Regularization for Non linear regression

[NiceToBeHere]

How can I run a non linear regression with regularization?

Thanks

[Ksharp]

PROC ADAPTATIVE

PROC LOESS

PROC GAML

PROC GAM

[NiceToBeHere]

Hi,

Thanks - I would like to clarify my question:

I would like to run a parametric model, it can be linear or non linear but I would like to ensure that the coefficients are positive and that they have small magnitutes.

If I understand correctly, the methods you have mentioned are non parametric.

Thanks

[Ksharp]

OK. You might want check EFFECT statement.

Here is a blog written by  @Rick_SAS . You could find more blog about non-linear regression in his blog.

http://blogs.sas.com/content/iml/2017/04/19/restricted-cubic-splines-sas.html

[NiceToBeHere]

Thanks for the reply - 

Can you point me to any tutorial that teaches the syntax and capabilties of these regression models and others?

[Ksharp]

I would like to leave it to @Rick_SAS

[Rick_SAS]

> Can you point me to any tutorial that teaches the syntax and capabilties of these regression models and others?

For parametric linear models, I recommend the GLMSELECT and HPGENSELECT procedures. The HPGENSELECT procedure provides link functions which enable you to model a variety of response distributions, such as binary, binomial, Poisson, etc. The GLMSELECT procedure supports the EFFECT statement which enables you to use splines to model nonlinear relationships in the data. (A spline model is not really parametric in the usual sense, so might be what you need when you say "nonlinear.")   Both procedures permit you to use regularization methods that shrink the coefficients of some variables to zero, thus resulting in a parsimonious model.

If you want a PARAMETRIC but NONLINEAR regression model, then PROC NLMIXED is the best option. This SAS Note shows how to set up a penalized likelihood function.

For reference, see the previous SAS Note, which includes many links to reference material.  Also see the article about penalized regression by Funde Gunes, which includes references at the end. 

[Rick_SAS]

> Can you point me to any tutorial that teaches the syntax and capabilties of these regression models and others?

For parametric linear models, I recommend the GLMSELECT and HPGENSELECT procedures. The HPGENSELECT procedure provides link functions which enable you to model a variety of response distributions, such as binary, binomial, Poisson, etc. The GLMSELECT procedure supports the EFFECT statement which enables you to use splines to model nonlinear relationships in the data. (A spline model is not really parametric in the usual sense, so might be what you need when you say "nonlinear.")   Both procedures permit you to use regularization methods that shrink the coefficients of some variables to zero, thus resulting in a parsimonious model.

If you want a PARAMETRIC but NONLINEAR regression model, then PROC NLMIXED is the best option. This SAS Note shows how to set up a penalized likelihood function.

For reference, see the previous SAS Note, which includes many links to reference material.  Also see the article about penalized regression by Funde Gunes, which includes references at the end.