- Dear all,

>The algebraic expression for the AIC results from the bias in the maximum

Please, let me know. I'm interested in the AIC.

>log-likelihood of a model as estimator of the mean expected log-likelihood,

>this bias being a function of the number of free parameters in the model.

>So it only covers those models fitted by maximum likelihood.

If I have 3 models each one fitted with a least square method, are them

suitable for AIC application?

Are their SSRs the correct ones to use in the AIC?

Many thanks to all

Claudio Cocheo

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* Support to the list is provided at http://www.ai-geostats.org - suspect Ruben would note that, under a normal assumption, OLS and ML

coincide. also, I suspect that Ruben's comments also apply to REML

results--altho in that case you may need to restrict inference to random

components. brian

****************************************************************

Brian Gray

USGS Upper Midwest Environmental Sciences Center

575 Lester Avenue, Onalaska, WI 54650

ph 608-783-7550 ext 19, FAX 608-783-8058

brgray@...

*****************************************************************

"Ruben Roa"

<rroa@...> To: vanessa stelzenmüller <vstelzenmueller@...>

Sent by: cc: ai-geostats@...

ai-geostats-list@ Subject: Re: AI-GEOSTATS: Akaike's information criterion (AIC)

unil.ch

12/18/2002 10:26

AM

Please respond to

"Ruben Roa"

>Dear all,

Yes. The model must be fitted my maximum likelihood.

>

>The AIC is used to select the "best" model from a list

>of theoretical functions. I wonder if its necessary

>the models need to be fitted by the same method ?

>Would it be possible to stress the AIC to select the

The algebraic expression for the AIC results from the bias in the maximum

>"best" model from models which were fitted for example

>by OLS,WLS, REML etc. This means to use AIC to choose

>the model and the fitting method ?

log-likelihood of a model as estimator of the mean expected log-likelihood,

this bias being a function of the number of free parameters in the model.

So it only covers those models fitted by maximum likelihood.

Rubén

http://webmail.udec.cl

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* Support to the list is provided at http://www.ai-geostats.org >suspect Ruben would note that, under a normal assumption, OLS and ML

coincide.

True, though i'd say that OLS is a particular case of MLE iff the process

being modelled is additive and the additive stochastic component is normal.

>also, I suspect that Ruben's comments also apply to REML

components. brian

>results--altho in that case you may need to restrict inference to random

There are so many acronyms that i got lost with REML. Is it Random Effects

etc...?

Rubén

http://webmail.udec.cl

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* Support to the list is provided at http://www.ai-geostats.org>>The algebraic expression for the AIC results from the bias in the maximum

log-likelihood of a model as estimator of the mean expected log-likelihood,

this bias being a function of the number of free parameters in the model.

So it only covers those models fitted by maximum likelihood.>

Check out 'Akaike Information Criterion Statistics', 1986, by Sakamoto,

>Please, let me know. I'm interested in the AIC.

Ishiguro, and Kitagawa (who are working associates to Akaike himself). KTK

Scientific Publishers, Tokyo. There is an English translation distributed

by Kluwer.

>If I have 3 models each one fitted with a least square method, are them

suitable for AIC application?

Yes if the models have different number of free parameters, they have an

additive stochastic component, and this component distributes normally.

>Are their SSRs the correct ones to use in the AIC?

Not quite. Compute the log likelihood under the normal assumption for each

model and use that in the AIC. If both the mean and variance of the normal

stochastic component are unknown, the log likelihood is

L(mu,sigma^2)=

-(n/2)ln(2*pi*sigma^2)-(1/2sigma^2)SUM_n(x_i-mu)^2

By taking the partial derivative of the log likelihood with respect to mu

and sigma^2, making it zero, solving for the MLE of mu and sigma^2, and

replacing these solutions into L, you get the maximum log likelihood of

each model,

L(mu_hat,sigma^2_hat)=-(n/2)ln(2*pi*sigma^2_hat)-n/2

=-(n/2)ln[(2*pi/n)SUM_n(x_i-mu_hat)^2]-n/2

Note that mu_hat would be each one of your models.

Cheers

Rubén

http://webmail.udec.cl

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* Support to the list is provided at http://www.ai-geostats.org- REML = variously, restricted or residual ML. the kicker is that, under

REML, a function of the outcomes are estimated, such that the function

contains none of the fixed effects present/suspected in the original

outcomes. brian

****************************************************************

Brian Gray

USGS Upper Midwest Environmental Sciences Center

575 Lester Avenue, Onalaska, WI 54650

ph 608-783-7550 ext 19, FAX 608-783-8058

brgray@...

*****************************************************************

"Ruben Roa"

<rroa@...> To: "Brian R Gray" <brgray@...>

Sent by: cc: ai-geostats@...

rroa@... Subject: Re: AI-GEOSTATS: Akaike's information criterion (AIC)

12/18/2002 12:45

PM

Please respond to

rroa

>suspect Ruben would note that, under a normal assumption, OLS and ML

coincide.

True, though i'd say that OLS is a particular case of MLE iff the process

being modelled is additive and the additive stochastic component is normal.

>also, I suspect that Ruben's comments also apply to REML

components. brian

>results--altho in that case you may need to restrict inference to random

There are so many acronyms that i got lost with REML. Is it Random Effects

etc...?

Rubén

http://webmail.udec.cl

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