What statistical test is performed by summary(glht(model, linfct=mcp(factor="Tukey")), test=adjusted(type="none"))?

Question

I have data that I have fit using lme with the following structure (Subject is implemented as a random effect in order to account for multiple paired comparisons):

model <- lme(values ~ factor, data=mydata.df, random=~1|Subject, 
             na.action=na.omit, contrasts=c("contr.sum","contr. poly"))

anova(model) performs an F test and reports the significance of the relationship between values and factor. Then I use glht to do posthoc comparisons among the levels of factor. I don't want summary to apply a correction for multiple comparisons, I just want the raw p-values, because later I pool all the raw p-values for a larger set of related models and hypotheses, and perform a false discovery rate (FDR) correction.

I'm having trouble navigating the documentation to determine exactly what statistical test is being performed by glht. Is it performing univariate t-tests between two factor levels at a time, without considering pooled variance across all levels, or is it in fact considering the full variance of the model (that's what I want it to do)? Actually, it reports z values, not t values, so does that imply that it is referring to the population variance? Is the test, then, simply called a "z-test"?

Answer 1

It does individual $z$ tests (asymptotic $t$ tests, since df are not available) for each comparison. It uses the results of vcov to obtain standard errors for each comparison. These use the model error, not individual parts of the dataset.

You can specify type="fdr" directly though, as glht can support all the methods in p.adjust.methods.