On Thu, 2008-06-19 at 10:42 -0400, Bryan Hanson wrote: > [I've ommitted some of the conversation so far...] > > > E.g. in a logistic model, with (say) eta = beta_0 + beta_1*x one may > > find, on the > > linear predictor scale, A and B (say) such that P(A <= eta <= B) = 0.95. > > > > Then P(expit(A) <= expit(eta) <= expit(B)) = 0.95, which is exactly > > what is wanted. > > I think I follow the above conceptually, but I don't know how to implement > it, though I fooled around (unsuccessfully) with some of the variations on > predict(). > > I'm trying to learn this in response to a biology colleague who did > something similar in SigmaPlot. I can already tell that SigmaPlot did a lot > of stuff for him in the background. The responses are 0/1 of a particular > observation by date. The following code simulates what's going on (note > that I didn't use 0/1 since this leads to a recognized condition/warning of > fitting 1's and 0's. I've requested Brian's Pattern Recognition book so I > know what the problem is and how to solve it). My colleague is looking at > two populations in which the "LD50" would differ. I'd like to be able to > put the "pointwise confidence bounds" on each curve so he can tell if the > populations are really different. > > By the way, this code does give a (minor?) error from glm (which you will > see). > > Can you make a suggestion about how to get those "confidence bounds" on > there? > > Also, is a probit link more appropriate here? > > Thanks, Bryan > > x <- c(1:40) > y1 <- c(rep(0.1,10), rep(NA, 10), rep(0.9,20)) > y2 <- c(rep(0.1,15), rep(NA, 10), rep(0.9,15)) > data <- as.data.frame(cbind(x,y1,y2)) > plot(x, y1, pch = 1, ylim = c(0,1), col = "red") > points(x, y2, pch = 3, col = "blue") > abline(h = 0.5, col = "gray") > fit1 <- glm(y1~x, family = binomial(link = "logit"), data, na.action = > na.omit) > fit2 <- glm(y2~x, family = binomial(link = "logit"), data, na.action = > na.omit) > lines(fit1$model$x, fit1$fitted.values, col = "red") > lines(fit2$model$x, fit2$fitted.values, col = "blue")
The point is to get predictions on the scale of the link function, generate 95% confidence bands in the normal way and then transform the confidence bands onto the scale of the response using the inverse of the link function used to fit the model. [note, am doing this from memory, so best to check this is right -- I'm sure someone will tell me very quickly if I have gone wrong anywhere!] ## predictions on scale of link function pred1 <- predict(fit1, se.fit = TRUE) pred2 <- predict(fit2, se.fit = TRUE) ## constant for 95% confidence bands ## getting two t values is redundant here as fit1 and fit2 ## have same residual df, but the real world may be different res.df <- c(fit1$df.residual, fit2$df.residual) ## 0.975 because we want 2.5% in upper and lower tail const <- qt(0.975, df = res.df) ## confidence bands on scale of link function upper1 <- pred1$fit + (const[1] * pred1$se.fit) lower1 <- pred1$fit - (const[1] * pred1$se.fit) upper2 <- pred2$fit + (const[2] * pred2$se.fit) lower2 <- pred2$fit - (const[2] * pred2$se.fit) ## bind together into a data frame bands <- data.frame(upper1, lower1, upper2, lower2) ## transform on to scale of response bands <- data.frame(lapply(bands, binomial(link = "logit")$linkinv)) ## plot confidence bands lines(fit1$model$x, bands$upper1, col = "red", lty = "dotted") lines(fit1$model$x, bands$lower1, col = "red", lty = "dotted") lines(fit2$model$x, bands$upper2, col = "blue", lty = "dotted") lines(fit2$model$x, bands$lower2, col = "blue", lty = "dotted") HTH G > ______________________________________________ > 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. -- %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% Dr. Gavin Simpson [t] +44 (0)20 7679 0522 ECRC, UCL Geography, [f] +44 (0)20 7679 0565 Pearson Building, [e] gavin.simpsonATNOSPAMucl.ac.uk Gower Street, London [w] http://www.ucl.ac.uk/~ucfagls/ UK. WC1E 6BT. [w] http://www.freshwaters.org.uk %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% ______________________________________________ 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.
