3D plot of Akaike Information Criterion (AIC) for suitable ranges of Lˆ and k












3












$begingroup$


Giving that Akaike Information Criterion (AIC) is as follow:



enter image description here



How can I Produce a 3D plot of AIC for suitable ranges of Lˆ and k.



In other words what could be a suitable ranges of L to try?



Moreover, what is the function of L^? I am struggling to find the equation to represent L^ so that I can plot it.



Thanks.






data-visualization model aic bic







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    3












    $begingroup$


    Giving that Akaike Information Criterion (AIC) is as follow:



    enter image description here



    How can I Produce a 3D plot of AIC for suitable ranges of Lˆ and k.



    In other words what could be a suitable ranges of L to try?



    Moreover, what is the function of L^? I am struggling to find the equation to represent L^ so that I can plot it.



    Thanks.






    data-visualization model aic bic







    share|cite|improve this question









    New contributor




    Jan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      3












      3








      3





      $begingroup$


      Giving that Akaike Information Criterion (AIC) is as follow:



      enter image description here



      How can I Produce a 3D plot of AIC for suitable ranges of Lˆ and k.



      In other words what could be a suitable ranges of L to try?



      Moreover, what is the function of L^? I am struggling to find the equation to represent L^ so that I can plot it.



      Thanks.






      data-visualization model aic bic







      share|cite|improve this question









      New contributor




      Jan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      Giving that Akaike Information Criterion (AIC) is as follow:



      enter image description here



      How can I Produce a 3D plot of AIC for suitable ranges of Lˆ and k.



      In other words what could be a suitable ranges of L to try?



      Moreover, what is the function of L^? I am struggling to find the equation to represent L^ so that I can plot it.



      Thanks.






      data-visualization model aic bic




      data-visualization model aic bic






      share|cite|improve this question









      New contributor




      Jan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      Jan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question








      edited 5 hours ago







      Jan













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      asked 5 hours ago









      JanJan

      1464




      1464




      New contributor




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      Jan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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          2 Answers
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          1












          $begingroup$

          According to wiki, for the specification you presented:




          Let $k$ be the number of estimated parameters in the model. Let
          $hat{L}$ be the maximum value of the function for the model.




          While $k$ is always non-negative, the range and shape of the model likelihood function $hat{L}$ is different for each problem, since it depends on the densities and data you are working with.



          For this reason, even though you can create the surface you want for different specifications of the same model, it's impossible to obtain an AIC surface that is representative for all types of models.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
            $endgroup$
            – Jan
            40 mins ago



















          1












          $begingroup$

          $hat{L}$ is the value of the assumed likelihood function evaluated at $hat{theta}$, i.e. at its maximum value for the observed data. If our likelihood function is $L(mathbf{X};theta)$ then $hat{L}=L(mathbf{X};hat{theta})$. $k$ is the number of model parameters being estimated.



          For comparing 2 models, the one with lower AIC is preferred. Higher values of the log-likelihood imply lower values of the AIC, holding $k$ constant, while fewer model parameters also imply lower values of AIC, holding $hat{L}$ constant. The idea is to reward higher likelihood and penalize each time you add a parameter to the model, as you are losing degrees of freedom.



          Assuming you are intending to construct a 3-D plot using triplets (AIC,$hat{L},k$) from various models you have estimated, I'm not sure the plot will give you much insight beyond simply looking at AIC. The problem with creating a surface (as mentioned in the answer from @Lucas Farias) is that $k$ alone does not tell us which regressors we are including. For example $y=a_0+a_1x+a_2z$ and $y=b_0+b_1w+b_2v$ both have $k=2$, but will yield different values of $hat{L}$ and AIC.






          share|cite|improve this answer










          New contributor




          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.






          $endgroup$













          • $begingroup$
            Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
            $endgroup$
            – Jan
            38 mins ago











          Your Answer





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          2 Answers
          2






          active

          oldest

          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          1












          $begingroup$

          According to wiki, for the specification you presented:




          Let $k$ be the number of estimated parameters in the model. Let
          $hat{L}$ be the maximum value of the function for the model.




          While $k$ is always non-negative, the range and shape of the model likelihood function $hat{L}$ is different for each problem, since it depends on the densities and data you are working with.



          For this reason, even though you can create the surface you want for different specifications of the same model, it's impossible to obtain an AIC surface that is representative for all types of models.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
            $endgroup$
            – Jan
            40 mins ago
















          1












          $begingroup$

          According to wiki, for the specification you presented:




          Let $k$ be the number of estimated parameters in the model. Let
          $hat{L}$ be the maximum value of the function for the model.




          While $k$ is always non-negative, the range and shape of the model likelihood function $hat{L}$ is different for each problem, since it depends on the densities and data you are working with.



          For this reason, even though you can create the surface you want for different specifications of the same model, it's impossible to obtain an AIC surface that is representative for all types of models.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
            $endgroup$
            – Jan
            40 mins ago














          1












          1








          1





          $begingroup$

          According to wiki, for the specification you presented:




          Let $k$ be the number of estimated parameters in the model. Let
          $hat{L}$ be the maximum value of the function for the model.




          While $k$ is always non-negative, the range and shape of the model likelihood function $hat{L}$ is different for each problem, since it depends on the densities and data you are working with.



          For this reason, even though you can create the surface you want for different specifications of the same model, it's impossible to obtain an AIC surface that is representative for all types of models.






          share|cite|improve this answer









          $endgroup$



          According to wiki, for the specification you presented:




          Let $k$ be the number of estimated parameters in the model. Let
          $hat{L}$ be the maximum value of the function for the model.




          While $k$ is always non-negative, the range and shape of the model likelihood function $hat{L}$ is different for each problem, since it depends on the densities and data you are working with.



          For this reason, even though you can create the surface you want for different specifications of the same model, it's impossible to obtain an AIC surface that is representative for all types of models.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 4 hours ago









          Lucas FariasLucas Farias

          8251522




          8251522












          • $begingroup$
            Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
            $endgroup$
            – Jan
            40 mins ago


















          • $begingroup$
            Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
            $endgroup$
            – Jan
            40 mins ago
















          $begingroup$
          Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
          $endgroup$
          – Jan
          40 mins ago




          $begingroup$
          Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
          $endgroup$
          – Jan
          40 mins ago













          1












          $begingroup$

          $hat{L}$ is the value of the assumed likelihood function evaluated at $hat{theta}$, i.e. at its maximum value for the observed data. If our likelihood function is $L(mathbf{X};theta)$ then $hat{L}=L(mathbf{X};hat{theta})$. $k$ is the number of model parameters being estimated.



          For comparing 2 models, the one with lower AIC is preferred. Higher values of the log-likelihood imply lower values of the AIC, holding $k$ constant, while fewer model parameters also imply lower values of AIC, holding $hat{L}$ constant. The idea is to reward higher likelihood and penalize each time you add a parameter to the model, as you are losing degrees of freedom.



          Assuming you are intending to construct a 3-D plot using triplets (AIC,$hat{L},k$) from various models you have estimated, I'm not sure the plot will give you much insight beyond simply looking at AIC. The problem with creating a surface (as mentioned in the answer from @Lucas Farias) is that $k$ alone does not tell us which regressors we are including. For example $y=a_0+a_1x+a_2z$ and $y=b_0+b_1w+b_2v$ both have $k=2$, but will yield different values of $hat{L}$ and AIC.






          share|cite|improve this answer










          New contributor




          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.






          $endgroup$













          • $begingroup$
            Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
            $endgroup$
            – Jan
            38 mins ago
















          1












          $begingroup$

          $hat{L}$ is the value of the assumed likelihood function evaluated at $hat{theta}$, i.e. at its maximum value for the observed data. If our likelihood function is $L(mathbf{X};theta)$ then $hat{L}=L(mathbf{X};hat{theta})$. $k$ is the number of model parameters being estimated.



          For comparing 2 models, the one with lower AIC is preferred. Higher values of the log-likelihood imply lower values of the AIC, holding $k$ constant, while fewer model parameters also imply lower values of AIC, holding $hat{L}$ constant. The idea is to reward higher likelihood and penalize each time you add a parameter to the model, as you are losing degrees of freedom.



          Assuming you are intending to construct a 3-D plot using triplets (AIC,$hat{L},k$) from various models you have estimated, I'm not sure the plot will give you much insight beyond simply looking at AIC. The problem with creating a surface (as mentioned in the answer from @Lucas Farias) is that $k$ alone does not tell us which regressors we are including. For example $y=a_0+a_1x+a_2z$ and $y=b_0+b_1w+b_2v$ both have $k=2$, but will yield different values of $hat{L}$ and AIC.






          share|cite|improve this answer










          New contributor




          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.






          $endgroup$













          • $begingroup$
            Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
            $endgroup$
            – Jan
            38 mins ago














          1












          1








          1





          $begingroup$

          $hat{L}$ is the value of the assumed likelihood function evaluated at $hat{theta}$, i.e. at its maximum value for the observed data. If our likelihood function is $L(mathbf{X};theta)$ then $hat{L}=L(mathbf{X};hat{theta})$. $k$ is the number of model parameters being estimated.



          For comparing 2 models, the one with lower AIC is preferred. Higher values of the log-likelihood imply lower values of the AIC, holding $k$ constant, while fewer model parameters also imply lower values of AIC, holding $hat{L}$ constant. The idea is to reward higher likelihood and penalize each time you add a parameter to the model, as you are losing degrees of freedom.



          Assuming you are intending to construct a 3-D plot using triplets (AIC,$hat{L},k$) from various models you have estimated, I'm not sure the plot will give you much insight beyond simply looking at AIC. The problem with creating a surface (as mentioned in the answer from @Lucas Farias) is that $k$ alone does not tell us which regressors we are including. For example $y=a_0+a_1x+a_2z$ and $y=b_0+b_1w+b_2v$ both have $k=2$, but will yield different values of $hat{L}$ and AIC.






          share|cite|improve this answer










          New contributor




          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.






          $endgroup$



          $hat{L}$ is the value of the assumed likelihood function evaluated at $hat{theta}$, i.e. at its maximum value for the observed data. If our likelihood function is $L(mathbf{X};theta)$ then $hat{L}=L(mathbf{X};hat{theta})$. $k$ is the number of model parameters being estimated.



          For comparing 2 models, the one with lower AIC is preferred. Higher values of the log-likelihood imply lower values of the AIC, holding $k$ constant, while fewer model parameters also imply lower values of AIC, holding $hat{L}$ constant. The idea is to reward higher likelihood and penalize each time you add a parameter to the model, as you are losing degrees of freedom.



          Assuming you are intending to construct a 3-D plot using triplets (AIC,$hat{L},k$) from various models you have estimated, I'm not sure the plot will give you much insight beyond simply looking at AIC. The problem with creating a surface (as mentioned in the answer from @Lucas Farias) is that $k$ alone does not tell us which regressors we are including. For example $y=a_0+a_1x+a_2z$ and $y=b_0+b_1w+b_2v$ both have $k=2$, but will yield different values of $hat{L}$ and AIC.







          share|cite|improve this answer










          New contributor




          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.









          share|cite|improve this answer



          share|cite|improve this answer








          edited 4 hours ago





















          New contributor




          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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          answered 4 hours ago









          dlnBdlnB

          6989




          6989




          New contributor




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          New contributor





          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.






          dlnB is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.












          • $begingroup$
            Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
            $endgroup$
            – Jan
            38 mins ago


















          • $begingroup$
            Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
            $endgroup$
            – Jan
            38 mins ago
















          $begingroup$
          Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
          $endgroup$
          – Jan
          38 mins ago




          $begingroup$
          Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
          $endgroup$
          – Jan
          38 mins ago










          Jan is a new contributor. Be nice, and check out our Code of Conduct.










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          Jan is a new contributor. Be nice, and check out our Code of Conduct.













          Jan is a new contributor. Be nice, and check out our Code of Conduct.












          Jan is a new contributor. Be nice, and check out our Code of Conduct.
















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