Stixbox

Issue 1699: There is no method to compute AIC/BIC criterion for regression analysis and model selection

Reported by Michael Baudin, Jul 7, 2017

The files in attachment provide an implementation.

Comment 1 by Michael Baudin, Jul 7, 2017

The log-Likelihood for regression can be computed as :

    // Compute Log-Likelihood
    sigma2 = fullstats.ResidualSS/m
    fullstats.LogLikelihood = -0.5*m*(log(2*%pi*sigma2)+1)

as in done in the attached regress.sci attached file.

Comment 2 by Michael Baudin, Sep 1, 2017

There is a bug when we execute the tests of regress.

 !--error 32 
Singularity of log or tan function.
at line     395 of function regress called by :  
B = regress(Y,X);

The bug happens when sigma2 is zero, which can be triggered when the 
data has only one element.

The following fixes the bug.

if (sigma2==0) then
        fullstats.LogLikelihood = %nan
else
        fullstats.LogLikelihood = -0.5*m*(log(2*%pi*sigma2)+1)
end

Comment 3 by Michael Baudin, Sep 1, 2017

In regress.sci, there is a small bug :

    // Check type
    
apifun_checktype("regress",y,"y",1,"constant
");
    
apifun_checktype("regress",X,"X",2,"constant
");

Comment 4 by Michael Baudin, Sep 1, 2017

Draft of an implementation. 
Caution : it probably won't work.

Comment 5 by Michael Baudin, Sep 6, 2017

A better implementation, with comments. The missing part is a good 
example, in which the selection leads to a model where not all 
predictors are selected. With the current examples, both the forward 
and backward selection lead to a model with all predictors selected.

Comment 6 by Michael Baudin, Sep 12, 2017

A much better implementation :
* added algorithm "both"
* added selection history
* factored the code into separate function
* improved testing

Comment 7 by Michael Baudin, Oct 20, 2017

Fixed a bug in stepwiselm_generate with the polyijk option.

Comment 8 by Michael Baudin, Oct 20, 2017

Improved speed of stepwiselm.

Comment 9 by Michael Baudin, Nov 16, 2017

Added an optionnal argument in order to manage a selection. This 
allows to evaluate a large regression model, for which the selected 
predictors can be evaluated, but not the full unselected inputs.

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