[R-sig-ME] z-scores and glht

[Ben Bolker]

   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]]
>>
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>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
> 
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