Dear list members,
I posted the question below a few weeks ago on this list and didn't receive
any answers (but an email from one other person showing interest in an
answer). I was wondering whether this was because of summertime or my poor
phrasing of the question or did I really land somewhere outside the area of
expertise of this enlightened and helpful group of people? If the latter was
true, could you maybe suggest colleagues who might be able to help?
Thank you.
Volker Bahn
Old question:
I'm running spatial linear models (slm) of the CAR family in Splus 6.1 on a
7.2 RedHat Linux machine (but the same effect described below is true for my
Splus 6.1 Windows Version running on a XP machine).
I want to compare the slm model to a similar lm model by AIC and use the
log-likelihood to calculate the AIC. However, the loglik given for the slm
model by Splus does not seem to be correct to me. Two observations lead me
to this conclusion:
1) If I calculate loglik myself based on the residual standard error (RSE)
with a formula from Burnham and Anderson (2002) I get a value completely
different from Splus:
Loglik = (-n / 2) * LN(RSE^2 * df / n) - (n / 2) * LN(2*PI()) - (n / 2)
With
RSE = residual standard error (in output)
df = degrees of freedom on the RSE
n = sample size
2) If I base AIC comparisons on the loglik value given by Splus they don't
make sense, whereas when I base them on my own values (see above) they are
very reasonable (the slm models almost always outperform the equivalent lm
models by a reasonable margin). Also when I calculate Rsquared for the slm
with the following formula (from Lichstein et al. 2002) it turns out
reasonable with my loglik calculation but not with the Splus loglik:
R2 = 1 - exp[-2(lA - l0)/n]
where
n = sample size
lA = log-likelihood of the model
and l0 = log-likelihood of a null model that only contains the intercept
Can anyone help me on this issue? Am I missing or misunderstanding
something?
Thanks
Volker
Literature cited
Burnham, K. P., and D. R. Anderson 2002. Model selection and multimodel
inference : a practical information-theoretic approach. Springer, New York.
Lichstein, J. W., T. R. Simons, S. A. Shriner, and K. E. Franzreb. 2002.
Spatial autocorrelation and autoregressive models in ecology. Ecological
Monographs 72:445-463.
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