topic Re: Regression using maximum likelihood estimation in Statistical Procedures

Regression using maximum likelihood estimation

bwar88 — Fri, 15 Jul 2016 01:27:06 GMT

I need to run a distributed lag regression with a lagged dependent variable of the form:

St = µ + βAt + λSt−1 + v

where v = et - λet-1

According to the literature this needs to be computed using MLE rather than OLS. Proc reg obviously uses OLS, so what PROC do I need to run?

Re: Regression using maximum likelihood estimation

Ksharp — Fri, 15 Jul 2016 02:06:16 GMT

Use PROC GENMOD :

proc genmod data=sashelp.class;
model weight=age height/dist=normal link=identity noscale;
run;

Re: Regression using maximum likelihood estimation

stat_sas — Fri, 15 Jul 2016 02:35:10 GMT

Hi,

This is a time series data. One key assumption in OLS is that the errors are independent of each other. In your model residuals seem to be correlated which is not desirable to use OLS for time series data since the assumptions on which the classical linear regression model is based will be violated. Try looking into SAS procedures for time series analysis. This requires SAS ETS.

Re: Regression using maximum likelihood estimation

Ksharp — Fri, 15 Jul 2016 03:37:45 GMT

It is ARIMA Model. Check ARIMA Procedure .

Re: Regression using maximum likelihood estimation

bwar88 — Fri, 15 Jul 2016 10:36:16 GMT

It needs to be a regression model as I need to see the coefficients rather than just forecast the future. So is PROC GENMOD what I need?

Re: Regression using maximum likelihood estimation

SteveDenham — Fri, 15 Jul 2016 19:04:41 GMT

You can get "regression" coefficients from time series analysis--what @stat_sas says about the errors is absolutely correct. You could use @Ksharp's suggestion of PROC ARIMA, or look at PROC MODEL. If you do not have access to SAS/ETS, then fitting this sort of model is going to require a fair amount of macro code, as you will have to iteratively refit the data using one of the procedures that allow you to specify a time-dependent error structure--going back and forth between the original data and the lagged data.

Steve Denham

Re: Regression using maximum likelihood estimation

Ksharp — Sun, 17 Jul 2016 01:16:57 GMT

If you need constrain the coefficients sum to 1, I think you need PROC GENMOD + offset= option. PROC ARIMA can't do that.