topic Regression analysis with only positive coefficients in Statistical Procedures

Regression analysis with only positive coefficients

AndrewBronson — Mon, 25 Jun 2018 17:19:39 GMT

I am looking to run a regression analysis but only get positive coefficients just based on the scenario of my calculation negative coefficients are nonsensical. I am currently using PROC REG with a LSMEANS but I dont know if this is the only way to run it. I have tried to use RESTRICT and BOUNDS but neither have worked.

Thanks in advance

Re: Regression analysis with only positive coefficients

PaigeMiller — Mon, 25 Jun 2018 17:25:57 GMT

Well, here's the problem. If you have multiple X variables in your regression, and they are correlated with one another, you can get slopes that seem to have the wrong sign. This is a consequence of including variables that are correlated with one another.

You can try removing variables from the model, or use PROC PLS instead of PROC REG, which is less susceptible to this problem.

Re: Regression analysis with only positive coefficients

AndrewBronson — Mon, 25 Jun 2018 17:29:00 GMT

Yes I figured the multicollinearity is likely a problem. I will try the PROC PLS. Thank you for the suggestion

Re: Regression analysis with only positive coefficients

stanmarciano — Wed, 27 Jun 2018 12:37:29 GMT

If you have a very sound theoretical backing for your coefficients to be positive, then you could use bayesian regression method and set the prior distributions from positive distributions:

Here are some helpful links for bayesian regression:

1) Basic setup of model using proc Genmod: https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_genmod_sect007.htm

1a) How to change priors:

https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_genmod_sect012.htm

Alternatively (This might be the best proc to use in your case):

Proc MCMC is another possible solution:

3) Proc MCMC linear regression: https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_mcmc_sect004.htm

Here note that I am assuming that you have very solid theoretical backing for your Beta coefficients to be positive. This is a very strong assumption and has to be based on evidence from prior literature or some other source.