glmer and nAGQ
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 at 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.