Two related questions.

First, I am fitting a model with a single predictor, and then a null model
with only the intercept.  In theory, the fitted model should have a higher
log-likelihood than the null model, but that does not happen.  See the
output below.  My first question is, how can this happen?

> m

Call:  glm(formula = school ~ sv_conform, family = binomial, data = dat,
    weights = weight)

Coefficients:
(Intercept)   sv_conform
    -2.5430       0.2122

Degrees of Freedom: 1488 Total (i.e. Null);  1487 Residual
Null Deviance:    786.1
Residual Deviance: 781.9 AIC: 764.4
> null

Call:  glm(formula = school ~ 1, family = binomial, data = dat, weights =
weight)

Coefficients:
(Intercept)
     -2.532

Degrees of Freedom: 1488 Total (i.e. Null);  1488 Residual
Null Deviance:    786.1
Residual Deviance: 786.1 AIC: 761.9
> logLik(m); logLik(null)
'log Lik.' -380.1908 (df=2)
'log Lik.' -379.9327 (df=1)
>

My second question grows out of the first.  I ran the same two model on the
same data in Stata and got identical coefficients.  However, the
log-likelihoods were different than the one's I got in R, and followed my
expectations - that is, the null model has a lower log-likelihood than the
fitted model.  See the Stata model comparison below.  So my question is,
why do identical models fit in R and Stata have different log-likelihoods?
-----------------------------------------------------------------------------
       Model |    Obs    ll(null)        ll(model)     df          AIC
    BIC
-------------+---------------------------------------------------------------
        mod1 |   1489    -393.064   -390.9304     2    785.8608    796.4725
        null |      1489    -393.064   -393.064      1     788.1279
 793.4338

Thanks in advance for any input or references.

Andrew Miles

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