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Why HPGENSELECT uses chi-square to test the significance of coefficient estimates?

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New Contributor
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Why HPGENSELECT uses chi-square to test the significance of coefficient estimates?

Usually t-test is applied to test the significance of coefficient estimates. But HPGENSELECT uses chi-square test (see table below). Why?

 

Parameter Estimates from HPGENSELECT

Parameter

DF

Estimate

Standard Error

Chi-Square

Pr > ChiSq

Intercept

1

3.405338

0.142788

568.768

<.0001

Super User
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Re: Why HPGENSELECT uses chi-square to test the significance of coefficient estimates?

New Contributor
Posts: 4

Re: Why HPGENSELECT uses chi-square to test the significance of coefficient estimates?

Reeza, thanks a lot for your help. I try to understand that how Chi-square can be used to test the significance of coefficient. Do you have any reference? thanks!

SAS Super FREQ
Posts: 3,540

Re: Why HPGENSELECT uses chi-square to test the significance of coefficient estimates?

You are correct that for OLS regression and normally distributed errors you can use t tests. However, HPGENSELECT is most closely related to the GENMOD procedure, not the GLM procedure. For generalized linear models, the errors are not normally distributed and the solution technique is maximum likelihood estimation. The docs for PROC LOGISTIC and PROC GENMOD mention that confidence intervals are based on the likelihood ratio, and the statstic that is used has an asymptotic chi-square distribution:

LOGISTIC: http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_logistic_det...

GENMOD: http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_genmod_detai...

New Contributor
Posts: 4

Re: Why HPGENSELECT uses chi-square to test the significance of coefficient estimates?

Thanks for your reply. The links you attached is very helpful.

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