Can I find likelihood function of an objective function?
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Sorry this is not a question 100% related to MATLAB.
I have some data. I used
nlinfit
and got the parameters for these three functions (model), as well as MSE
$f_1=b1*x1+b2*x2+b3$
$f_2=b1*x1^b2+b3*x2+b4$
$f_3=b1*x1^b2+b3*x2^b4+b5$
Besides comparing their MSE, I read some model selection method, but they need maximized value of the likelihood function for the model. What I know about liklihood is for some data with dirstributions
So is there a way or is that ok to find likelihood function for f1, f2, and f3?
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Star Strider
2022-11-28
If you have the Statistics and Machine Learning Toolbox, see if the mle function (and associated functions) will do what you want. It estimated the parameters of a probability distribution. There are several to choose from, dependong on how your data are distributed.
Search the documentation for ‘likelihood’ for all the functions that mention it.
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Jeff Miller
2022-11-29
A lot depends on the details of these models, but one way to proceed would be in terms of the error scores. Consider the full model to be
$f_1=b1*x1+b2*x2+b3 + e_{1i}$
where
is the residual for case i according to model 1 (and similarly for models 2 & 3). If you assume that the e values are normally distributed with mean 0 and some unknown variance
(as I believe would be appropriate for some models), then you can use the computed e values for each model to get the maximum likelihood estimate of
for that model, compute the likelihood of each e value within the model's estimated normal(0,
) distribution, and finally compute the likelihood of the whole dataset under the model as the product of the likelihood values of the individual e's.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1211733/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1211738/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1211743/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1211748/image.png)
Looking at the models this way, the only random values are the e's, so they are the only quantities relevant to the computation of likelihood.
HTH,
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