RE: Help: Non-positive semi-definite message

From: "KOWALSKI, KENNETH G. [R&D/1825]" <kenneth.g.kowalski@pharmacia.com> Subject: RE: Help: Non-positive semi-definite message Date: Wed, 22 Aug 2001 11:02:36 -0500 Nick and Lew, In the discussion that Nick and I were having I was assuming that the only information available was based on the data at hand which ML wants to estimate a singular cov matrix. When I used the term "arbitrary" for setting the correlation to 0.3 I was assuming there was no other information available. That is, there is no prior knowledge that the true correlation is 0.3. Certainly if other data is available perhaps from a design that allows better estimation of the correlation and an informative prior can be developed that says the correlation is 0.3 I wouldn't take the bet either. My point is that in the absence of an informative prior if ML wants to estimate a singular cov matrix it seems doubtful that the true correlation would be 0.3. A correlation of 0.3 is fairly weak and I would expect that for most data/designs if the true correlation was 0.3 you wouldn't run into a singular cov matrix due to ML trying to estimate the correlation as 1.0. It seems to me there must be sufficient information in the data to make ML want to drive the correlation to 1. So, I guess I'm saying that if you put a mild prior on the correlation centered about 0.3 its still likely to move the correlation considerably away from 0.3. Perhaps I'm wrong and a poor design could still drive ML to estimate the correlation as 1 when the true value is 0.3...I don't know. It just seems more likely that the true correlation would be considerably higher...perhaps 0.8 or 0.9. In any event, the six-pack is on me. Best regards, Ken