This isn't a question about R, but I'm hoping someone will be willing to help. I've been looking at calibration plots in multiple regression (plotting observed response Y on the vertical axis versus predicted response [Y hat] on the horizontal axis).
According to Frank Harrell's "Regression Modeling Strategies" book (pp. 61-63), when making such a plot on new data (having obtained a model from other data) we should expect the points to be around a line with slope < 1, indicating overfitting. As he writes, "Typically, low predictions will be too low and high predictions too high." However, when I make these plots, both with real data and with simple simulated data, I get the opposite: the points are scattered around a line with slope >1. Low predictions are too high and high predictions are too low. For example, I generated 200 cases, fitted models on the first half of the data, and made calibration plots for those models on the second half of the data: > x1 <- rnorm(200, 0, 1) > x2 <- rnorm(200, 0, 1) > x3 <- rnorm(200, 0, 1) > x4 <- rnorm(200, 0, 1) > x5 <- rnorm(200, 0, 1) > x6 <- rnorm(200, 0, 1) > y <- x1 + x2 + rnorm(200, 0, 2) > d <- data.frame(y, x1, x2, x3, x4, x5, x6) > > lm1 <- lm(y ~ ., data = d[1:100,]) > lm2 <- lm(y ~ x1 + x2, data = d[1:100,]) > > plot(predict(lm1, d[101:200, ]), d$y[101:200]); abline(0,1) > x11(); plot(predict(lm2, d[101:200, ]), d$y[101:200]); abline(0,1) The plots for both lm1 and lm2 show the points scattered around a line with slope > 1, contrary to what Frank Harrell says should happen. I am either misunderstanding something or making a mistake in the code (I'm almost 100% certain I'm not mixing up the axes). I would be most appreciative if anyone could explain where I'm going wrong. Thanks for any help you can provide. Mark Seeto ______________________________________________ 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.
