3D plot of Akaike Information Criterion (AIC) for suitable ranges of Lˆ and k
$begingroup$
Giving that Akaike Information Criterion (AIC) is as follow:
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
asked 19 hours ago
JanJan
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add a comment |
$begingroup$
Giving that Akaike Information Criterion (AIC) is as follow:
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
asked 19 hours ago
JanJan
1514
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.
$endgroup$
add a comment |
$begingroup$
Giving that Akaike Information Criterion (AIC) is as follow:
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
asked 19 hours ago
JanJan
1514
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:
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
asked 19 hours ago
JanJan
1514
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.
asked 19 hours ago
JanJan
1514
New contributor
Jan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 18 hours ago
Jan
asked 19 hours ago
JanJan
1514
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asked 19 hours ago
JanJan
1514
asked 19 hours ago
JanJan
1514
1514
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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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$begingroup$
$hat{L}$ 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.
answered 18 hours ago
dlnBdlnB
75311
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$begingroup$
Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
$endgroup$
– Jan
14 hours ago
add a comment |
$begingroup$
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 if 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.
answered 18 hours ago
Lucas FariasLucas Farias
8401522
$endgroup$
$begingroup$
Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
$endgroup$
– Jan
14 hours ago
2
$begingroup$
@Jan what didn't you understand?
$endgroup$
– Lucas Farias
12 hours ago
$begingroup$
Is it possible to plot a Surface of AIC in a 3D space base on L and k inputs? I want to plot it based on any suitable range of L and K just to get a feel of it. I know that K cannot be negative (since it denotes the parameters size) so I can choose a range from 1 to 60 for example. However, since L is different for each problem, what could be a reasonable range (even if it is hypothetical)?
$endgroup$
– Jan
9 hours ago
add a comment |
Your Answer
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2 Answers
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2 Answers
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$begingroup$
$hat{L}$ 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.
answered 18 hours ago
dlnBdlnB
75311
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
14 hours ago
add a comment |
$begingroup$
$hat{L}$ 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.
answered 18 hours ago
dlnBdlnB
75311
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
14 hours ago
add a comment |
$begingroup$
$hat{L}$ 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.
answered 18 hours ago
dlnBdlnB
75311
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.
answered 18 hours ago
dlnBdlnB
75311
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.
edited 18 hours ago
answered 18 hours ago
dlnBdlnB
75311
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.
answered 18 hours ago
dlnBdlnB
75311
answered 18 hours ago
dlnBdlnB
75311
75311
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.
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
14 hours ago
add a comment |
$begingroup$
Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
$endgroup$
– Jan
14 hours ago
$begingroup$
Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
$endgroup$
– Jan
14 hours ago
$begingroup$
Thanks dlnB for the clarification. In simple words, what do you suggest values to use to plot this 3D plot.
$endgroup$
– Jan
14 hours ago
add a comment |
$begingroup$
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 if 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.
answered 18 hours ago
Lucas FariasLucas Farias
8401522
$endgroup$
$begingroup$
Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
$endgroup$
– Jan
14 hours ago
2
$begingroup$
@Jan what didn't you understand?
$endgroup$
– Lucas Farias
12 hours ago
$begingroup$
Is it possible to plot a Surface of AIC in a 3D space base on L and k inputs? I want to plot it based on any suitable range of L and K just to get a feel of it. I know that K cannot be negative (since it denotes the parameters size) so I can choose a range from 1 to 60 for example. However, since L is different for each problem, what could be a reasonable range (even if it is hypothetical)?
$endgroup$
– Jan
9 hours ago
add a comment |
$begingroup$
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 if 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.
answered 18 hours ago
Lucas FariasLucas Farias
8401522
$endgroup$
$begingroup$
Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
$endgroup$
– Jan
14 hours ago
2
$begingroup$
@Jan what didn't you understand?
$endgroup$
– Lucas Farias
12 hours ago
$begingroup$
Is it possible to plot a Surface of AIC in a 3D space base on L and k inputs? I want to plot it based on any suitable range of L and K just to get a feel of it. I know that K cannot be negative (since it denotes the parameters size) so I can choose a range from 1 to 60 for example. However, since L is different for each problem, what could be a reasonable range (even if it is hypothetical)?
$endgroup$
– Jan
9 hours ago
add a comment |
$begingroup$
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 if 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.
answered 18 hours ago
Lucas FariasLucas Farias
8401522
$endgroup$
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 if 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.
answered 18 hours ago
Lucas FariasLucas Farias
8401522
edited 12 hours ago
answered 18 hours ago
Lucas FariasLucas Farias
8401522
answered 18 hours ago
Lucas FariasLucas Farias
8401522
answered 18 hours ago
Lucas FariasLucas Farias
8401522
8401522
$begingroup$
Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
$endgroup$
– Jan
14 hours ago
2
$begingroup$
@Jan what didn't you understand?
$endgroup$
– Lucas Farias
12 hours ago
$begingroup$
Is it possible to plot a Surface of AIC in a 3D space base on L and k inputs? I want to plot it based on any suitable range of L and K just to get a feel of it. I know that K cannot be negative (since it denotes the parameters size) so I can choose a range from 1 to 60 for example. However, since L is different for each problem, what could be a reasonable range (even if it is hypothetical)?
$endgroup$
– Jan
9 hours ago
add a comment |
$begingroup$
Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
$endgroup$
– Jan
14 hours ago
2
$begingroup$
@Jan what didn't you understand?
$endgroup$
– Lucas Farias
12 hours ago
$begingroup$
Is it possible to plot a Surface of AIC in a 3D space base on L and k inputs? I want to plot it based on any suitable range of L and K just to get a feel of it. I know that K cannot be negative (since it denotes the parameters size) so I can choose a range from 1 to 60 for example. However, since L is different for each problem, what could be a reasonable range (even if it is hypothetical)?
$endgroup$
– Jan
9 hours ago
$begingroup$
Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
$endgroup$
– Jan
14 hours ago
$begingroup$
Thanks Lucas, but I feel that I got confused with your answer. Can you please explain more?
$endgroup$
– Jan
14 hours ago
2
2
$begingroup$
@Jan what didn't you understand?
$endgroup$
– Lucas Farias
12 hours ago
$begingroup$
@Jan what didn't you understand?
$endgroup$
– Lucas Farias
12 hours ago
$begingroup$
Is it possible to plot a Surface of AIC in a 3D space base on L and k inputs? I want to plot it based on any suitable range of L and K just to get a feel of it. I know that K cannot be negative (since it denotes the parameters size) so I can choose a range from 1 to 60 for example. However, since L is different for each problem, what could be a reasonable range (even if it is hypothetical)?
$endgroup$
– Jan
9 hours ago
$begingroup$
Is it possible to plot a Surface of AIC in a 3D space base on L and k inputs? I want to plot it based on any suitable range of L and K just to get a feel of it. I know that K cannot be negative (since it denotes the parameters size) so I can choose a range from 1 to 60 for example. However, since L is different for each problem, what could be a reasonable range (even if it is hypothetical)?
$endgroup$
– Jan
9 hours ago
add a comment |
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.
Jan is a new contributor. Be nice, and check out our Code of Conduct.
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