# [R] glm null deviance

yudi@hermes.ucd.ie yudi at hermes.ucd.ie
Wed Feb 3 09:39:56 CET 1999

```> Date:          Wed, 03 Feb 1999 08:47:55 +0100 (MET)
> From:          Jim Lindsey <jlindsey at alpha.luc.ac.be>

> > Before some people think this is a bug, there is nothing
> > pathological or undesirable in Jim's examples. First,
>
> pathological no, undesirable yes. a null deviance is generally
> meaningless. The important thing is the minimal model in a given
> context and software cannot detect that as it depends on the question

A change in deviance is typically meaningful, so in general we want the
null deviance too. In the following example:
> y_ rbinom(20,1,.8)
> sum(y)
[1] 15
> ind_ rep(1,20)
> glm(y~ind-1,family=binomial)

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

Coefficients:
ind
1.099

Degrees of Freedom: 20 Total (i.e. Null);  19 Residual
Null Deviance:      27.73
Residual Deviance: 22.49        AIC: 24.49
> 1-pchisq(27.73-22.49,1)   # testing H_0: logit p=0 or p=0.5
[1] 0.02207327             # it'd be annoying to know null-deviance

> dbinom(15,20,.5) + 2*sum(dbinom(16:20,20,.5))
[1] 0.0266037           # mid-p value is closest to chi^2-based p-val.
> binom.test(15,20,.5)
number of successes = 15, number of trials = 20, p-value = 0.04139
# this is 'exact' 2-sided p-value, it's
# not necessarily 'better' than mid-p value above.

I know Jim knows all this stuff inside out, so maybe there is
some miscommunication here.

-Yudi-

------------------------------
Yudi Pawitan: yudi at ucd.ie
Department of Statistics, UCD
Dublin 4, Ireland
Ph : 353-1-706 7641
Fax: 353-1-706 1186
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