[R] change of variance components depending on scaling of fixed effects

[Arild Husby]

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 (covariate running from 
1955-2004). I.e. biologically I am interested to see how the proportion 
of recruits from the second clutch has changed over time between the 
different populations. I've used the Laplace optimization method, due to 
earlier reports of unstability of PQL when running binomial models.

First example: (ja 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.

Thanks very much,

Arild

-- 
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