[R] anova on binomial LMER objects

[Spencer Graves]

	  I agree:  Something looks strange to me in this example also;  I have 
therefore copied Douglas Bates and  Deepayan Sarkar.  You've provided a 
nice simulation.  If either of them have time to look at this, I think 
they could tell us what is happening here.

	  If you need an answer to your particular problem, you could run that 
simulation 1000 or 1,000 times.  That would tell you whether to believe 
the summary or the anova, or neither.  If you want to understand the 
algorithm, you could walk through the code.  However, "lmer" is a 
generic, and I don't have time now to figure out how to find the source. 
  A response from Brian Ripley to a question from me a couple of days 
ago provides a nice summary of how to do that, but I don't have time to 
check that now.

	  Sorry I couldn't help more.
	  spencer graves

Robert Bagchi wrote:

> 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
> 
> 

-- 
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
333 West San Carlos Street Suite 700
San Jose, CA 95110, USA

spencer.graves at pdf.com
www.pdf.com <http://www.pdf.com>
Tel:  408-938-4420
Fax: 408-280-7915