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Re: st: gradient and the inverse of the information matrix

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To   <>
Subject   Re: st: gradient and the inverse of the information matrix
Date   Fri, 3 May 2013 13:23:39 +0100

I have a manuscript that is exactly related to your question. The article also briefs some possible reasons why the score test conducted by SAS and STATA can be different. (See the footnote 6.)
You can download the article from:

Chi-lin Tsai

-----Original Message----- From: Jon Mu
Sent: Wednesday, May 01, 2013 10:01 PM
To: Listserv STATA
Subject: st: gradient and the inverse of the information matrix

Hi Statalisters,

I am trying to check into the (Rao's) score (or commonly known as the Lagrange Multiplier) test for a model that I am working on. I got results from SAS already, and I want to see if those from SAS would square with the one produced from my own Stata codes.

They don't match, and looks like I probably made some mistakes in my Stata codes. For the generalized formula to get the Chi-Square statistic, I need to get the gradient and the inverse of the information matrix. For the inverse of the information matrix, I can grab from e(V) directly without any further calculation.

So I might've made some mistake in the gradient. I've searched through the voluminous Stata pdf documentation using gradient as the key word, and I was not able to find useful information. But I vaguely remember a while back ago when I was also checking into related issues, I read somewhere that the e(gradient) matrix is a gradient with respect to xb, not b, so I suspect that might be the cause. I am wondering if that's the case. If I am right on this, then a follow-up question is how to recover the gradient with respect to b since I feel there might not be a linear transformation that I can use to get it directly. Any input/suggestion would be appreciated.

Jun Xu, PhD
Associate Professor
Department of Sociology
Ball State University
Muncie, IN 46037
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