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

[Jun Xu <mystata@hotmail.com>]

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
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
> > * http://www.stata.com/support/faqs/resources/statalist-faq/
> > * http://www.ats.ucla.edu/stat/stata/
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/faqs/resources/statalist-faq/
> * http://www.ats.ucla.edu/stat/stata/ 		 	   		  
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/