[R-sig-ME] Mixed-effects modelling on data from a highly unbalanced design

D. Rizopoulos d@r|zopou|o@ @end|ng |rom er@@mu@mc@n|
Wed Mar 27 13:35:20 CET 2019


You could also give a try in the GLMMadaptive package that can fit the 
same model but using the more accurate adaptive Gaussian quadrature 
method to approximate the integrals in the definition of the likelihood 
instead of the Laplace approximation.

You can find several examples in the following links:

https://drizopoulos.github.io/GLMMadaptive/

https://drizopoulos.github.io/GLMMadaptive/articles/Custom_Models.html#negative-binomial-mixed-effects-model

https://drizopoulos.github.io/GLMMadaptive/articles/ZeroInflated_and_TwoPart_Models.html

https://drizopoulos.github.io/GLMMadaptive/articles/Goodness_of_Fit.html

Best,
Dimitris


On 3/27/2019 10:50 AM, Adriaan De Jong wrote:
> Dear forum,
> 
> I'm struggling with a data set from 12 years of breeding bird monitoring on 13 sites that were affected by the construction of a new railway (there are control sites, too, but these fall outside the scope of this question). I have data from (a) before, (b) during construction, (c) "ready" (= railway ready but no traffic) and (d) traffic. Obviously, these four steps came in a fixed sequence. Because the railway was built in separate sections, the numbers of years of Before, Construction and Ready (coded in variable Status) vary among sites in terms of timing and duration, but all sites were monitored for the same three years while traffic was on. In short, the "design" is highly unbalanced.
> 
> At this stage, I'm looking at the possible effect of railway construction on avian biodiversity expressed as the total number of species observed per year per site (data below). I've used the following script to prepare the data:
> 
> ArterYears$ArterI<-as.integer(ArterYears$Arter) ## Arter = number of observed species
> ArterYears$Site<-as.factor(ArterYears$Site)
> ArterYears$NArea<-ArterYears$Areal/mean(ArterYears$Areal) ## Areal = area in hectares
> ArterYears$NArea2<-ArterYears$NArea^2
> ArterYears$YearS<-as.integer(ArterYears$Year - 2001) ## the study was performed 2002-2015
> ArterYears$Status<-as.factor(ArterYears$Status)
> ArterYears$response<-ArterYears$ArterI
> 
> (Some of these steps are not really necessary, but I've included them just to be sure. The same goes for the assignment of NA's to the model names below.)
> 
> The data for species number (range 28 - 83) are overdispersed for all sites combined, but not for the individual sites (rather underdispersed). To be on the safe side, I chose to use a negative binomial family anyway: nbinom2 in glmmTMB (I've tested glmm.nb as well with the same kind of problematic results).
> 
>>From biological reasoning, the following model is the one I'd prefer. It uses Status, adjusted Year and log("normalized" area) as fixed effects and Site as random effect. For the avian biodiversity data, this model works technically fine. Biologically speaking, the later Status classes did not differ significantly from Before (the intercept). So far so good.
> 
> glmmTMB31B<-NA
> glmmTMB31B<-glmmTMB(response ~ Status + YearS + log(NArea) + (1|Site), data=ArterYears, family = nbinom2)
> summary(glmmTMB31B)
> AICc(glmmTMB31B)
> 
> Now I would like to evaluate this model, either against other models or with an R2 of some sort. Now problems pile up.
> 
> The "null" model (Site needs to be in the model because numbers really vary among sites, see: plot(ArterYears$ArterI ~ ArterYears$Site) )
> 
> glmmTMB0<-NA
> glmmTMB0<-glmmTMB(response ~ 1 + (1|Site), data=ArterYears, family = nbinom2)
> summary(glmmTMB0)
> AICc(glmmTMB0)
> 
> generates the following warning messages:
> 
> 
> 1: In fitTMB(TMBStruc) :
> 
>    Model convergence problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
> 
> 2: In fitTMB(TMBStruc) :
> 
>    Model convergence problem; false convergence (8). See vignette('troubleshooting')
> 
> Most other models including combinations of YearS, NArea and Status generate these warning messages (in particular the second one). This puzzles me, but unfortunately, I'm not capable of interpreting the troubleshooting messages. If the model without fixed effects had worked fine and the complex model had failed, I would suspect overparameterization (N = 156), but now I have no clue.
> 
> When I apply r.squaredGLMM (MuMIn) to the complex model, warning messages come up even here, despite the fact that they were not generated for the model as such. How should I interpret this?
> 
>> r.squaredGLMM(glmmTMB31B)
>                     R2m          R2c
> delta     1.112643e-18 2.247703e-18
> lognormal 4.805332e-04 9.707482e-04
> trigamma  6.896496e-35 1.393194e-34
> Warning messages:
> 1: 'r.squaredGLMM' now calculates a revised statistic. See the help page.
> 2: The null model is correct only if all variables used by the original model remain unchanged.
> 3: In fitTMB(TMBStruc) :
>    Model convergence problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
> 4: In fitTMB(TMBStruc) :
>    Model convergence problem; false convergence (8). See vignette('troubleshooting')
> 
> 
> I assume that I either make a fundamental mistake somewhere, or the data are "problematic". Could I solve all this by abandoning family = nbinom2 and go back to family = poisson (which worked fine technically)? Or test yet another package?
> Thanks in advance for any suggestions.
> 
> Cheers,
> Adriaan "Adjan" de Jong
> Senior researcher
> Swedish University of Agricultural Sciences
> 
> Data:
> Site                Year              Status            Areal             Arter
> Nyland          2002              Before           33.6               54
> Nyland          2003              Construction 33.6               51
> Nyland          2004              Construction 33.6               56
> Nyland          2005              Construction 33.6               52
> Nyland          2006              Ready           33.6               48
> Nyland          2007              Ready           33.6               43
> Nyland          2008              Ready           33.6               64
> Nyland          2009              Ready           33.6               58
> Nyland          2010              Ready           33.6               57
> Nyland          2013              Traffic           33.6               50
> Nyland          2014              Traffic           33.6               53
> Nyland          2015              Traffic           33.6               61
> Kornsjo          2002              Before           82.8               59
> Kornsjo          2003              Before           82.8               66
> Kornsjo          2004              Construction 82.8               62
> Kornsjo          2005              Construction 82.8               58
> Kornsjo          2006              Ready           82.8               60
> Kornsjo          2007              Ready           82.8               68
> Kornsjo          2008              Ready           82.8               70
> Kornsjo          2009              Ready           82.8               59
> Kornsjo          2010              Ready           82.8               62
> Kornsjo          2013              Traffic           82.8               57
> Kornsjo          2014              Traffic           82.8               58
> Kornsjo          2015              Traffic           82.8               63
> Stranne         2002              Construction 37.0               53
> Stranne         2003              Construction 37.0               64
> Stranne         2004              Ready           37.0               60
> Stranne         2005              Ready           37.0               60
> Stranne         2006              Ready           37.0               59
> Stranne         2007              Ready           37.0               60
> Stranne         2008              Ready           37.0               55
> Stranne         2009              Ready           37.0               53
> Stranne         2010              Ready           37.0               46
> Stranne         2013              Traffic           37.0               58
> Stranne         2014              Traffic           37.0               53
> Stranne         2015              Traffic           37.0               56
> Strandnyland 2002              Construction 69.2               43
> Strandnyland 2003              Construction 69.2               44
> Strandnyland 2004              Ready           69.2               52
> Strandnyland 2005              Ready           69.2               56
> Strandnyland 2006              Ready           69.2               46
> Strandnyland 2007              Ready           69.2               52
> Strandnyland 2008              Ready           69.2               48
> Strandnyland 2009              Ready           69.2               43
> Strandnyland 2010              Ready           69.2               55
> Strandnyland 2013              Traffic           69.2               38
> Strandnyland 2014              Traffic           69.2               41
> Strandnyland 2015              Traffic           69.2               46
> Hjalta             2002              Ready           91.1               61
> Hjalta             2003              Ready           91.1               61
> Hjalta             2004              Ready           91.1               62
> Hjalta             2005              Ready           91.1               61
> Hjalta             2006              Ready           91.1               66
> Hjalta             2007              Ready           91.1               71
> Hjalta             2008              Ready           91.1               73
> Hjalta             2009              Ready           91.1               58
> Hjalta             2010              Ready           91.1               64
> Hjalta             2013              Traffic           91.1               67
> Hjalta             2014              Traffic           91.1               71
> Hjalta             2015              Traffic           91.1               67
> Kasa              2002              Construction 98.3               65
> Kasa              2003              Ready           98.3               59
> Kasa              2004              Ready           98.3               59
> Kasa              2005              Ready           98.3               66
> Kasa              2006              Ready           98.3               52
> Kasa              2007              Ready           98.3               53
> Kasa              2008              Ready           98.3               56
> Kasa              2009              Ready           98.3               53
> Kasa              2010              Ready           98.3               51
> Kasa              2013              Traffic           98.3               51
> Kasa              2014              Traffic           98.3               54
> Kasa              2015              Traffic           98.3               64
> Ava               2002              Before           109.5             67
> Ava               2003              Before           109.5             79
> Ava               2004              Construction 109.5             70
> Ava               2005              Construction 109.5             77
> Ava               2006              Construction 109.5             76
> Ava               2007              Ready           109.5             80
> Ava               2008              Ready           109.5             77
> Ava               2009              Ready           109.5             81
> Ava               2010              Ready           109.5             83
> Ava               2013              Traffic           109.5             76
> Ava               2014              Traffic           109.5             81
> Ava               2015              Traffic           109.5             78
> Logdea          2002              Before           67.4               54
> Logdea          2003              Before           67.4               53
> Logdea          2004              Before           67.4               57
> Logdea          2005              Construction 67.4               55
> Logdea          2006              Construction 67.4               49
> Logdea          2007              Ready           67.4               61
> Logdea          2008              Ready           67.4               56
> Logdea          2009              Ready           67.4               56
> Logdea          2010              Ready           67.4               53
> Logdea          2013              Traffic           67.4               55
> Logdea          2014              Traffic           67.4               53
> Logdea          2015              Traffic           67.4               51
> Langed          2002              Before           34.2               49
> Langed          2003              Before           34.2               56
> Langed          2004              Before           34.2               51
> Langed          2005              Before           34.2               52
> Langed          2006              Construction 34.2               47
> Langed          2007              Ready           34.2               56
> Langed          2008              Ready           34.2               54
> Langed          2009              Ready           34.2               51
> Langed          2010              Ready           34.2               54
> Langed          2013              Traffic           34.2               57
> Langed          2014              Traffic           34.2               51
> Langed          2015              Traffic           34.2               50
> Hornea          2002              Before           48.9               48
> Hornea          2003              Before           48.9               49
> Hornea          2004              Before           48.9               41
> Hornea          2005              Before           48.9               37
> Hornea          2006              Construction 48.9               40
> Hornea          2007              Construction 48.9               48
> Hornea          2008              Ready           48.9               48
> Hornea          2009              Ready           48.9               39
> Hornea          2010              Ready           48.9               47
> Hornea          2013              Traffic           48.9               47
> Hornea          2014              Traffic           48.9               43
> Hornea          2015              Traffic           48.9               47
> Stocke          2002              Before           208.4             58
> Stocke          2003              Before           208.4             69
> Stocke          2004              Before           208.4             73
> Stocke          2005              Before           208.4             67
> Stocke          2006              Before           208.4             66
> Stocke          2007              Construction 208.4             71
> Stocke          2008              Construction 208.4             75
> Stocke          2009              Construction 208.4             60
> Stocke          2010              Ready           208.4             68
> Stocke          2013              Traffic           208.4             73
> Stocke          2014              Traffic           208.4             67
> Stocke          2015              Traffic           208.4             75
> StockeNE     2002              Before           33.9               34
> StockeNE     2003              Before           33.9               36
> StockeNE     2004              Before           33.9               32
> StockeNE     2005              Before           33.9               28
> StockeNE     2006              Before           33.9               35
> StockeNE     2007              Construction 33.9               43
> StockeNE     2008              Construction 33.9               41
> StockeNE     2009              Construction 33.9               34
> StockeNE     2010              Ready           33.9               34
> StockeNE     2013              Traffic           33.9               33
> StockeNE     2014              Traffic           33.9               32
> StockeNE     2015              Traffic           33.9               37
> Degernas      2002              Before           68.8               56
> Degernas      2003              Before           68.8               56
> Degernas      2004              Before           68.8               66
> Degernas      2005              Before           68.8               64
> Degernas      2006              Before           68.8               58
> Degernas      2007              Before           68.8               64
> Degernas      2008              Construction 68.8               62
> Degernas      2009              Construction 68.8               61
> Degernas      2010              Construction 68.8               68
> Degernas      2013              Traffic           68.8               69
> Degernas      2014              Traffic           68.8               57
> Degernas      2015              Traffic           68.8               70
> 
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-- 
Dimitris Rizopoulos
Professor of Biostatistics
Department of Biostatistics
Erasmus University Medical Center

Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands
Tel: +31/(0)10/7043478
Fax: +31/(0)10/7043014
Web (personal): http://www.drizopoulos.com/
Web (work): http://www.erasmusmc.nl/biostatistiek/
Blog: http://iprogn.blogspot.nl/


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