z-scores and glht

The z-scores are computed by dividing the Estimate by the SE. As for why
these are not t-statistics, the short answer is that the degrees of freedom
are not trivial to compute. I believe Doug Bates' response is often cited
by way of explanation:
http://stat.ethz.ch/pipermail/r-help/2006-May/094765.html and it is covered
in the FAQ:
http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#why-doesnt-lme4-display-denominator-degrees-of-freedomp-values-what-other-options-do-i-have
(for more discussion of alternatives see Luke, 2017,
http://link.springer.com/article/10.3758%2Fs13428-016-0809-y).

glht() is side-stepping all of that and just using a normal approximation.
For what it's worth, my own experience is that this approximation is only
slightly anti-conservative, so I usually feel comfortable using it.

Hope that helps,
Dan

On Wed, Apr 25, 2018 at 12:26 PM, Cristiano Alessandro <
cri.alessandro at gmail.com> wrote:

Hi all,

something is wrong with my email, so I am sorry for possible multiple
postings.

After fitting a model with lme, I run post-hoc tests with glht. The results
are repored in the following:

lev.ph <- glht(lev.lm, linfct = ph_conditional);
summary(lev.ph, test=adjusted("bonferroni"))

Simultaneous Tests for General Linear Hypotheses

Fit: lme.formula(fixed = data ~ des_days, data = data_red_trf, random =
~des_days |
    ratID, method = "ML", na.action = na.omit, control = lCtr)

Linear Hypotheses:
                                 Estimate   Std. Error  z value
Pr(>|z|)
des_days1 == 0     3232.2      443.2         7.294        9.05e-13 ***
des_days14 == 0   3356.1      912.2         3.679        0.000702 ***
des_days48 == 0   2688.4     1078.5        2.493        0.038025 *

I am trying to understand the output values. How are the z-scores computed?
If the function uses standard errors, should these be t-statistics (and not
z-scores)?

Thanks for your help, and sorry for the naive question.

Best
Cristiano

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