extracting p values for main effects of binomial glmm

Hi,

I'm fairly new to mixed models and have done a lot of reading without much
success. Unfortunately there is no one at my institution who is really
familiar with them so I thought I would try this list.

I'm running a binomial generalized linear mixed effects model and I need
p-values for the main effects. I know this isn't entirely correct with this
type of model but my supervisor wants the p-values!

The model is:

glmer (Proportion hatched ~ Diet * Infection status * Day + (1|SubjectID) +
(1|Day), family=binomial)

where,

Proportion hatched = cbind(Offspring, Eggs-Offspring)
Diet is a factor with 2 levels
Infection status is a factor with 4 levels
Day is a factor with 3 levels

Using Subject ID number and Day as random effects is supposed to control
for pseudoreplication in the model, although I am not entirely sure that
this is specified in the correct way. I wanted to include experimental
replicate here too but the model failed to converge.

My question is: is there a way to get p-values for the main fixed effects
of Diet, Infection and Day?

If you need more specific model information or the model output I would be
happy to provide it.

Thanks,
Megan

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