On 12-05-31 8:53 AM, Andrew Miles wrote:
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?
I suspect you'll need to give sample data before anyone can really help
with this.
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?
That's easier: they use different base measures. The likelihood is
only defined up to a multiplicative constant, so the log likelihoods can
have an arbitrary constant added to them and still be valid. But I
would have expected both models to use the same base measure, so the
differences in log-likelihood should match.
Duncan Murdoch
-----------------------------------------------------------------------------
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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