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

From: Roel de Jong <dejongroel_at_gmail.com>
Date: Mon 19 Dec 2005 - 23:29:58 EST

One thing I forgot to mention: the data was generated and fitted with the binomial probit (not logit) link

Roel de Jong

Roel de Jong wrote:
> 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
> 0 0.0865897190005032 -1.28701512066411 4
> 0 -0.59359121771434 0.137688285767041 4
> 0 1.29103265636505 -1.20664947663906 4
> 0 0.593107076808349 0.398984411079726 4
> 0 -0.226418280356368 0.252338568472061 4
> 0 -0.622343771507656 -0.150521153702500 4
> 0 -0.430960330395192 -0.61365230036041 4
> 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
> 0 2.56322137123985 -0.773240110395935 7
> 0 -0.507174946504427 0.040499359830619 7
> 1 1.47453663326518 0.394613501208432 7
> 1 0.566343961852793 -0.358372221352661 7
> 0 1.07987945451752 -1.26905542641279 7
> 0 0.48707001768777 -0.832979997875164 7
> 0 -2.55931246086968 -0.0387626614737304 7
> 0 0.6047256807427 -1.27952621228527 7
> 0 -0.800975639650827 -1.19892253215496 7
> 0 0.716445890243245 1.86048748902398 7
> 0 2.57842613918261 1.11040509258097 7
> 0 0.161390247713138 -1.25216129083268 7
> 0 0.692254615374798 -0.273053701220116 7
> 0 0.580742663805351 -0.440022666876242 7
> 0 0.0333740430940438 -1.29808134689932 7
> 0 0.429181268475771 0.891622761392008 7
> 0 -0.957211975299114 1.74875584749294 7
> 0 -0.320315263904051 1.38442720841526 7
> 0 -0.518641939927687 -0.617700091693557 7
> 0 -1.20846935175166 -1.08696366448480 7
> 0 0.409554570285672 0.144434888179345 7
> 0 -0.515552017873684 -0.070428657566001 7
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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Dec 20 02:25:55 2005

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