Ben's answer already covered the statistical points, so I'll just clarify
my (perhaps odd) description of the glht() output: it is treating that
ratio as a z-score, which allows easy calculation of a p-value. And my
experience is that this p-value is only slightly different from what you'd
get by treating that ratio as a t-statistic and figuring out the
appropriate df (based on K-R or Satterthwaite approximations), but that's
just my experience based on the kinds of data that I work with.
On Wed, Apr 25, 2018 at 1:53 PM, Ben Bolker <bbolker at gmail.com> wrote:
>
> A little more detail:
>
> if we take the ratio R=(estimated coefficient)/(standard error), that
> is not yet either a "Z score" or a "t score". If we assume the standard
> error is itself estimated without error (i.e. we have an arbitrarily
> large amount of data), then we expect R to be normally distributed and
> we call it a "Z-score". If we take into account the expected
> uncertainty in the standard error, which in simple cases we can quantify
> by knowing the number of residual degrees of freedom, we expect R to be
> t-distributed with df=(residual degrees of freedom); then we call R a
> "t-score".
>
> If we are not in a simple case, figuring out the appropriate df can be
> difficult.
>
> cheers
> Ben Bolker
>
>
> On 2018-04-25 02:49 PM, Cristiano Alessandro wrote:
> > Hi Dan,
> >
> > thanks for your answer. Sorry about my naive question, from a
> > non-statistician. I still have trouble understanding; you say that
> z-scores
> > are the estimates divided by the SE. Isn't this the definition of a
> > t-statistic under the null hypothesis that the mean is equal to zero?
> >
> > Also, when you say that glht() is side-stepping all of that and just
> using
> > a normal approximation. What does it mean/imply exactly, as far as
> > computing the z-scores (the ones I see in the output of the summary)
> goes?
> >
> > Best
> > Cristiano
> >
> > On Wed, Apr 25, 2018 at 1:25 PM, Dan Mirman <dan at danmirman.org> wrote:
> >
> >> 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
> >>>
> >>> [[alternative HTML version deleted]]
> >>>
> >>> _______________________________________________
> >>> R-sig-mixed-models at r-project.org mailing list
> >>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>>
> >>
> >>
> >>
> >> --
> >> -----------------------------------------------------
> >> Dan Mirman
> >> Associate Professor
> >> Department of Psychology
> >> University of Alabama at Birmingham
> >> http://www.danmirman.org
> >> -----------------------------------------------------
> >>
> >> [[alternative HTML version deleted]]
> >>
> >> _______________________________________________
> >> R-sig-mixed-models at r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
> _______________________________________________
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>
--
-----------------------------------------------------
Dan Mirman
Associate Professor
Department of Psychology
University of Alabama at Birmingham
http://www.danmirman.org
-----------------------------------------------------
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