 Dear all, I try to consider overdispersion in a lmer model. But using
family=quasibinomial rather than family=binomial seems to change the fit but
not the result of an anova test. In addition if we specify test="F" as it is
recomanded for glm using quasibinomial, the test remains a Chisq test. Are
all tests scaled for dispersion, or none? Why is there a difference between
glm and lmer for this? And why summary does not test estimates only in the
quasibinomial case? Thank you.

Here is an simple example using a simulated dataset (with anova tests at the
end):

library(lme4)
Y1<-sample(c(rbinom(90,10,0.1),rbinom(90,10,0.7)))
Y2<-10-Y1
Y<-cbind(Y1,Y2)
Group<-c(rep("A",80),rep("B",50),rep("C",50))
Group<-as.factor(sample(Group))
X<-Y1*rnorm(180,mean=0,sd=10)

mod0<-lmer(Y~X+(1|Group),family=binomial) #model using binomial family
summary(mod0)

Generalized linear mixed model fit using Laplace
Formula: Y ~ X + (1 | Group)
Family: binomial(logit link)
AIC BIC logLik deviance
872.9 882.4 -433.4 866.9
Random effects:
Groups Name Variance Std.Dev.
Group (Intercept) 0.012863 0.11341
number of obs: 180, groups: Group, 3
Estimated scale (compare to 1 ) 2.025698
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.451023 0.082160 -5.490 4.03e-08 ***
X 0.002388 0.001092 2.187 0.0287 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
X -0.076

mod1<-lmer(Y~X+(1|Group),family=quasibinomial)    #model using quasibinomial
family
summary(mod1)
Generalized linear mixed model fit using Laplace
Formula: Y ~ X + (1 | Group)
Family: quasibinomial(logit link)
AIC BIC logLik deviance
872.9 882.4 -433.4 866.9
Random effects:
Groups Name Variance Std.Dev.
Group (Intercept) 0.052785 0.22975
Residual 4.103452 2.02570
number of obs: 180, groups: Group, 3
Fixed effects:
Estimate Std. Error t value
(Intercept) -0.451020 0.166434 -2.710
X 0.002389 0.002212 1.080
Correlation of Fixed Effects:
(Intr)
X -0.076

mod0ML<-lmer(Y~X+(1|Group),family=binomial,type="ML")
mod0NULLML<-lmer(Y~1+(1|Group),family=binomial,type="ML")
anova(mod0ML,mod0NULLML)

mod0NULLML: Y ~ 1 + (1 | Group)
mod0ML: Y ~ X + (1 | Group)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
mod0NULLML 2 875.68 882.07 -435.84
mod0ML 3 872.85 882.43 -433.43 4.8307 1 0.02796 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

mod1ML<-lmer(Y~X+(1|Group),family=quasibinomial,type="ML")
mod1NULLML<-lmer(Y~1+(1|Group),family=quasibinomial,type="ML")
anova(mod1ML,mod1NULLML,test="F")

mod1NULLML: Y ~ 1 + (1 | Group)
mod1ML: Y ~ X + (1 | Group)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)        # F test does not occur!!!
mod1NULLML 2 875.68 882.07 -435.84
mod1ML 3 872.85 882.43 -433.43 4.8307 1 0.02796 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

	[[alternative HTML version deleted]]

