Michael Friendly
2011-Dec-05 14:16 UTC
[R] finding interpolated values along an empirical parametric curve
Given the following data, I am plotting log.det ~ norm.beta, where the
points depend on a parameter, lambda
(but there is no functional form).
I want to find the (x,y) positions along this curve corresponding to two
special values of lambda
lambda.HKB <- 0.004275357
lambda.LW <- 0.03229531
and draw reference lines at ~ -45 degrees (or normal to the curve) thru
these points.
How can I do this? A complete example is below
> pd
lambda log.det norm.beta
0.000 0.000 -12.92710 3.806801
0.005 0.005 -14.41144 2.819460
0.010 0.010 -15.41069 2.423197
0.020 0.020 -16.82581 2.010924
0.040 0.040 -18.69819 1.611304
0.080 0.080 -21.05065 1.283928
>
pd <-
structure(list(lambda = c(0, 0.005, 0.01, 0.02, 0.04, 0.08),
log.det = c(-12.9270978142337, -14.411442487768, -15.4106886674014,
-16.8258120792945, -18.6981870228698, -21.050646106925),
norm.beta = c(3.8068008759562, 2.81945995964196, 2.42319655878575,
2.01092421747594, 1.6113040561427, 1.28392804825009)), .Names =
c("lambda",
"log.det", "norm.beta"), class = "data.frame",
row.names = c("0.000",
"0.005", "0.010", "0.020", "0.040",
"0.080"))
clr <- c("black", rainbow(5, start=.6, end=.1))
lambdaf <- c(expression(~widehat(beta)^OLS), ".005",
".01", ".02",
".04", ".08")
op <- par(mar=c(4, 4, 1, 1) + 0.2, xpd=TRUE)
with(pd, {plot(norm.beta, log.det, type="b",
cex.lab=1.25, pch=16, cex=1.5, col=clr,
xlab='shrinkage: ||b||',
ylab='variance: log |(Var(b)|)')
text(norm.beta, log.det, lambdaf, cex=1.25, pos=2)
text(min(norm.beta), max(log.det), "Variance vs. Shrinkage",
cex=1.5, pos=4)
})
# How to find the (x,y) positions for these values of lambda along the
curve of log.det ~ norm.beta ?
lambda.HKB <- 0.004275357
lambda.LW <- 0.03229531
--
Michael Friendly Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
York University Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street Web: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA
John Fox
2011-Dec-05 14:50 UTC
[R] finding interpolated values along an empirical parametric curve
Hi Michael, I can get what appears to be a good interpolation with a regression spline in a multivariate LM, playing around with the tuning parameter to leave 1 residual df. Try this: library(splines) mod <- lm(cbind(log.det, norm.beta) ~ bs(lambda, df=4), data=pd) summary(mod) x <- data.frame(lambda=seq(min(pd$lambda), max(pd$lambda), length=100)) fit <- predict(mod, newdata=x) points(fit[, "norm.beta"], fit[, "log.det"], pch=16, cex=0.5) x.2 <- data.frame(lambda=c(lambda.HKB, lambda.LW)) fit.2 <- predict(mod, x.2) points(fit.2[, "norm.beta"], fit.2[, "log.det"], pch=15, col="green") That doesn't solve the problem of calculating the normal, however. I hope this helps, John> -----Original Message----- > From: r-help-bounces at r-project.org [mailto:r-help-bounces at r- > project.org] On Behalf Of Michael Friendly > Sent: December-05-11 9:16 AM > To: R-help > Subject: [R] finding interpolated values along an empirical parametric > curve > > Given the following data, I am plotting log.det ~ norm.beta, where the > points depend on a parameter, lambda (but there is no functional form). > I want to find the (x,y) positions along this curve corresponding to > two special values of lambda > > lambda.HKB <- 0.004275357 > lambda.LW <- 0.03229531 > > and draw reference lines at ~ -45 degrees (or normal to the curve) thru > these points. > How can I do this? A complete example is below > > > pd > lambda log.det norm.beta > 0.000 0.000 -12.92710 3.806801 > 0.005 0.005 -14.41144 2.819460 > 0.010 0.010 -15.41069 2.423197 > 0.020 0.020 -16.82581 2.010924 > 0.040 0.040 -18.69819 1.611304 > 0.080 0.080 -21.05065 1.283928 > > > > pd <- > structure(list(lambda = c(0, 0.005, 0.01, 0.02, 0.04, 0.08), > log.det = c(-12.9270978142337, -14.411442487768, - > 15.4106886674014, > -16.8258120792945, -18.6981870228698, -21.050646106925), > norm.beta = c(3.8068008759562, 2.81945995964196, 2.42319655878575, > 2.01092421747594, 1.6113040561427, 1.28392804825009)), .Names > c("lambda", "log.det", "norm.beta"), class = "data.frame", row.names > c("0.000", "0.005", "0.010", "0.020", "0.040", "0.080")) > > clr <- c("black", rainbow(5, start=.6, end=.1)) lambdaf <- > c(expression(~widehat(beta)^OLS), ".005", ".01", ".02", ".04", ".08") > op <- par(mar=c(4, 4, 1, 1) + 0.2, xpd=TRUE) with(pd, {plot(norm.beta, > log.det, type="b", > cex.lab=1.25, pch=16, cex=1.5, col=clr, > xlab='shrinkage: ||b||', > ylab='variance: log |(Var(b)|)') > text(norm.beta, log.det, lambdaf, cex=1.25, pos=2) > text(min(norm.beta), max(log.det), "Variance vs. Shrinkage", > cex=1.5, pos=4) > }) > > > # How to find the (x,y) positions for these values of lambda along the > curve of log.det ~ norm.beta ? > lambda.HKB <- 0.004275357 > lambda.LW <- 0.03229531 > > -- > Michael Friendly Email: friendly AT yorku DOT ca > Professor, Psychology Dept. > York University Voice: 416 736-5115 x66249 Fax: 416 736-5814 > 4700 Keele Street Web: http://www.datavis.ca > Toronto, ONT M3J 1P3 CANADA > > ______________________________________________ > R-help at 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.