On 22-Sep-06 Ted Harding wrote: > I've just come across a kind of problem which leads > me to wonder how to approach it in R. > > Basically, each a set of items is subjected to a series > of "impacts" until it eventually "fails". The "force" > of each impact would depend on covariates X,Y say; > [...] > ... one could envisage > something like a logistic model for the probabiliy > of failure at each impact, leading to a kind of > generalised "geometric distribution" -- that is, > the likelihood for each item would be of the form > > (1-P[1])*(1-P[2])*...*(1-P[n-1])*P[n] > > where P[i] could have a logistic model in terms of > the values of X[i] and Y[i], and n is the index of > the impact at which failure occurred. That is then > a solvable problem.
I may be getting closer, but am well off target still! Starting with the case of no covariates, one has p*(1-p)^(n-1) (n = 1,2,...) or p*(1-p)^y (y = 0,1,...) which is a particular case of a negative binomial, with "target successes" = 1. In terms of the two-stage model for a negative binomial (see V&R MASS section 7.4), this corresponds to (mu^y * theta^theta)/(mu + theta)^(theta + y) *gamma(theta + y)/(gamma(theta)*y!) with theta = 1 and p = theta/(mu + theta) = 1/(mu + 1). This was in the context of having landed on glm.nb in MASS. However, glm.nb fits theta, which I would want to fix at 1. I don't see anything in ?glm.nb which allows theta to be held at a fixed value. The next snag is that it would not be straightforward, as far as I can see, to introduce covariates. The typical data set would be a set of sequences each of the form X1 Y1 0 X2 Y2 0 ....... Xn Yn 1 where the value of n is random, so varies from sequence to sequence. In the above negative binomial framework, y=(n-1) and the covariates for that value of y would be the set (X1,X2,...,Xn, Y1,Y2,...,Yn) and therefore of variable length for each observation (i.e. sequence as above, or value of y per sequence). I don't know how one can accomodate a variable length of covariates per observation. So it looks as though glm.nb, while thinking along the lines I want, won't fit the bill! However, other features of glm.nb would be suitable, since p/(1-p) = 1/mu and a logistic model for p therefore means a linear fit to log(mu), and glm.nb allows a log link. Comments welcome! With thanks, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 23-Sep-06 Time: 16:15:14 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@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 and provide commented, minimal, self-contained, reproducible code.