Loading ...
Sorry, an error occurred while loading the content.

AI-GEOSTATS: Akaike's information criterion (AIC)

Expand Messages
  • vanessa stelzenmüller
    Dear all, 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
    Message 1 of 7 , Dec 18, 2002
    • 0 Attachment
      Dear all,

      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
      "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 ?

      Best wishes
      Vanessa

      __________________________________________________________________

      Gesendet von Yahoo! Mail - http://mail.yahoo.de
      Weihnachts-Einkäufe ohne Stress! http://shopping.yahoo.de

      --
      * To post a message to the list, send it to ai-geostats@...
      * As a general service to the users, please remember to post a summary of any useful responses to your questions.
      * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
      * Support to the list is provided at http://www.ai-geostats.org
    • Claudio Cocheo
      Dear all, ... Please, let me know. I m interested in the AIC. If I have 3 models each one fitted with a least square method, are them suitable for AIC
      Message 2 of 7 , Dec 18, 2002
      • 0 Attachment
        Dear all,

        >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.

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


        --
        * To post a message to the list, send it to ai-geostats@...
        * As a general service to the users, please remember to post a summary of any useful responses to your questions.
        * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
        * Support to the list is provided at http://www.ai-geostats.org
      • Brian R Gray
        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
        Message 3 of 7 , Dec 18, 2002
        • 0 Attachment
          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,
          >
          >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 ?

          Yes. The model must be fitted my maximum likelihood.

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

          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.

          Rubén
          http://webmail.udec.cl

          --
          * To post a message to the list, send it to ai-geostats@...
          * As a general service to the users, please remember to post a summary of
          any useful responses to your questions.
          * To unsubscribe, send an email to majordomo@... with no subject and
          "unsubscribe ai-geostats" followed by "end" on the next line in the message
          body. DO NOT SEND Subscribe/Unsubscribe requests to the list
          * Support to the list is provided at http://www.ai-geostats.org






          --
          * To post a message to the list, send it to ai-geostats@...
          * As a general service to the users, please remember to post a summary of any useful responses to your questions.
          * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
          * Support to the list is provided at http://www.ai-geostats.org
        • Ruben Roa
          ... 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
          Message 4 of 7 , Dec 18, 2002
          • 0 Attachment
            >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
            >results--altho in that case you may need to restrict inference to random
            components. brian

            There are so many acronyms that i got lost with REML. Is it Random Effects
            etc...?
            Rubén
            http://webmail.udec.cl

            --
            * To post a message to the list, send it to ai-geostats@...
            * As a general service to the users, please remember to post a summary of any useful responses to your questions.
            * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
            * Support to the list is provided at http://www.ai-geostats.org
          • Ruben Roa
            ... 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
            Message 5 of 7 , Dec 18, 2002
            • 0 Attachment
              >>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.
              >
              >Please, let me know. I'm interested in the AIC.

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

              --
              * To post a message to the list, send it to ai-geostats@...
              * As a general service to the users, please remember to post a summary of any useful responses to your questions.
              * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
              * Support to the list is provided at http://www.ai-geostats.org
            • Brian R Gray
              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
              Message 6 of 7 , Dec 18, 2002
              • 0 Attachment
                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
                >results--altho in that case you may need to restrict inference to random
                components. brian

                There are so many acronyms that i got lost with REML. Is it Random Effects
                etc...?
                Rubén
                http://webmail.udec.cl






                --
                * To post a message to the list, send it to ai-geostats@...
                * As a general service to the users, please remember to post a summary of any useful responses to your questions.
                * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
                * Support to the list is provided at http://www.ai-geostats.org
              Your message has been successfully submitted and would be delivered to recipients shortly.