[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 StreetWeb: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA
__
R-help@r-project.org mailing list
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [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-boun...@r-project.org [mailto:r-help-bounces@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 StreetWeb: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA
__
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.
__
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.
Re: [R] finding interpolated values along an empirical parametric curve
Thanks, John
That's very clever. I didn't realize that the splines package supports
multivariate regression
splines and that works well enough for my purposes; plus this solution
is very transparent.
best,
-Michael
On 12/5/2011 9:50 AM, John Fox wrote:
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-boun...@r-project.org [mailto:r-help-bounces@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 StreetWeb: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA
__
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.
--
Michael Friendly Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
York University Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele StreetWeb: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA
__
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.
