Computation of AIC and AIC with weights

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In accordance with Venables and Ripley, SAS documentation and other
sources AIC with sigma^2 unknown is calculated as:
AIC = -2LL + 2* #parameters = n log(RSS/n) + 2p
For the fitness data: (http://support.sas.com/ctx/samples/index.jsp?
sid=927), SAS gets an AIC of 64.534 with model oxygen = runtime. (SAS
STAT User's Guide. Chapter 61. pp 3956, the REG Procedure). This value
of AIC accords with n log(RSS/n) + 2p and p = 2.

When I run the same problem in R ver 2.5.1, I get

rt.glm =glm(oxy ~ runtime, data=fitness)
rt.glm
Call: glm(formula = oxy ~ runtime, data = fitness)

Coefficients:
(Intercept) runtime
82.422 -3.311

Degrees of Freedom: 30 Total (i.e. Null); 29 Residual
Null Deviance: 851.4
Residual Deviance: 218.5 AIC: 154.5

I get very close to what R gets if the constant term is included in
-2LL, (31*Log(2*pi)+n-1), divide RSS by n-1 and the number of
parameters is 3 (the predictor, the intercept and the error term)
31 * (log(2*pi)+log(sum(rt.glm$res^2)/30)) + 30 + 2 * 3
[1] 154.5248
AIC(rt.glm)
[1] 154.5083

3 questions:
1) Why the discrepancy between SAS and R?
2) Why the slight difference between my calculation in R and R's AIC?
3) How should AIC be computed if row weights are used in the linear
model?

Thanks!

-joe yarmus

.

Relevant Pages

  • Re: Computation of AIC and AIC with weights
    ... In accordance with Venables and Ripley, SAS documentation and other ... Why the slight difference between my calculation in R and R's AIC? ... -joe yarmus ... represented by the constant + 2) and the unknown ...
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