topic Re: Can i change the Maximum Likelihood Estimates in logistic regression to least squares ? in Statistical Procedures

Can i change the Maximum Likelihood Estimates in logistic regression to least squares ?

smadlindl0 — Tue, 03 May 2016 16:37:28 GMT

In my solution after the logit-regression the Maximum Likelihood Estimate is the standardmethod. Is it possible to change to least-squares estimate and compare the difference between the two methods in the results?

Re: Can i change the Maximum Likelihood Estimates in logistic regression to least squares ?

ballardw — Tue, 03 May 2016 16:47:35 GMT

You may need to specify which procedure you are using. Proc Logistic supports least squares using the LSMEANS and LSMESTIMATE statements.

Re: Can i change the Maximum Likelihood Estimates in logistic regression to least squares ?

Rick_SAS — Tue, 03 May 2016 17:54:44 GMT

I'm not certain what you intend, but PROC LOGISTIC support iteratively reweighted least square solutions, and in fact that is the default solution technique. You can read about the numerical solution algorithms in PROC LOGISTIC in the doc. To compare you would need to run the procedure twice, once with each method.

But as far as I know there is no direct method for using least squares to compute a logistic regression, only iterative methods. The problem is that the conditional probability of the response p_i = E(Y_i | X_i) is not observed. So you have to use some iterative technique to optimize the likelihood function.

Re: Can i change the Maximum Likelihood Estimates in logistic regression to least squares ?

StatDave — Tue, 03 May 2016 19:22:17 GMT

The LSMEANS and LSMESTIMATE statements compute marginal (least squares) means and compares them using the maximum likelihood estimates. They do NOT involve estimation using least squares. Logistic models are one in the class of generalized linear models which are all estimated using maximum likelihood estimation.