# [R] Testing a linear hypothesis after maximum likelihood

Spencer Graves spencer.graves at pdf.com
Thu Dec 29 19:35:52 CET 2005

```	  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 at 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
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
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help

--
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
333 West San Carlos Street Suite 700
San Jose, CA 95110, USA

spencer.graves at pdf.com
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Fax: 408-280-7915

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