[R-sig-ME] glmer() Gamma distribution - constant coefficient of variation
Ben Bolker
bbo|ker @end|ng |rom gm@||@com
Wed Mar 31 03:02:08 CEST 2021
On 3/30/21 2:23 PM, Hedyeh Ahmadi wrote:
> *Thank you for the informative suggestion - please see my
> question/comments below in bold:*
>
> I would start by checking the scale-location plot, i.e.
>
> plot(fitted_model, sqrt(abs(resid(., type="pearson"))) ~ fitted(.))
>
> if that's fairly flat, you should be OK. *I actually ended up doing this
> last week as one of my colleage suggested as well. I ran a slightly
> different version of what you suggested, with deviance residual and
> lowess; I got a straight line (see below, the plot of the left) but when
> I plot exactly what you suggest, I get the following plot on the right
> which is kind of weird. I am leaning toward giving the deviance plot a
> pass since deviance residuals are suggested for GLMM. _Any feedback
> would be appreciated here._*
>
> *_Additional question:_ I can't figure out the connection between
> constant coefficient of determination and scale-location plot. Do you
> mind elaborating here?*
The scale-location plot is based on the Pearson residuals, which
divide the residuals by their expected (theoretical) standard deviation.
If the variance model is correct (i.e. the mean-variance relationship
in the data matches that assumed by the model), then the expected
magnitude of abs(Pearson resids) (or the square root thereof, which is
applied to reduce skew) should be constant as a function of the
predicted (fitted) mean.
>
>
> Not that important, but can you tell me why you're fitting an
> identity-link Gamma model? I'm always curious (I've read Lo and Andrews
> [2015] but don't find their argument particularly convincing ...). Do
> you have reasons to believe the relationships are linear rather than
> log-linear?
*We originally hypothesized a linear relationship but then
> when we * *ran lmer() the residual diagnostic plots were highly skewed
> and log transformation did not help at all. Then we implemnted the Gamma
> distribution assumption in glmer() with identity link to keep the
> linearity part. After this, I have been asked the same question of "why
> identity link?" then I doubted my intuition and I ran the model with
> inverse and log link as ad hoc exploration; I could not get thes emodels
> to converge so we decided to keep Gamma with identity link.
Surprising that the log-link Gamma didn't converge (usually it works
better than the identity link ...)
From the diagnostic plots, it looks like your data are discrete. Is
there a particular reason you're not using a discrete response
distribution (like the [perhaps 0-truncated] negative binomial) ?
> *
>
> Best,
>
> Hedyeh Ahmadi, Ph.D.
> Statistician
> Keck School of Medicine
> Department of Preventive Medicine
> University of Southern California
>
> Postdoctoral Scholar
> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
> University of California, Irvine
>
> LinkedIn
> www.linkedin.com/in/hedyeh-ahmadi <http://www.linkedin.com/in/hedyeh-ahmadi>
> <http://www.linkedin.com/in/hedyeh-ahmadi><http://www.linkedin.com/in/hedyeh-ahmadi>
>
>
>
>
> ------------------------------------------------------------------------
> *From:* R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> on
> behalf of Ben Bolker <bbolker using gmail.com>
> *Sent:* Monday, March 29, 2021 5:54 PM
> *To:* r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>
> *Subject:* Re: [R-sig-ME] glmer() Gamma distribution - constant
> coefficient of variation
>
> I would start by checking the scale-location plot, i.e.
>
> plot(fitted_model, sqrt(abs(resid(., type="pearson"))) ~ fitted(.))
>
> if that's fairly flat, you should be OK.
>
> Not that important, but can you tell me why you're fitting an
> identity-link Gamma model? I'm always curious (I've read Lo and Andrews
> [2015] but don't find their argument particularly convincing ...). Do
> you have reasons to believe the relationships are linear rather than
> log-linear?
>
> Lo, Steson, and Sally Andrews. “To Transform or Not to Transform: Using
> Generalized Linear Mixed Models to Analyse Reaction Time Data.”
> Frontiers in Psychology 6 (August 7, 2015).
> https://urldefense.com/v3/__https://doi.org/10.3389/fpsyg.2015.01171__;!!LIr3w8kk_Xxm!_Hr0ANVe7S49QG8nq1EQIqnN8L6onW_Ej2H41C7LDOubwInvN-KOjzKV5IDIz28$
> <https://urldefense.com/v3/__https://doi.org/10.3389/fpsyg.2015.01171__;!!LIr3w8kk_Xxm!_Hr0ANVe7S49QG8nq1EQIqnN8L6onW_Ej2H41C7LDOubwInvN-KOjzKV5IDIz28$>
> .
>
>
>
>
> On 3/22/21 5:24 PM, Hedyeh Ahmadi wrote:
>> Hi all,
>> I am running a glmer() with Gamma distribution and identity link. The R output is as follows. I would like to check the constant coefficient of variation assumption in R but I am not sure where to start. Any help would be appreciated.
>>
>> Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
>> Family: Gamma ( identity )
>> Formula: Y ~ 1 + pm252016aa + race +prnt.empl + overall.income + (1 | site)
>> Data: Family
>> Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 100000))
>>
>> AIC BIC logLik deviance df.resid
>> 68781.7 68917.1 -34371.8 68743.7 9180
>>
>> Scaled residuals:
>> Min 1Q Median 3Q Max
>> -1.9286 -0.7314 -0.0598 0.6770 3.9599
>>
>> Random effects:
>> Groups Name Variance Std.Dev.
>> site (Intercept) 0.66157 0.8134
>> Residual 0.04502 0.2122
>> Number of obs: 9199, groups: site, 21
>>
>> Fixed effects:
>> Estimate Std. Error t value Pr(>|z|)
>> (Intercept) 52.3578 1.3102 39.962 < 0.0000000000000002 ***
>> pm252016aa -0.1260 0.1099 -1.147 0.251212
>> race_1 1.0913 0.7106 -1.536 0.124628
>> race_2 -1.1787 0.6870 3.171 0.001518 **
>> prnt.empl 2.8852 0.4377 4.307 0.000016517 **
>> overall.income[>=100K] -1.8476 0.3693 -5.003 0.000000566 ***
>> overall.income[>=50K & <100K] -0.8644 0.3403 -2.540 0.011078 *
>> ---
>> Signif. codes: 0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1
>>
>>
>> Best,
>>
>> Hedyeh Ahmadi, Ph.D.
>> Statistician
>> Keck School of Medicine
>> Department of Preventive Medicine
>> University of Southern California
>>
>> Postdoctoral Scholar
>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>> University of California, Irvine
>>
>> LinkedIn
>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!_Hr0ANVe7S49QG8nq1EQIqnN8L6onW_Ej2H41C7LDOubwInvN-KOjzKVbeztxWs$
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!_Hr0ANVe7S49QG8nq1EQIqnN8L6onW_Ej2H41C7LDOubwInvN-KOjzKVbeztxWs$>
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!_Hr0ANVe7S49QG8nq1EQIqnN8L6onW_Ej2H41C7LDOubwInvN-KOjzKVbeztxWs$
> >
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!_Hr0ANVe7S49QG8nq1EQIqnN8L6onW_Ej2H41C7LDOubwInvN-KOjzKVbeztxWs$
> ><https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!_Hr0ANVe7S49QG8nq1EQIqnN8L6onW_Ej2H41C7LDOubwInvN-KOjzKVbeztxWs$ >
>>
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>>
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