VGAM (version 1.1-8)

lms.bcg: LMS Quantile Regression with a Box-Cox transformation to a Gamma Distribution

Description

LMS quantile regression with the Box-Cox transformation to the gamma distribution.

Usage

lms.bcg(percentiles = c(25, 50, 75), zero = c("lambda", "sigma"),
   llambda = "identitylink", lmu = "identitylink", lsigma = "loglink",
   idf.mu = 4, idf.sigma = 2, ilambda = 1, isigma = NULL)

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm,

rrvglm

and vgam.

Arguments

percentiles

A numerical vector containing values between 0 and 100, which are the quantiles. They will be returned as `fitted values'.

zero

See lms.bcn. See CommonVGAMffArguments for more information.

llambda, lmu, lsigma

See lms.bcn.

idf.mu, idf.sigma

See lms.bcn.

ilambda, isigma

See lms.bcn.

Author

Thomas W. Yee

Warning

This VGAM family function comes with the same warnings as lms.bcn. Also, the expected value of the second derivative with respect to lambda may be incorrect (my calculations do not agree with the Lopatatzidis and Green manuscript.)

Details

Given a value of the covariate, this function applies a Box-Cox transformation to the response to best obtain a gamma distribution. The parameters chosen to do this are estimated by maximum likelihood or penalized maximum likelihood. Similar details can be found at lms.bcn.

References

Lopatatzidis A. and Green, P. J. (unpublished manuscript). Semiparametric quantile regression using the gamma distribution.

Yee, T. W. (2004). Quantile regression via vector generalized additive models. Statistics in Medicine, 23, 2295--2315.

See Also

lms.bcn, lms.yjn, qtplot.lmscreg, deplot.lmscreg, cdf.lmscreg, bmi.nz, amlexponential.

Examples

# This converges, but deplot(fit) and qtplot(fit) do not work
fit0 <- vglm(BMI ~ sm.bs(age, df = 4), lms.bcg, bmi.nz, trace = TRUE)
coef(fit0, matrix = TRUE)
if (FALSE) {
par(mfrow = c(1, 1))
plotvgam(fit0, se = TRUE)  # Plot mu function (only)
}

# Use a trick: fit0 is used for initial values for fit1.
fit1 <- vgam(BMI ~ s(age, df = c(4, 2)), etastart = predict(fit0),
             lms.bcg(zero = 1), bmi.nz, trace = TRUE)

# Difficult to get a model that converges.  Here, we prematurely
# stop iterations because it fails near the solution.
fit2 <- vgam(BMI ~ s(age, df = c(4, 2)), maxit = 4,
             lms.bcg(zero = 1, ilam = 3), bmi.nz, trace = TRUE)
summary(fit1)
head(predict(fit1))
head(fitted(fit1))
head(bmi.nz)
# Person 1 is near the lower quartile of BMI amongst people his age
head(cdf(fit1))

if (FALSE) {
# Quantile plot
par(bty = "l", mar=c(5, 4, 4, 3) + 0.1, xpd = TRUE)
qtplot(fit1, percentiles=c(5, 50, 90, 99), main = "Quantiles",
       xlim = c(15, 90), las = 1, ylab = "BMI", lwd = 2, lcol = 4)

# Density plot
ygrid <- seq(15, 43, len = 100)  # BMI ranges
par(mfrow = c(1, 1), lwd = 2)
(aa <- deplot(fit1, x0 = 20, y = ygrid, xlab = "BMI", col = "black",
  main = "PDFs at Age = 20 (black), 42 (red) and 55 (blue)"))
aa <- deplot(fit1, x0 = 42, y = ygrid, add=TRUE, llty=2, col="red")
aa <- deplot(fit1, x0 = 55, y = ygrid, add=TRUE, llty=4, col="blue",
             Attach = TRUE)
aa@post$deplot  # Contains density function values
}