[R] anova on binomial LMER objects

[Robert Bagchi]

Dear R users,

I have been having problems getting believable estimates from anova on a 
model fit from lmer. I get the impression that F is being greatly 
underestimated, as can be seen by running the example I have given below.

First an explanation of what I'm trying to do. I am trying to fit a glmm 
with binomial errors to some data. The experiment involves 10 
shadehouses, divided between 2 light treatments (high, low). Within each 
shadehouse there are 12 seedlings of each of 2 species (hn & sl). 3 
damage treatments (0, 0.1, 0.25 leaf area removal) were applied to the 
seedlings (at random) so that there are 4 seedlings of each 
species*damage treatment in each shadehouse.  There maybe a shadehouse 
effect, so I need to include it as a random effect. Light is applied to 
a shadehouse, so it is outer to shadehouse. The other 2 factors are 
inner to shadehouse.

We want to assess if light, damage and species affect survival of 
seedlings. To test this I fitted a binomial mixed effects model with 
lmer (actually with quasibinomial errors). THe summary function suggests 
a large effect of both light and species (which agrees with graphical 
analysis). However, anova produces F values close to 0 and p values 
close to 1 (see example below).

Is this a bug, or am I doing something fundamentally wrong? If anova 
doesn't work with lmer is there a way to perform hypothesis tests on 
fixed effects in an lmer model? I was going to just delete terms and 
then do liklihood ratio tests, but according to Pinheiro & Bates (p. 87) 
that's very untrustworthy. Any suggestions?

I'm using R 2.1.1 on windows XP and lme4 0.98-1

Any help will be much appreciated.

many thanks
Robert

###############################
The data are somewhat like this

#setting up the dataframe

bm.surv<-data.frame(
                    house=rep(1:10, each=6),
                    light=rep(c("h", "l"), each=6, 5),
                    species=rep(c("sl", "hn"), each=3, 10),
                    damage=rep(c(0,.1,.25), 20)
                    )

bm.surv$survival<-ifelse(bm.surv$light=="h", rbinom(60, 4, .9), 
rbinom(60, 4, .6))       # difference in probablility should ensure a 
light effect
bm.surv$death<-4-bm.surv$survival

# fitting the model
m1<-lmer(cbind(survival, death)~light+species+damage+(1|house), 
data=bm.surv, family="quasibinomial")

summary(m1)         # suggests that light is very significant
Generalized linear mixed model fit using PQL
Formula: cbind(survival, death) ~ light + species + damage + (1 | table)
   Data: bm.surv
 Family: quasibinomial(logit link)
      AIC      BIC    logLik deviance
 227.0558 239.6218 -107.5279 215.0558
Random effects:
 Groups   Name        Variance   Std.Dev. 
 table    (Intercept) 1.8158e-09 4.2613e-05
 Residual             3.6317e+00 1.9057e+00
# of obs: 60, groups: table, 10

Fixed effects:
            Estimate Std. Error DF t value  Pr(>|t|)   
(Intercept)  2.35140    0.36832 56  6.3841 3.581e-08 ***
lightl      -1.71517    0.33281 56 -5.1535 3.447e-06 ***
speciessl   -0.57418    0.30085 56 -1.9085   0.06145 . 
damage       1.49963    1.46596 56  1.0230   0.31072   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
          (Intr) lightl spcssl
lightl    -0.665             
speciessl -0.494  0.070      
damage    -0.407 -0.038 -0.017


anova(m1)             # very low F value for light, corresponding to p 
values approaching 1

Analysis of Variance Table
        Df Sum Sq Mean Sq  Denom F value Pr(>F)
light    1  0.014   0.014 56.000  0.0018 0.9661
species  1  0.002   0.002 56.000  0.0002 0.9887
damage   1  0.011   0.011 56.000  0.0014 0.9704


-- 
Robert Bagchi
Animal & Plant Science
Alfred Denny Building
University of Sheffield
Western Bank
Sheffield S10 2TN
UK

t: +44 (0)114 2220062
e: r.bagchi at sheffield.ac.uk
   bagchi.r at gmail.com

http://www.shef.ac.uk/aps/apsrtp/bagchi-r