Wald Chi Square statistics - Logistic Regression

[vishal_prof_gmail_com]

"The estimates and test of coefficients depend on the distribution of the response variable, not the distribution of the coefficients themselves. "

Can you elaborate on it,how the estimates depend on the distribution of response variables?

The difference between Linear and Logistic regression is response variable. So, indeed distribution of response variable is one of the reason for Chi square distribution being used for testing the coefficients. However, this needs to be supported with arguments. 

" If the response variable is a binary variable, then after the logit transformation, the Wald Chi Square statistic of the coefficient follows an asymptotic chi-square distribution, then we use this inference to test the significance of the coefficient or its CI. "

Question is still the same. Why did we use Chi-Square statistics which is square of t-statistics and not t-statistics.

[PaigeMiller]

I think you are asking for material that is way beyond what we normally provide here in the SAS communities and your questions have nothing to do with SAS. You are asking for mathematical proofs. We generally do not provide mathematical proofs here in the SAS communities, these can be found in textbooks and possibly on appropriate web sites.

[vishal_prof_gmail_com]

Hi,

I found that R and Python gives z statistics for the significance of coefficients and results match.

Hence the arguments that since the target variable is binary in Logistic regression and hence Chi-square distribution is used to test coefficients does not appear to be true. The coefficients can be tested by both z statistics as well as  Chi-Square statistics.

The question actually is why SAS gives Chi Square and R , Python gives z. I think it's a basis Statistical question not requiring any complicated mathematical derivation , very much in scope for people using SAS Stat.

Regards,

Vishal