Re: [R] glmmADMB: Generalized Linear Mixed Models using AD Model Builder

From: Roel de Jong <dejongroel_at_gmail.com>
Date: Mon 19 Dec 2005 - 10:16:13 EST

Dear professor Bates,

thank you for your reaction. To make sure that no errors occur in the data generation process I used the elegant function you so neatly provided to generate a couple of datasets under the model specification specified earlier. Running lmer with a Laplace approximation to the high-dimensional integral in the likelihood gives me a warning an then this show-stopper:

Warning: IRLS iterations for PQL did not converge Error in objective(.par, ...) : Unable to invert singular factor of downdated X'X

Fitting the dataset with glmmADMB gives no apparent problems and reasonable estimates. I attached the particular dataset to the email.

The difference in computation time can be attributed to the fact that glmmadmb uses a generic technique called automatic differentiation with the Laplace approximation. The same technique can be employed to fit much more complex nonlinear models, but I'm sure Hans & Dave can tell more about it.

Best regards,

        Roel de Jong

Douglas Bates wrote:
> On 12/15/05, Roel de Jong <dejongroel@gmail.com> wrote:
>

>>Dear R-users,
>>
>>because lme(r) & glmmpql, which are based on Penalized Quasi Likelihood,
>>are not very robust with Bernoulli responses,

>
>
> The current version of lmer takes method = "PQL" (the default) or
> "Laplace" or "AGQ" although AGQ is not available for vector-valued
> random effects in that version so one must be content with "PQL" or
> "Laplace"
>
>
>>I wanted to test glmmADMB.  I run the following simulation study:

>
>
>>500 samples are drawn with the model specification:
>>y = (intercept*f1+pred2*f2+pred3*f3)+(intercept*ri+pred2*rs)
>>     where pred2 and pred3 are predictors distributed N(0,1)
>>     f1..f3 are fixed effects, f1=-1, f2=1.5, f3=0.5
>>     ri is random intercept with associated variance var_ri=0.2
>>     rs is random slope with associated variance var_rs=0.4
>>     the covariance between ri and rs "covr"=0.1
>>
>>1500 units/dataset, class size=30

>
>
> Could you make the datasets, or the code that generates them,
> available? My code for such a simulation would be
>
> genGLMM <- function(nobs, gsiz, fxd, Sigma, linkinv = binomial()$linkinv)
> {
> ngrp <- nobs/gsiz
> ranef <- matrix(rnorm(ngrp * ncol(Sigma)), nr = ngrp) %*% chol(Sigma)
> pred2 <- rnorm(nobs)
> pred3 <- rnorm(nobs)
> mm <- model.matrix(~pred2 + pred3)
> rmm <- model.matrix(~pred2)
> grp <- gl(n = 1500/30, k = 30, len = 1500)
> # linear predictor
> lp <- as.vector(mm %*% fxd + rowSums(rmm * ranef[grp,]))
> resp <- as.integer(runif(nobs) < linkinv(lp))
> data.frame(resp = resp, pred2 = pred2, pred3 = pred3, grp = grp)
> }
>
> Running this function gives
>
>>nobs <- 1500
>>gsiz <- 30
>>fxd <- c(-1, 1.5, 0.5)
>>Sigma <- matrix(c(0.2, 0.1, 0.1, 0.4), nc = 2)
>>set.seed(123454321)
>>sim1 <- genGLMM(nobs, gsiz, fxd, Sigma)
>>(fm1 <- lmer(resp ~ pred2 + pred3 + (pred2|grp), sim1, binomial))

>
> Generalized linear mixed model fit using PQL
> Formula: resp ~ pred2 + pred3 + (pred2 | grp)
> Data: sim1
> Family: binomial(logit link)
> AIC BIC logLik deviance
> 1403.522 1440.714 -694.7609 1389.522
> Random effects:
> Groups Name Variance Std.Dev. Corr
> grp (Intercept) 0.44672 0.66837
> pred2 0.55629 0.74585 0.070
> # of obs: 1500, groups: grp, 50
>
> Estimated scale (compare to 1) 0.9032712
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -1.081710 0.121640 -8.8927 < 2.2e-16
> pred2 1.607273 0.141697 11.3430 < 2.2e-16
> pred3 0.531071 0.072643 7.3107 2.657e-13
>
>>system.time(fm1 <- lmer(resp ~ pred2 + pred3 + (pred2|grp), sim1, binomial))

>
> [1] 0.33 0.00 0.33 0.00 0.00
>
>>(fm2 <- lmer(resp ~ pred2 + pred3 + (pred2|grp), sim1, binomial, method = "Laplace"))

>
> Generalized linear mixed model fit using Laplace
> Formula: resp ~ pred2 + pred3 + (pred2 | grp)
> Data: sim1
> Family: binomial(logit link)
> AIC BIC logLik deviance
> 1401.396 1438.588 -693.6979 1387.396
> Random effects:
> Groups Name Variance Std.Dev. Corr
> grp (Intercept) 0.35248 0.59370
> pred2 0.46641 0.68294 0.077
> # of obs: 1500, groups: grp, 50
>
> Estimated scale (compare to 1) 0.9854841
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -1.119008 0.121640 -9.1993 < 2.2e-16
> pred2 1.680916 0.141697 11.8627 < 2.2e-16
> pred3 0.543548 0.072643 7.4825 7.293e-14
>
>>system.time(fm2 <- lmer(resp ~ pred2 + pred3 + (pred2|grp), sim1, binomial, method = "Laplace"))

>
> [1] 4.62 0.01 4.65 0.00 0.00
>
> Fitting that model using glmmADMB gives
>
>>(fm3 <- glmm.admb(resp ~ pred2 + pred3, ~ pred2, "grp", sim1, "binomial", "logit", "full"))

>
> ...
> iteration output omitted
> ...
>
> GLMM's in R powered by AD Model Builder:
>
> Family: binomial
>
> Fixed effects:
> Log-likelihood: -602.035
> Formula: resp ~ pred2 + pred3
> (Intercept) pred2 pred3
> -1.11990 1.69030 0.54619
>
> Random effects:
> Grouping factor: grp
> Formula: ~pred2
> Structure: General positive-definite
> StdDev Corr
> (Intercept) 0.5890755
> pred2 0.6712377 0.1023698
>
> Number of Observations: 1500
> Number of Groups: 50
>
> The "Laplace" method in lmer and the default method in glmm.admb,
> which according to the documentation is the Laplace approximation,
> produce essentially the same model fit. One difference is the
> reported value of the log-likelihood, which we should cross-check, and
> another difference is in the execution time
>
>
>>system.time(fm3 <- glmm.admb(resp ~ pred2 + pred3, ~ pred2, "grp", sim1, "binomial", "logit", "full"))

>
> ...
> Iteration output omitted
> ...
> [1] 0.23 0.02 21.44 19.45 0.24
>
> Fitting this model takes about 4.7 seconds with the Laplace
> approximation in lmer (and only 0.33 seconds for PQL, which is not
> that far off) and about 20 seconds in glmm.admb
>
>
>
>
>>convergence:
>>~~~~~~~~~~~~
>>No crashes.
>>5/500 Datasets had on exit a gradient of the log-likelihood > 0.001
>>though. Removing the datasets with questionable convergence doesn't seem
>>to effect the simulation analysis.
>>
>>bias:
>>~~~~~~
>>f1=-1.00531376
>>f2= 1.49891060
>>f3= 0.50211520
>>ri= 0.20075947
>>covr=0.09886267
>>rs= 0.38948382
>>
>>Only the random slope "rs" is somewhat low, but i don't think it is of
>>significance
>>
>>coverage alpha=.95: (using asymmetric confidence intervals)
>>~~~~~~~~~~~~~~~~~~~~~~~~
>>f1=0.950
>>f2=0.950
>>f3=0.966
>>ri=0.974
>>covr=0.970
>>rs=0.970
>>
>>While some coverages are somewhat high, confidence intervals based on
>>asymptotic theory will not have exactly the nominal coverage level, but
>>with simulations (parametric bootstrap) that can be corrected for.
>>
>>I can highly recommend this excellent package to anyone fitting these
>>kinds of models, and want to thank Hans Skaug & Dave Fournier for their
>>hard work!

>
>
> I agree. I am particularly pleased that Otter Research allows access
> to a Linux executable of their code (although I would, naturally,
> prefer the code to be Open Source).
>
>
>>Roel de Jong.
>>
>>
>>Hans Julius Skaug wrote:
>>
>>>Dear R-users,
>>>
>>>Half a year ago we put out the R package "glmmADMB" for fitting
>>>overdispersed count data.
>>>
>>>http://otter-rsch.com/admbre/examples/glmmadmb/glmmADMB.html
>>>
>>>Several people who used this package have requested
>>>additional features. We now have a new version ready.
>>>The major new feature is that glmmADMB allows Bernoulli responses
>>>with logistic and probit links. In addition there is
>>>a "ranef.glmm.admb()" function for getting the random effects.
>>>
>>>The download site is still:
>>>
>>>http://otter-rsch.com/admbre/examples/glmmadmb/glmmADMB.html
>>>
>>>The package is based on the software ADMB-RE, but the full
>>>unrestricted R-package is made freely available by Otter Research Ltd
>>>and does not require ADMB-RE to run. Versions for Linux and Windows
>>>are available.
>>>
>>>We are still happy to get feedback for users, and to get suggestions
>>>for improvement.
>>>
>>>We have set up a forum at http://www.otter-rsch.ca/phpbb/ for discussions
>>>about the software.
>>>
>>>Regards,
>>>
>>>Hans
>>>
>>>_____________________________
>>>Hans Julius Skaug
>>>
>>>Department of Mathematics
>>>University of Bergen
>>>Johannes Brunsgate 12
>>>5008 Bergen
>>>Norway
>>>ph. (+47) 55 58 48 61
>>>
>>>______________________________________________
>>>R-help@stat.math.ethz.ch mailing list
>>>https://stat.ethz.ch/mailman/listinfo/r-help
>>>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>>>
>>
>>______________________________________________
>>R-help@stat.math.ethz.ch mailing list
>>https://stat.ethz.ch/mailman/listinfo/r-help
>>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>>

>
>

dep	pred2	pred3	grp
0	-0.832299769325581	-1.67880317415923	1
0	-0.308299055464121	-0.364611545217099	1
1	0.630598386837566	-0.830616438489193	1
1	3.10913858356640	-0.521767356153283	1
1	0.903471812881371	1.91484272352174	1
0	0.90426769897266	-0.513292891585524	1
1	1.14495484917281	0.78473139460995	1
0	-0.234525952851387	-0.50697276499942	1
1	0.631041223657181	0.0885911624846033	1
0	-1.28176856712309	0.381144997887118	1
0	-0.199575490516357	-0.816864500080217	1
0	1.1185927379226	-1.89658827063818	1
0	-0.166954429106639	-1.72768529536314	1
0	0.410078885348753	-2.37013110454109	1
0	0.37016590773711	-0.320034871756389	1
0	-1.29319553111599	-0.243436474810949	1
1	1.44188541761604	0.46171661294066	1
1	1.03439142621889	-0.0934696125911877	1
1	0.941957044041486	1.46031495794676	1
0	0.63243411925538	-0.376900200288554	1
0	0.782797578938882	-2.17296669618680	1
0	-0.0434466627421846	-0.897181210612278	1
0	-0.918950768280257	1.40593647574051	1
0	-0.266797680590651	1.32852283384323	1
0	-1.97795808769759	-0.340096532983713	1
0	0.338662524103419	0.317005354534584	1
1	-0.778330737845841	1.83714022902796	1
1	0.167661592741467	-0.898198193914343	1
0	0.108266386948271	-1.31922947083775	1
1	0.799587591780234	1.20654772520622	1
0	-1.39792357224312	-1.17382560290430	2
1	1.41625128975700	0.0321732274019762	2
1	-0.0781989965585817	1.66218225184847	2
0	-1.57620982406135	0.122918359084620	2
0	-0.169615551813902	-1.32992468631561	2
0	0.0744278240167874	-0.793642608076887	2
1	1.33756270180946	1.43265155843536	2
0	0.171687202226864	-0.197474664007768	2
0	-0.253842074055872	0.422229019624458	2
1	1.51037367919741	0.708493875055813	2
0	0.126257617278352	-0.698370297940141	2
0	-1.41052021563966	-0.580830471211872	2
0	-0.740991848275336	-0.831723737484574	2
0	-1.38752149645338	-0.0645813982998873	2
0	-1.48202337888827	-0.810824176493156	2
0	0.434323217159074	-0.235959885057200	2
0	-0.3660190454198	-0.207497034351587	2
0	-1.55757318106926	-0.649666741994972	2
0	0.200298815968865	-1.25786648414456	2
1	0.60068195996731	1.39546043864496	2
1	0.92181552285589	0.169900540315928	2
1	0.963639582191724	-0.96652696802166	2
0	-1.10894528405182	-0.826447468782818	2
1	-0.143705873984295	0.85696358848945	2
1	-0.227197073907219	0.163108840069261	2
0	0.260778722736436	0.702350481108482	2
1	0.0079839656810117	0.640974302851168	2
1	0.520335955317318	0.82948476190548	2
0	-0.470053854425421	-1.41586935932929	2
0	0.318269807834773	0.221705522455281	2
0	-0.490245326301728	0.553620570804301	3
0	-0.276149978720162	-0.88110452374587	3
0	0.220721777999604	-0.653256457257882	3
0	-0.703075262079484	0.329683608971329	3
0	-0.22696243906353	-2.61950724697562	3
0	-1.09431005668124	-0.0232909455712828	3
1	1.28711954899881	0.344320685687299	3
0	-0.151754090955171	-0.0744843243935522	3
0	0.341919519960378	-0.0964112795642981	3
0	-1.12551027730654	-0.84933031360325	3
0	-0.83446590590987	-0.158563062623380	3
0	-0.519454023512489	-1.24574306199025	3
0	0.273951811480161	-0.738838977465222	3
1	0.644417981459438	0.48825723724319	3
0	0.80733294439454	0.38447235881228	3
0	-1.30801233701682	1.32830707446622	3
0	-0.691273996772228	-1.03695064187955	3
0	-0.55275315135725	0.712670673357253	3
1	1.18912706586104	-0.797779680340233	3
0	0.173813919484423	-0.212804192064869	3
0	0.510051214308946	0.407985297642093	3
0	0.0460404954363198	0.0781827813302751	3
0	-0.812726427004377	-0.961698454122676	3
0	0.316803703625498	0.436795213783597	3
0	1.59372338969642	-0.646972799801143	3
0	-0.264479048468343	0.436583419258436	3
1	1.79785791935398	-2.19022854850479	3
0	-1.25542914249998	0.759841939131259	3
0	-0.556703265843941	-0.596140993896742	3
0	-0.138859132587877	0.353420559076652	3
0	-0.54936814739631	0.5651403571148	4
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0	0.593107076808349	0.398984411079726	4
0	-0.226418280356368	0.252338568472061	4
0	-0.622343771507656	-0.150521153702500	4
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0	-0.897917002717756	1.24600197335951	4
0	-0.131652665221839	-1.14902442133866	4
1	1.05932918053364	-0.208043968099735	4
1	2.21374179592236	-2.11459091350310	4
0	-0.0984023158102187	0.620618589465858	4
0	-0.301419555524483	-1.51777513767374	4
0	0.705447946370506	0.535510970861683	4
0	-0.740935396882992	-0.554365880210576	4
1	1.05185254417717	1.44454045163646	4
0	-0.976862868950618	-0.28295698647597	4
0	-1.81719506639831	-0.214322369708696	4
0	-0.249925818554222	0.183451295261106	4
0	-2.21228328895419	0.123877231369233	4
1	1.38439754243109	0.505675670636377	4
0	-0.837221588634301	-1.50135483614086	4
0	-1.17154448913943	-0.708764217205316	4
1	1.50155644902162	0.43999620318975	4
0	-0.516075651409885	1.10156000900777	4
0	-0.583328580107054	-0.136624407275739	4
0	-0.805969095827047	1.23242239143692	4
0	0.520037308192361	-0.0532028414333528	4
0	-1.07675357578869	-0.246422992512653	4
1	0.84674606454176	1.24706822832629	5
1	0.50225429700895	-0.753501502939139	5
0	-0.110696991251422	-1.28963013849050	5
1	1.45669586789922	-0.0266212621300831	5
0	1.19164829320594	-1.6384147982708	5
1	1.2497582567896	-0.366144380048512	5
0	-1.59200279904562	-0.605612412386137	5
1	0.701642320563013	-0.692590957893450	5
0	0.826729750207121	0.104040242709383	5
0	-0.251589578605641	-1.20008533845167	5
0	1.18981892198469	-1.03838218637413	5
0	-0.48226798541373	-0.103516021510253	5
1	0.902430923145418	-1.25114657112499	5
0	0.480518605880176	0.223857697801260	5
0	-2.25438268634199	1.21126580568773	5
0	-0.383234731665990	-0.766293999344111	5
0	0.581319800323777	0.817394753080253	5
0	-3.3165427929598	-0.121062111785958	5
0	-0.1322580996873	-0.150578017302552	5
1	1.53193807897104	0.733939342102887	5
1	1.11908937603262	0.196818601090142	5
0	0.437875954273944	-0.0197136588508132	5
0	-0.0331688915453021	0.33400847926927	5
1	1.34543708556248	0.00907648260071153	5
0	0.213075347139783	-0.646249613641689	5
0	-0.69524684216634	-2.33922277678765	5
0	-1.57279905654483	-1.87538951834327	5
1	1.07936855487838	1.18446965022099	5
1	0.306985931587578	0.724405953653822	5
1	1.23181672693378	-0.0701925304204026	5
0	-0.919888911082209	0.477276404654286	6
0	-0.663571170286572	-1.46630908083576	6
0	-0.724039231476495	-0.061019673195811	6
0	0.0634460402565889	-1.08461362641975	6
1	-0.269323637008873	0.731446475758064	6
1	-0.146752286719258	1.51369083876776	6
0	-0.35095531255735	-0.234620941343001	6
0	0.273206507398862	-0.393903382508312	6
1	-0.182666577034182	1.83249929313715	6
0	0.681588488289945	-0.375859982611083	6
0	0.242434133831772	-1.64320325331244	6
1	0.188017184214761	-0.228076562308703	6
1	0.166649765922797	0.511793542958201	6
1	2.16402504068409	1.66375788446841	6
1	0.586097780802391	-0.289750400216476	6
0	-0.757716234538208	-0.356355379036605	6
0	-1.11703624150270	-1.02103411104842	6
1	1.32065912451240	-0.529344207548823	6
0	-0.563323776359257	-0.575116970325914	6
0	0.0761081554417085	0.466755576888024	6
0	-0.0393307073575922	-2.09949197028072	6
0	-1.45391429237201	-1.78607291521398	6
0	0.180700026079273	0.785140819957987	6
1	0.842204310528479	-0.078203655202921	6
0	0.957483010083191	0.0933486661821926	6
0	-1.34841123138060	-1.25281641699431	6
0	0.460944146864481	-0.516097804035054	6
1	1.67680834988551	-0.7539974457697	6
1	0.204256257528345	-0.389312192486669	6
1	0.546750712218541	3.06217530791803	6
0	0.0172078969431791	-0.101707833219385	7
0	-1.37010127340567	-1.02691608953111	7
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