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


From   John Antonakis <John.Antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: gradient and the inverse of the information matrix
Date   Wed, 01 May 2013 23:46:27 +0200

Well, if your model is that straightforward just do a likelihood ratio test, by estimating the constrained model, then storing the estimates

est store constrained

Then estimate the unconstrained model and store the estimates:

est store unconstrained

Then do the lrtest:

lrtest unconstrained constrained

If you have not used a -robust vce- then you can use this test.

HTH,
J.

__________________________________________

John Antonakis
Professor of Organizational Behavior
Director, Ph.D. Program in Management

Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
The Leadership Quarterly
__________________________________________

On 01.05.2013 23:40, Jun Xu wrote:
Dear Professor Antonakis,

Thanks a lot for those useful leads. I am working on a single-equation categorical dependent variable model. I estimated the model with constraints imposed. Then if I understand the score test correctly, it would be a simple matrix operation of

gradient * inv(information matrix) * gradient'

where gradient = e(gradient) and inv(information matrix) = e(V)

But the results do not match those from SAS, at least not to the point of having rounding errors. Either e(gradient) does not mean what it's named or the inverse of information matrix != e(V), I couldn't think of other possibilities.

Jun

----------------------------------------
Date: Wed, 1 May 2013 23:22:03 +0200
From: John.Antonakis@unil.ch
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: gradient and the inverse of the information matrix

Hi:

If you estimate your model with -sem- score tests are possible by using
-estat mindices-; see also -estat scoretests.

Also see the userwritten command -scoregrp- (available through ssc).

Best,
J.

__________________________________________

John Antonakis
Professor of Organizational Behavior
Director, Ph.D. Program in Management

Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor
The Leadership Quarterly
__________________________________________

On 01.05.2013 23:01, Jon Mu wrote:
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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