Re: [R] Testing a linear hypothesis after maximum likelihood

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Fri 30 Dec 2005 - 05:35:52 EST

          I think the question was appropriate for this list. If you want to do a Wald test, you might consider asking "optim" for "hessian=TRUE". If the function that "optim" minimizes is (-log(likelihood)), then the optional component "hessian" of the output of optim should be the observed information matrix. An inverse of that should then estimate the parameter covariance matrix. I often use that when "nls" dies on me, because "optim" will give me an answer. If the hessian is singular, I can sometimes diagnose the problem by looking at eigenvalues and eigenvectors of the hessian.

	  hope this helps.
	  spencer graves

####################

On 12/29/05 7:04 AM, "Spencer Graves" <spencer.graves@pdf.com> wrote:
 >>  Why can't you use a likelihood ratio?  I would write two slightly
 >> different functions, the second of which would use the linear constraint
 >> to eliminate one of the coefficients.  Then I'd refer 2*log(likelihood
 >> ratio) to chi-square(1).  If I had some question about the chi-square
 >> approximation to the distribution of that 2*log(likelihood ratio)
 >> statistic, I'm use some kind of Monte Carlo, e.g., MCMC.
 >>


Neat solution, thanks! I didn't see that, having focused my attention on finding some way to do a Wald test. I think I was so focused because I thought it would be good to have some way of testing hypotheses w/o having to rerun my model every time.

 >>  If you'd like more help from this listserve, PLEASE do read the
 >> posting guide! "www.R-project.org/posting-guide.html".  Anecdotal
 >> evidence suggests that posts that follow more closely the suggestions in
 >> that guide tend to get more useful replies quicker.


Ok, I guess you're hinting that I'm violating the 'do your homework' norm. I'm not a statistician (I'm a social scientist) & was thinking about alternatives to the likelihood ratio test, so the self-evident solution you mention above didn't occur to me. I did spend a long time trying to figure out whether there were facilities for Wald tests and whether they might work w/ ML output. It wasn't clear what would work & it would have taken even more time to try some alternatives out, so I thought I'd just ask the list--surely people have tests they typically run after ML.

In hindsight, I guess the question as asked was rather dumb, so my apologies. Perhaps I should have asked if anyone uses a built-in Wald function after ML? Or perhaps even that question is far too basic for a list composed of such capable people.

Anyway, thanks for the insight!

Peter

#####################################################
	  Why can't you use a likelihood ratio?  I would write two slightly
different functions, the second of which would use the linear constraint to eliminate one of the coefficients. Then I'd refer 2*log(likelihood ratio) to chi-square(1). If I had some question about the chi-square approximation to the distribution of that 2*log(likelihood ratio) statistic, I'm use some kind of Monte Carlo, e.g., MCMC.

          If you'd like more help from this listserve, PLEASE do read the posting guide! "www.R-project.org/posting-guide.html". Anecdotal evidence suggests that posts that follow more closely the suggestions in that guide tend to get more useful replies quicker.

	  hope this helps.
	  spencer graves


Peter Muhlberger wrote:

> I'd like to be able to test linear hypotheses after setting up and running a
> model using optim or perhaps nlm. One hypothesis I need to test are that
> the average of several coefficients is less than zero, so I don't believe I
> can use the likelihood ratio test.
>
> I can't seem to find a provision anywhere for testing linear combinations of
> coefficients after max. likelihood.
>
> Cheers & happy holidays,
>
> Peter
>
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-- 
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
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spencer.graves@pdf.com
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Received on Fri Dec 30 05:41:14 2005

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