Testing a linear hypothesis after maximum likelihood
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 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
______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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 www.pdf.com <http://www.pdf.com> Tel: 408-938-4420 Fax: 408-280-7915