 ***
Status_Qmind-wandering   0.2660     0.1303   2.042   0.0412 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Variance Components for Random Effects (P-values are one-tailed):
Estimate Std. Error z value Pr(>|z|)/2
Participant      2.29233    0.27786   8.250    < 2e-16 ***
activity         0.26057    0.08107   3.214   0.000655 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


From the p-values of fixe effects I know both coefficients of at-present and mind-wandering were significant (both B !=0). But how do i know if the B(at-present) significantly larger than B(mind-wandering)? I searched on-line but wasn't able to find the answer that I want.

Please let me know if my approach is sensible to the original question, which is "are mind-wandering minds more likely to lead to deliberate thought than at-present minds"?

The $p$-value doesn't tell you anything useful about the differences between deliberation among wandering versus at-present minds. Generally, because the $p$-value does not account for effect size and it is misinterpreted by everybody. But specifically for a GLMM, the $p$-values printed in the call to summary are calculated incorrectly. See ?confint.glmer.
To directly compare the groups, suppress the 0+ from your formula object. This will estimate a log odds ratio comparing the groups. Then fit the random effects model which omits the terms. Compare them with anova. See ?glmm for examples of how that's done.
• @potpot_g sorry I was assuming you were using the lme4 package instead. I don't know how inference is done in this package. You'll have to look up that info elsewhere. There should be a way to compare nested models. Good luck! – AdamO May 20 '18 at 2:10