C. Nicolay writes: > I want to fit a curve by means of logistic regression with the > following parameters: > > p(x) = exp(a + bx) / (1 + exp(a + bx)) > > with x: foil of a certain thickness and p(x): detection (yes > / no). I want to estimate x for p(x)=1/2. > > This is a problem within psychometrics (psychophysics). > But unlike the normal psychometric problems concerning > discrimination, I would like to estimate the above mentioned threshold. > > This can be seen as being equivalent to a bio-assay problem. > But in my case all observations (n=160) are made by one person (I > have n=62 persons). Hence, they are dependent. But estimation > within logistic regression requests independent observations.
I'm not entirely clear what you mean, because you use n to represent both the number of observations and the number of subjects. I assume that you have an average of 2.6 observations per person. With k=62 people in your sample, you would have n=160 total observations. A simple solution is to randomly select one observation per person. This would reduce your sample size from 160 to 62, but then you still have independence. It does seem wasteful, though, to toss away so much data. Models that allow for dependence in logistic regression are quite complex. If you want to follow up on this, look for information about the generalized linear mixed model (GLMM). You might also consider a conditional logistic regression model, though, that is used more often for matched pairs data. I don't have too much experience with either model, so I can't help much more than that. > After my opinion the dependency of the observations do not > influence the estimate itsself but rather its variance. But I am not > sure. Who can give me some hints or literature?? Thank You in > advance for your help. Since the logistic regression model is non-linear, there is an influence on both the estimates and the standard errors. But the influence on the estimates is not terribly large. Good luck! Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. The STATS web page has moved to http://www.childrens-mercy.org/stats. -----Original Message----- From: C. Nicolay [mailto:[EMAIL PROTECTED] Sent: Tuesday, November 25, 2003 2:33 AM To: [EMAIL PROTECTED] Subject: Logistic regression with dependent observations I want to fit a curve by means of logistic regression with the following parameters: p(x) = exp(a + bx) / (1 + exp(a + bx)) with x: foil of a certain thickness and p(x): detection (yes / no). I want to estimate x for p(x)=1/2. This is a problem within psychometrics (psychophysics). But unlike the normal psychometric problems concerning discrimination, I would like to estimate the above mentionned threshold. This can be seen as being equivalent to a bio-assay problem. But in my case all observations (n=160) are made by one person (I have n=62 persons). Hence, they are dependent. But estimation within logistic regression requests independent observations. After my opinion the dependency of the observations do not influence the estimate itsself but rather its variance. But I am not sure. Who can give me some hints or literature?? Thank You in advance for your help. C. Nicolay, MS University of Bonn (Germany) . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
