[R] glm: quasi models with logit link function and binary data

[Hong Ooi]

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This would be because quasi(link=logit) doesn't actually fit a logistic regression. The default variance function for quasi is the identity, not binomial variance. To emulate a logistic regression, use var="mu(1-mu)" in addition to link=logit.


> y <- runif(100)
> glm(y ~ 1, family=binomial)

Call:  glm(formula = y ~ 1, family = binomial) 

Coefficients:
(Intercept)  
   -0.01208  

Degrees of Freedom: 99 Total (i.e. Null);  99 Residual
Null Deviance:      37.15 
Residual Deviance: 37.15        AIC: 140.6 
Warning message:
non-integer #successes in a binomial glm! in: eval(expr, envir, enclos)


> glm(y ~ 1, family=quasi(var="mu(1-mu)", link=logit))

Call:  glm(formula = y ~ 1, family = quasi(var = "mu(1-mu)", link = logit)) 

Coefficients:
(Intercept)  
   -0.01208  

Degrees of Freedom: 99 Total (i.e. Null);  99 Residual
Null Deviance:      37.15 
Residual Deviance: 37.15        AIC: NA


-- 
Hong Ooi
Senior Research Analyst, IAG Limited
388 George St, Sydney NSW 2000
(02) 9292 1566

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Björn Stollenwerk
Sent: Monday, 28 November 2005 10:18 PM
To: R-help at stat.math.ethz.ch
Subject: [R] glm: quasi models with logit link function and binary data


# Hello R Users,
#
# I would like to fit a glm model with quasi family and
# logistical link function, but this does not seam to work
# with binary data.
#
# Please don't suggest to use the quasibinomial family. This
# works out, but when applied to the true data, the
# variance function does not seams to be
# appropriate.
#
# I couldn't see in the
# theory why this does not work.
# Is this a bug, or are there theoretical reasons?
# One problem might be, that logit(0)=-Inf and logit(1)=Inf.
# But I can't see how this disturbes the calculation of quasi-Likelihood.
#
# Thank you very much,
# best,
#
# Björn

set.seed(0)
y <- sample(c(0,1), size=100, replace=T)

# the following models work:
glm(y ~ 1)
glm(y ~ 1, family=binomial(link=logit))
glm(y ~ 1, family=quasibinomial(link=logit))

# the next model doesn't work:
glm(y ~ 1, family=quasi(link=logit))

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