Hi Duncan: I don't know if the following can help but I checked the code and logLik defines the log likelihood as (p - glmobject$aic/2) where p is the glmobject$rank. So, the reason for the likelihood being less is that, in the null, it ends up being ( 1 - glmobject$aic/2) and in the other one it ends up being ( 2 - glmobject$aic/2).
so 2 - 764.4/2 = -380.2 and 1 - 761.9/2 = -379.95 ( close enough for govt work ) So, that's where the #'s are coming from but it really depends on how AIC is defined. Likelihoods should not involve degrees of freedom ( atleast not where they make likelihood less like in the above example ) so maybe backing the likelihood out using AIC is the issue ? ( AIC = -2 * likelihood + 2p so p - AIC/2 = likelihood). AIC is a function of the likelihood but , as far as I know, likelihood is not a function of the AIC. Thanks for any insight. On Thu, May 31, 2012 at 9:26 AM, Duncan Murdoch <murdoch.dun...@gmail.com>wrote: > 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 >> >> [[alternative HTML version deleted]] >> >> ______________________________**________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/**listinfo/r-help<https://stat.ethz.ch/mailman/listinfo/r-help> >> PLEASE do read the posting guide http://www.R-project.org/** >> posting-guide.html <http://www.R-project.org/posting-guide.html> >> and provide commented, minimal, self-contained, reproducible code. >> > > ______________________________**________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/**listinfo/r-help<https://stat.ethz.ch/mailman/listinfo/r-help> > PLEASE do read the posting guide http://www.R-project.org/** > posting-guide.html <http://www.R-project.org/posting-guide.html> > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
