Hello again, I studied your suggestion but still I disagree. You wrote:
"From the way you wrote the problem I assumed that there is some number of n "looks" at the subject and then you count them up." But this is not the case. My data is clearly continuous quantities and no discrete choices. I know nothing about the underlying choice process, the only thing I know is the final share of one of three regimes. So sorry for the bad description of the problem. So I stick with my censored data model. Still the hint about the p-values is very helpful because I actually ran into this problem. So thank you for the hint. Best, Geraldine Terry Therneau schrieb: > Apologies -- you are being more subtle than I thought. Nevertheless, I think > that the censoring language isn't quite right. > > You are thinking of a hierarchical model: > > z ~ N(Xb, sigma), where Xb is the linear predictor, whatever covariates > you > think belong in the model. Whether the distribution should be Gaussian or > somthing else depends not on the overall distribution of z, but on > distribution > of (z | Xb). We could have a skewed predictor leading to skewed z, even if > the > distribution about any given expectation is symmetric. > > y = F(z) is what you observe. The classic tobin model is y= max(0,z), > which > does lead to censored data. > > In your case y_i = Binomial(n_i, p_i = H(z)). Note a binomial is k heads > out of n tries with a coin of probability p, a "Bernouli" is a binomial > restricted to a single coin flip. From the way you wrote the problem I > assumed > that there is some number of n "looks" at the subject and then you count them > up. Note that var(y) = n p (1-p) > > H describes how the probability changes with z. In biology we very > rarely > use H(z)= max(min(z,1),0) because it gives a hard threshold, and the > probability > of nearly anything doesn't go all the way to zero or one. > > If H were as above and > var(y) = constant and > n is sufficiently large so that Binomial dist is approx Gaussian and > var(y |p) << var(z| Xb) > > then your y will fit a censored Gaussian. Since at least the second is > false, > it doesn't. > > A censored model may still be an ok first cut at fitting the data, but I > would be suspicious of variance estimates and particularly of any p-values. > The > bootstrap could help that. > > Terry T. > > > > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
