[R-sig-ME] Fw: glmer and nAGQ

[Peter R Law]

I am re-sending this query that I originally emailed June 13'th. I did not receive a copy of the sent email as I have with previous postings and my query doesn't appear in the archive of postings so does not seem to have been received.

Peter R Law

Sent with [ProtonMail](https://protonmail.com/) Secure Email.

‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
On Monday, June 14th, 2021 at 10:48 PM, Peter R Law <prldb using protonmail.com> wrote:

> Any help with the following query is much appreciated.
>
> I used some simulated data (not generated under any specific distributional assumption but all responses are positive quantities) to investigate the nAGQ argument in glmer, running a Gamma-distribution model. With nAAGQ=2 the logLik is dramatically different to the default value of nAGQ=1, while nAGQ=5 returned minus infinity for the logLik, but the estimates of the fixed effect parameters are somewhat consistent across each computation. Are the differences in the estimated logLik surprising or do they reflect the warnings glmer returns for this attempted modelling? I got similar results for a real dataset too.
>
> data.frame':500 obs. of8 variables:
>
> $ IBI: num25.5 25.4 25.2 25.6 25.8 ...
>
> $ MatID: Factor w/ 99 levels "M1","M10","M11",..: 1 1 1 1 1 12 12 12 12 12 ...
>
> $ Pop: Factor w/ 5 levels "P1","P2","P3",..: 1 1 1 1 1 1 1 1 1 1 ...
>
> $ density : int11 13 15 19 28 11 13 15 19 28 ...
>
> $ rain: num41.1 36.6 31.6 40 40.6 ...
>
> $ normIBI : num-1.28 -1.29 -1.31 -1.26 -1.24 ...
>
> $ normDens: num-1.72 -1.66 -1.61 -1.49 -1.23 ...
>
> $ normRain: num-0.249 -0.64 -1.073 -0.345 -0.287 ...
>
>> M61 <- glmer(IBI~normDens+normRain + (1|MatID), family=Gamma, data=Sim)
>
> Warning message:
>
> In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,:
>
> Model is nearly unidentifiable: very large eigenvalue
>
> - Rescale variables?
>
>> summary(M61)
>
> Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
>
> Family: Gamma( inverse )
>
> Formula: IBI ~ normDens + normRain + (1 | MatID)
>
> Data: Sim
>
> AICBIClogLik deviance df.resid
>
> 1297.61318.7-643.81287.6495
>
> Scaled residuals:
>
> Min1QMedian3QMax
>
> -1.58054 -0.306190.041690.367441.31012
>
> Random effects:
>
> GroupsNameVarianceStd.Dev.
>
> MatID(Intercept) 5.802e-06 0.002409
>
> Residual1.368e-03 0.036989
>
> Number of obs: 500, groups:MatID, 99
>
> Fixed effects:
>
> Estimate Std. Error t value Pr(>|z|)
>
> (Intercept)3.083e-026.090e-0450.63<2e-16 ***
>
> normDens -1.720e-037.946e-05-21.65<2e-16 ***
>
> normRain4.889e-042.463e-0519.85<2e-16 ***
>
> ---
>
> Signif. codes:0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
>
> (Intr) nrmDns
>
> normDens0.028
>
> normRain0.000 -0.044
>
> convergence code: 0
>
> Model is nearly unidentifiable: very large eigenvalue
>
> - Rescale variables?
>
> What kind of scaling is being suggested in the case of the default value of nAGQ? The predictors are already normalized.
>
>> M62 <- glmer(IBI~normDens+normRain + (1|MatID), family=Gamma, nAGQ=2,data=Sim)
>
> boundary (singular) fit: see ?isSingular
>
>> summary(M62)
>
> Generalized linear mixed model fit by maximum likelihood (Adaptive Gauss-Hermite Quadrature, nAGQ = 2) ['glmerMod']
>
> Family: Gamma( inverse )
>
> Formula: IBI ~ normDens + normRain + (1 | MatID)
>
> Data: Sim
>
> AICBIClogLik deviance df.resid
>
> 21.742.8-5.911.7495
>
> Scaled residuals:
>
> Min1QMedian3QMax
>
> -2.3532 -0.6617 -0.13050.51013.4180
>
> Random effects:
>
> GroupsNameVariance Std.Dev.
>
> MatID(Intercept) 0.000000.0000
>
> Residual0.024160.1554
>
> Number of obs: 500, groups:MatID, 99
>
> Fixed effects:
>
> Estimate Std. Error t value Pr(>|z|)
>
> (Intercept)0.02882820.001300822.161< 2e-16 ***
>
> normDens-0.00392740.0012153-3.2320.00123 **
>
> normRain0.00027830.00129940.2140.83042
>
> ---
>
> Signif. codes:0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
>
> (Intr) nrmDns
>
> normDens -0.275
>
> normRain0.019 -0.019
>
> convergence code: 0
>
> boundary (singular) fit: see ?isSingular
>
>> M65 <- glmer(IBI~normDens+normRain + (1|MatID), family=Gamma, nAGQ=5,data=Sim)
>
>> summary(M65)
>
> Generalized linear mixed model fit by maximum likelihood (Adaptive Gauss-Hermite Quadrature, nAGQ = 5) ['glmerMod']
>
> Family: Gamma( inverse )
>
> Formula: IBI ~ normDens + normRain + (1 | MatID)
>
> Data: Sim
>
> AICBIClogLik deviance df.resid
>
> InfInf-InfInf495
>
> Scaled residuals:
>
> Min1QMedian3QMax
>
> -2.2488 -0.39020.03160.34851.7127
>
> Random effects:
>
> GroupsNameVarianceStd.Dev.
>
> MatID(Intercept) 6.007e-06 0.002451
>
> Residual8.831e-04 0.029716
>
> Number of obs: 500, groups:MatID, 99
>
> Fixed effects:
>
> Estimate Std. Error t value Pr(>|z|)
>
> (Intercept)2.936e-022.495e-04117.68<2e-16 ***
>
> normDens-2.182e-031.163e-04-18.76<2e-16 ***
>
> normRain4.883e-043.973e-0512.29<2e-16 ***
>
> ---
>
> Signif. codes:0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
>
> (Intr) nrmDns
>
> normDens -0.013
>
> normRain0.004 -0.041
>
> convergence code: 0
>
> Gradient contains NAs
>
> Warning messages:
>
> 1: In vcov.merMod(object, use.hessian = use.hessian) :
>
> variance-covariance matrix computed from finite-difference Hessian is
>
> not positive definite or contains NA values: falling back to var-cov estimated from RX
>
> 2: In vcov.merMod(object, correlation = correlation, sigm = sig) :
>
> variance-covariance matrix computed from finite-difference Hessian is
>
> not positive definite or contains NA values: falling back to var-cov estimated from RX
>
> For comparison, the linear model seems to be well behaved:
>
> M1 <- lmer(IBI~normDens+normRain +(1|MatID), REML=FALSE, data=Sim)
>
>>
>
> summary(M1)
>
> Linear mixed model fit by maximum likelihood
>
> ['lmerMod']
>
> Formula: IBI ~ normDens + normRain + (1 | MatID)
>
> Data: Sim
>
> AIC
>
> BIC
>
> logLik deviance df.resid
>
> 1804.2
>
> 1825.2
>
> -897.1
>
> 1794.2
>
> 495
>
> Scaled residuals:
>
> Min
>
> 1Q
>
> Median
>
> 3Q
>
> Max
>
> -3.2970 -0.5304
>
> 0.0153
>
> 0.5484
>
> 3.4798
>
> Random effects:
>
> Groups
>
> Name
>
> Variance Std.Dev.
>
> MatID
>
> (Intercept) 43.5694
>
> 6.6007
>
> Residual
>
> 0.6737
>
> 0.8208
>
> Number of obs: 500, groups:
>
> MatID, 99
>
> Fixed effects:
>
> Estimate Std. Error t value
>
> (Intercept) 35.47121
>
> 0.66443
>
> 53.39
>
> normDens
>
> 2.00732
>
> 0.11816
>
> 16.99
>
> normRain
>
> -0.71747
>
> 0.04237
>
> -16.93
>
> Correlation of Fixed Effects:
>
> (Intr) nrmDns
>
> normDens -0.002
>
> normRain
>
> 0.000 -0.044
>
> Should I just conclude that the data is not well modelled by a Gamma GLMM?
>
> Peter R Law
> Research Associate
> Center for African Conservation Ecology
> Nelson Mandela University
> South Africa
>
> Sent with [ProtonMail](https://protonmail.com/) Secure Email.
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