[R-sig-ME] correlation between random effects
Thierry Onkelinx
thierry.onkelinx at inbo.be
Tue Feb 13 11:43:55 CET 2018
Dear Jana,
Please keep the mailing list in cc.
I meant both centering and scaling.
Based on the summary of the model, you have on average 3.7
observations per species, which is a bit small for a random slope
model. What worries me is that the summary of the data indicates
several species with > 20 observation. Hence you will have lot of
species with only 1 or 2 observations. A species with only 2
observations, a small difference in dB1 and a large difference in MC
will likely result in a large random slope for dB1. You'll need to
investigate which species have a strong random slope and why. Most of
the time that is obvious once you plotted the data for that species.
Tip: plot the observations, the fitted values of the model and the
predictions using only the fixed effects.
Best regards,
ir. Thierry Onkelinx
Statisticus / Statistician
Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be
///////////////////////////////////////////////////////////////////////////////////////////
To call in the statistician after the experiment is done may be no
more than asking him to perform a post-mortem examination: he may be
able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does
not ensure that a reasonable answer can be extracted from a given body
of data. ~ John Tukey
///////////////////////////////////////////////////////////////////////////////////////////
2018-02-13 11:23 GMT+01:00 Jana Dlouha <jana.dlouha at inra.fr>:
> Dear Thierry,
>
> Thanks a lot for your reply. Yes, I have used dB1c also in the random effect.
> I have just tried to scale dB1 but I have still the same problem. However, it is possible that I am not doing things well, I am not a statistician and moreover I am just discovering R...
> You say that I should provide more information so here is the summary of my data for the two columns I am using in this model:
> Species MCs dB1
> 327 :43 Min. 40.05 Min. :1.050
> 135 :35 1st Qu. 72.53 1st Qu. :1.400
> 307 :24 Median 89.11 Median :1.560
> 146 :23 Mean 99.56 Mean :1.671
> 328 :23 3rd Qu. 116.23 3rd Qu. :1.840
> 341 :22 Max. 351.49 Max. :4.220
> (Other):2051
>
> How I centered and scaled dB1:
> dB1c<-scale(data$dB1,center=TRUE)
> dB1s<-scale(data$dB1,center=FALSE, scale=TRUE)
>
> summary of the model without centering or scaling dB1:
> Linear mixed model fit by maximum likelihood t-tests use Satterthwaite approximations to
> degrees of freedom [lmerMod]
> Formula: MCs ~ dB1 + (1 + dB1 | Species)
> Data: data
>
> AIC BIC logLik deviance df.resid
> 10720.4 10754.7 -5354.2 10708.4 2215
>
> Scaled residuals:
> Min 1Q Median 3Q Max
> -8.7305 -0.3491 0.0651 0.4508 6.6068
>
> Random effects:
> Groups Name Variance Std.Dev. Corr
> Species (Intercept) 21.48 4.635
> dB1 11.25 3.355 -1.00
> Residual 6.19 2.488
> Number of obs: 2221, groups: Species, 598
>
> Fixed effects:
> Estimate Std. Error df t value Pr(>|t|)
> (Intercept) -64.2618 0.4249 273.4200 -151.2 <2e-16 ***
> dB1 98.0060 0.2800 271.1900 350.0 <2e-16 ***
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
> (Intr)
> dB1 -0.987
>
> summary of the centered model m4c:
>> summary(m4c)
> Linear mixed model fit by maximum likelihood t-tests use Satterthwaite approximations to
> degrees of freedom [lmerMod]
> Formula: MCs ~ dB1c + (1 + dB1c | Species)
> Data: data
>
> AIC BIC logLik deviance df.resid
> 10720.4 10754.7 -5354.2 10708.4 2215
>
> Scaled residuals:
> Min 1Q Median 3Q Max
> -8.7305 -0.3491 0.0651 0.4508 6.6068
>
> Random effects:
> Groups Name Variance Std.Dev. Corr
> Species (Intercept) 1.109 1.053
> dB1c 1.763 1.328 0.94
> Residual 6.190 2.488
> Number of obs: 2221, groups: Species, 598
>
> Fixed effects:
> Estimate Std. Error df t value Pr(>|t|)
> (Intercept) 99.54109 0.08466 290.67000 1176 <2e-16 ***
> dB1c 38.78838 0.11081 271.18000 350 <2e-16 ***
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
> (Intr)
> dB1c 0.575
>
> and summary of the scaled model m4s:
>> summary(m4s)
> Linear mixed model fit by maximum likelihood t-tests use Satterthwaite approximations to
> degrees of freedom [lmerMod]
> Formula: MCs ~ dB1s + (1 + dB1s | Species)
> Data: data
>
> AIC BIC logLik deviance df.resid
> 10720.4 10754.7 -5354.2 10708.4 2215
>
> Scaled residuals:
> Min 1Q Median 3Q Max
> -8.7305 -0.3491 0.0651 0.4508 6.6068
>
> Random effects:
> Groups Name Variance Std.Dev. Corr
> Species (Intercept) 21.48 4.635
> dB1s 33.22 5.763 -1.00
> Residual 6.19 2.488
> Number of obs: 2221, groups: Species, 598
>
> Fixed effects:
> Estimate Std. Error df t value Pr(>|t|)
> (Intercept) -64.2618 0.4249 273.4100 -151.2 <2e-16 ***
> dB1s 168.3687 0.4810 271.1800 350.0 <2e-16 ***
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
> (Intr)
> dB1s -0.987
>
> Thanks in advance for your help!
> Best regards
> Jana
>
> -----Message d'origine-----
> De : Thierry Onkelinx [mailto:thierry.onkelinx at inbo.be]
> Envoyé : mardi 13 février 2018 10:26
> À : Jana Dlouha <jana.dlouha at inra.fr>
> Cc : r-sig-mixed-models at r-project.org
> Objet : Re: [R-sig-ME] correlation between random effects
>
> Dear Jana,
>
> I assume that you uses the centered dB1c both in the random and the fixed effects? Another thing you can try is to scale dB1c. Using sensible units is often sufficient. Don't use large units (e.g.
> kilometers) when you are measuring small things (e.g. millimeters).
>
> You'll need to provide more information when you need more feedback.
> At least the summary of the data and the model.
>
> Best regards,
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND FOREST Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance thierry.onkelinx at inbo.be Havenlaan 88 bus 73, 1000 Brussel www.inbo.be
>
> ///////////////////////////////////////////////////////////////////////////////////////////
> To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher The plural of anecdote is not data. ~ Roger Brinner The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey ///////////////////////////////////////////////////////////////////////////////////////////
>
>
>
>
> 2018-02-13 10:00 GMT+01:00 Jana Dlouha <jana.dlouha at inra.fr>:
>> Hi all,
>>
>> I have a problem with a correlation between random effects. I have tested several models on my data:
>> m0<-lm(MCs~ dB1, data)
>> m1<- lmer(MCs~ dB1 + (1|Species), data, REML=FALSE)
>> m2 <- lmer(MCs~ dB1 + (-1+dB1|Species), data, REML=FALSE)
>> m3<- lmer(MCs~ dB1 + (1|Species)+(0+dB1|Species), data, REML=FALSE)
>> m4<- lmer(MCs ~ dB1 + (1+dB1 |Species), data,REML=FALSE)
>>
>> and when I compare the AIC criterion, the lowest one is for the model m4:
>> m0 m1 m2 m3 m4
>> 11086.51 10948.72 10828.75 10830.75 10720.43
>>
>> However, in the summary I see that there is a strong correlation between random effects and associated variances are huge:
>> Random effects:
>> Groups Name Variance Std.Dev. Corr
>> Species (Intercept) 21.48 4.635
>> dB1 11.25 3.355 -1.00
>> Residual 6.19 2.488
>> Number of obs: 2221, groups: Species, 598
>>
>> For m3, random effect associated with intercept has very low variance and residual variance is only a bit higher:
>> Random effects:
>> Groups Name Variance Std.Dev.
>> Species (Intercept) 3.419e-14 1.849e-07
>> Species.1 dB1 7.968e-01 8.927e-01
>> Residual 6.327e+00 2.515e+00
>> Number of obs: 2221, groups: Species, 598
>>
>> I am tempted to take into account only the randon effect associated with the slope however I don't know if i can do this considering that the AIC is not the lowest one for this model and how to justify it in my paper?
>> By the way, I don't really understand why the variances associated with the random effects change so much.
>> I have tried to center the regressor dB1 which removed the correlation between fixed effects and changed the sign of correlation but random effects remain strongly correlated and variances large:
>>
>> Random effects:
>> Groups Name Variance Std.Dev. Corr
>> Species (Intercept) 1.109 1.053
>> dB1c 11.255 3.355 0.94
>> Residual 6.190 2.488
>> Number of obs: 2221, groups: Species, 598
>>
>> Could you please give me some hint to solve my problem? Thanks a lot
>> in advance
>>
>> Jana
>>
>>
>>
>> [[alternative HTML version deleted]]
>>
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