# [R] glmer with non integer weights

Emmanuel Charpentier charpent at bacbuc.dyndns.org
Sun Apr 18 19:36:16 CEST 2010

```Addendum to my previous answer :

In that special case, the limited range of the asin(sqrt())
transformation, which is a shortcoming, turns out to be useful. The
fixed-effect doefficients seem semi-reasonable (except for stageB) :

> (sin(coef(lm(asin(sqrt(MH.Index))~0+stage, data=similarity))))^2
stageA    stageB    stageC    stageD
0.6164870 0.3389430 0.5083574 0.5672021

The random effects being nested in the fixed efect, one can't afford to
be lazy in the parametrization of the corresponding random effect :

> summary(lmer(asin(sqrt(MH.Index))~stage+(stage|site),
data=similarity))
Linear mixed model fit by REML
Formula: asin(sqrt(MH.Index)) ~ stage + (stage | site)
Data: similarity
AIC BIC logLik deviance REMLdev
155.3 199 -62.65    111.8   125.3
Random effects:
Groups   Name        Variance Std.Dev. Corr
site     (Intercept) 0.043579 0.20876
stageB      0.033423 0.18282  -0.999
stageC      0.043580 0.20876  -1.000  0.999
stageD      0.043575 0.20875  -1.000  0.999  1.000
Residual             0.128403 0.35833
Number of obs: 136, groups: site, 39

Fixed effects:
Estimate Std. Error t value
(Intercept)  0.93036    0.08431  11.035
stageB      -0.30879    0.10079  -3.064
stageC      -0.13660    0.09981  -1.369
stageD      -0.07755    0.14620  -0.530

Correlation of Fixed Effects:
(Intr) stageB stageC
stageB -0.836
stageC -0.845  0.707
stageD -0.577  0.482  0.487
> v<-fixef(lmer(asin(sqrt(MH.Index))~stage+(stage|site),
data=similarity))
> v[2:4]<-v[1]+v[2:4]
> names(v)[1]<-"stageA"
> (sin(v))^2
stageA    stageB    stageC    stageD
0.6429384 0.3390903 0.5083574 0.5672021

But again, we're exploiting a shortcoming of the asin(sqrt())
transformation.

HTH,

Emmanuel Charpentier

Le vendredi 16 avril 2010 à 00:15 -0800, Kay Cichini a écrit :
> thanks thierry,
>
> i considered this transformations already, but variance is not stabilized
> and/or normality is neither achieved.
> i guess i'll have to look out for non-parametrics?
>
> best regards,
> kay

```