[R-sig-ME] glmer() Gamma distribution - constant coefficient of variation
Hedyeh Ahmadi
hedyeh@h @end|ng |rom u@c@edu
Tue Mar 30 20:26:53 CEST 2021
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 attached the plot of the left) but when I plot exactly what you suggest, I get the attached 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?
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.
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$ .
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
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