[R-sig-ME] z-scores and glht
Ben Bolker
bbolker at gmail.com
Wed Apr 25 20:53:52 CEST 2018
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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