[R-sig-ME] change in variance components depending on scaling of fixed effects

[Ken Beath]

On 18/10/2007, at 6:53 PM, Arild Husby wrote:

> Dear all,
>
> I am trying to understand the output from a binomial lmer object  
> and why
> the scaling of a fixed effect changes the variance components.
>
> In the model p2rec is cbind(number recruits2,number recruits 1),  
> Pop is
> populations (five level factor) and ja is year (continous covariate
> running from 1955-2004). I've used the Laplace optimization method,  
> due
> to earlier reports of unstability of PQL when running binomial models.
>

This could be due to numerical problems, which are fixed by the  
centring. This sort of problem depends a lot on starting values.   
Another possibility is that the Laplace approximation is breaking  
down, which leads to similar numerical problems.  You haven't  
described the data, other than it is binomial but if the counts per  
observation is small, then there will be problems, especially  
considering there are 1323 in only 1088  groups. Unfortunately the  
AGQ is not implemented, as this is a better approximation. Trying  
with Stata would be worthwhile, either gllamm or xtlogit should work.

Ken



> First example: (ja continous covariate, range: 1955-2004)
>
>> totmod2 <- lmer(p2rec~Pop*ja + (1|VROUW)+(1|ja), data=dltab2,
> family=binomial, method="Laplace", na.action=na.omit)
>> summary(totmod2)
> Generalized linear mixed model fit using Laplace
> Formula: p2rec ~ Pop * ja + (1 | VROUW) + (1 | ja)
>  Data: dltab2
> Family: binomial(logit link)
>  AIC   BIC logLik deviance
> 12456 12519  -6216    12432
> Random effects:
> Groups Name        Variance Std.Dev.
> VROUW  (Intercept) 2.19300  1.48088
> ja     (Intercept) 0.09675  0.31105
> number of obs: 1323, groups: VROUW, 1088; ja, 48
>
> Estimated scale (compare to  1 )  22.97855
>
>
> I then scale  ja so that:  dltab2$ja<-scale(dltab2$ja, scale=FALSE)
>
>> totmod2 <- lmer(p2rec~Pop*ja + (1|VROUW)+(1|ja), data=dltab2,
> family=binomial, method="Laplace", na.action=na.omit)
>> summary(totmod2)
> Generalized linear mixed model fit using Laplace
> Formula: p2rec ~ Pop * ja + (1 | VROUW) + (1 | ja)
>  Data: dltab2
> Family: binomial(logit link)
>  AIC  BIC logLik deviance
> 983.8 1046 -479.9    959.8
> Random effects:
> Groups Name        Variance Std.Dev.
> VROUW  (Intercept) 0.54162  0.73595
> ja     (Intercept) 0.29192  0.54029
> number of obs: 1323, groups: VROUW, 1088; ja, 48
>
> Estimated scale (compare to  1 )  0.7061424
>
>
> Different scaling:  dltab2$ja<-scale(dltab2$ja, center=1000,  
> scale=FALSE)
>
>> totmod2 <- lmer(p2rec~Pop*ja + (1|VROUW)+(1|ja), data=dltab2,
> family=binomial, method="Laplace", na.action=na.omit)
>> summary(totmod2)
> Generalized linear mixed model fit using Laplace
> Formula: p2rec ~ Pop * ja + (1 | VROUW) + (1 | ja)
>  Data: dltab2
> Family: binomial(logit link)
> AIC  BIC logLik deviance
> 7136 7198  -3556     7112
> Random effects:
> Groups Name        Variance Std.Dev.
> VROUW  (Intercept) 2.19300  1.48088
> ja     (Intercept) 0.09675  0.31105
> number of obs: 1323, groups: VROUW, 1088; ja, 48
>
> Estimated scale (compare to  1 )  3.083302
>
>
> Estimates of fixed effects changes as one would expect (so have not
> printed them here), but I do not understand why there is such a  
> massive
> difference in the variance components.
>
> Note that the first and last example has the same estimates of  
> variance
> components, but that the estimated scale is massively different.
>
> All help is highly appreciated.
>
>
> (See also a posting by Steven Orzack on a similar problem:
> http://tolstoy.newcastle.edu.au/R/e2/help/07/07/22076.html)
>
>
> All help is highly appreciated.
>
> Thanks very much,
>
> Arild Husby
>
>> sessionInfo()
> R version 2.5.0 (2007-04-23)
> i386-pc-mingw32
>
> locale:
> LC_COLLATE=English_United Kingdom.1252;LC_CTYPE=English_United
> Kingdom.1252;LC_MONETARY=English_United
> Kingdom.1252;LC_NUMERIC=C;LC_TIME=English_United Kingdom.1252
>
> attached base packages:
> [1] "stats"     "graphics"  "grDevices" "utils"     "datasets"
> "methods"   "base"
> other attached packages:
>      lme4      Matrix     lattice
> "0.99875-2" "0.99875-2"   "0.15-11"
>
>
>
> -- 
> Arild Husby
> Institute of Evolutionary Biology
> Room 413, Ashworth Labs,
> King's Buildings,
> University of Edinburgh
> EH9 3JT, UK
>
> E-mail: arild.husby at ed.ac.uk
> web: http://homepages.ed.ac.uk/loeske/arild.html
> Tel: +44 (0)131 650 5990
> Mob: +44 (0)798 275 0668
>
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