anova on binomial LMER objects
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