| tram-methods {tram} | R Documentation |
Methods for Stratified Linear Transformation Models
Description
Methods for objects inheriting from class tram
Usage
## S3 method for class 'tram'
as.mlt(object)
## S3 method for class 'tram'
model.frame(formula, ...)
## S3 method for class 'tram'
model.matrix(object, data = object$data, with_baseline = FALSE, ...)
## S3 method for class 'stram'
model.matrix(object, data = object$data, with_baseline = FALSE,
what = c("shifting", "scaling"), ...)
## S3 method for class 'tram'
coef(object, with_baseline = FALSE, ...)
## S3 method for class 'Lm'
coef(object, as.lm = FALSE, ...)
## S3 method for class 'Survreg'
coef(object, as.survreg = FALSE, ...)
## S3 method for class 'tram'
vcov(object, with_baseline = FALSE, complete = FALSE, ...)
## S3 method for class 'tram'
logLik(object, parm = coef(as.mlt(object), fixed = FALSE), ...)
## S3 method for class 'tram'
estfun(x, parm = coef(as.mlt(x), fixed = FALSE), ...)
## S3 method for class 'tram'
predict(object, newdata = model.frame(object),
type = c("lp", "trafo", "distribution", "logdistribution",
"survivor", "logsurvivor", "density", "logdensity",
"hazard", "loghazard", "cumhazard", "logcumhazard",
"odds", "logodds", "quantile"), ...)
## S3 method for class 'stram'
predict(object, newdata = model.frame(object),
type = c("lp", "trafo", "distribution", "logdistribution",
"survivor", "logsurvivor", "density", "logdensity",
"hazard", "loghazard", "cumhazard", "logcumhazard",
"odds", "logodds", "quantile"),
what = c("shifting", "scaling"), ...)
## S3 method for class 'tram'
plot(x, newdata = model.frame(x),
which = c("QQ-PIT", "baseline only", "distribution"),
confidence = c("none", "interval", "band"), level = 0.95,
K = 50, cheat = K, col = "black", fill = "lightgrey", lwd = 1, ...)
## S3 method for class 'tram'
residuals(object, ...)
## S3 method for class 'tram'
PI(object, newdata = model.frame(object), reference = 0,
one2one = FALSE, ...)
## Default S3 method:
PI(object, prob, link = "logistic", ...)
## S3 method for class 'tram'
OVL(object, newdata = model.frame(object), reference = 0,
one2one = FALSE, ...)
## Default S3 method:
OVL(object, link = "logistic", ...)
## S3 method for class 'tram'
TV(object, newdata = model.frame(object), reference = 0,
one2one = FALSE, ...)
## Default S3 method:
TV(object, link = "logistic", ...)
## S3 method for class 'tram'
L1(object, newdata = model.frame(object), reference = 0,
one2one = FALSE, ...)
## Default S3 method:
L1(object, link = "logistic", ...)
## S3 method for class 'tram'
ROC(object, newdata = model.frame(object), reference = 0,
prob = 1:99 / 100, one2one = FALSE, ...)
## Default S3 method:
ROC(object, prob = 1:99 / 100, link = "logistic", ...)
## S3 method for class 'ROCtram'
plot(x, lty = 1:ncol(x), col = "black",
fill = "lightgrey", lwd = 1, ...)
Arguments
object, formula, x |
a fitted stratified linear transformation model inheriting
from class |
data |
an optional data frame. |
with_baseline |
logical, if |
as.lm |
logical, return parameters in the |
as.survreg |
logical, return parameters in the |
parm |
model parameters, including baseline parameters. |
complete |
currently ignored |
newdata |
an optional data frame of new observations. |
reference |
an optional data frame of reference observations, or a numeric vector of reference values. |
type |
type of prediction, current options include
linear predictors ( |
which |
type of plot, either a QQ plot of the probability-integral
transformed observations ( |
what |
type of model matrix / linear predictor: |
confidence |
type of uncertainty assessment. |
level |
confidence level. |
K |
number of grid points in the response, see
|
cheat |
reduced number of grid points for the computation
of confidence bands, see |
col |
line color. |
fill |
fill color. |
lwd |
line width. |
lty |
line type. |
prob |
a numeric vector of probabilities.. |
link |
a character identifying a link function. |
one2one |
logical, compute the ROC curve (and derived measures)
comparing each row in |
... |
additional arguments to the underlying methods for class
|
Details
coef can be used to get (and set) model parameters,
logLik evaluates the log-likelihood (also for
parameters other than the maximum likelihood estimate);
vcov returns the estimated variance-covariance matrix (possibly
taking cluster into account) and
and estfun gives the score contribution by each observation.
predict and plot can be used to inspect the model on
different scales.
PI computes the probabilistic index (or concordance probability or
AUC) for all observations in newdata, relative to reference,
ie the probability
P(Y_1 \le Y_0 \mid x_0, x_1)
of observing a smaller value of a randomly sampled observation conditional
on x_1 compared to a randomly sampled reference observation, which
is conditional on x_0. This is equivalent to the area under the
receiver operating curve (ROC). The probability only applies within
strata, response-varying coefficients are not allowed.
Under the same setup, OVL gives the overlap coefficient, which is
one minus the total variation and one minus half the L_1 distance
between the two conditional densities. The overlap coefficient is
identical to the Youden index and the Smirnov statistic.
PI and friends also accept an argument conf.level which
triggers computation of simultaneous
Wald confidence intervals for these measures.
Arguments in ... are forwarded to glht.
References
Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110–134, doi:10.1111/sjos.12291.
See Also
Examples
data("BostonHousing2", package = "mlbench")
### fit non-normal Box-Cox type linear model with two
### baseline functions (for houses near and off Charles River)
BC_BH_2 <- BoxCox(cmedv | 0 + chas ~ crim + zn + indus + nox +
rm + age + dis + rad + tax + ptratio + b + lstat,
data = BostonHousing2)
logLik(BC_BH_2)
### classical likelihood inference
summary(BC_BH_2)
### coefficients of the linear predictor
coef(BC_BH_2)
### plot linear predictor (mean of _transformed_ response)
### vs. observed values
plot(predict(BC_BH_2, type = "lp"), BostonHousing2$cmedv)
### all coefficients
coef(BC_BH_2, with_baseline = TRUE)
### compute predicted median along with 10% and 90% quantile for the first
### observations
predict(BC_BH_2, newdata = BostonHousing2[1:3,], type = "quantile",
prob = c(.1, .5, .9))
### plot the predicted density for these observations
plot(BC_BH_2, newdata = BostonHousing2[1:3, -1],
which = "distribution", type = "density", K = 1000)
### evaluate the two baseline transformations, with confidence intervals
nd <- model.frame(BC_BH_2)[1:2, -1]
nd$chas <- factor(c("0", "1"))
library("colorspace")
col <- diverge_hcl(2, h = c(246, 40), c = 96, l = c(65, 90))
fill <- diverge_hcl(2, h = c(246, 40), c = 96, l = c(65, 90), alpha = .3)
plot(BC_BH_2, which = "baseline only", newdata = nd, col = col,
confidence = "interval", fill = fill, lwd = 2,
xlab = "Median Value", ylab = expression(h[Y]))
legend("bottomright", lty = 1, col = col,
title = "Near Charles River", legend = c("no", "yes"), bty = "n")
### cars data; with quantile functions
plot(dist ~ speed, data = cars)
m <- Colr(dist ~ speed, data = cars)
q <- predict(as.mlt(m), newdata = data.frame(speed = s <- 6:25),
type = "quantile", prob = c(1, 5, 9) / 10)
lines(s, q[1,])
lines(s, q[2,])
lines(s, q[3,])
nd <- data.frame(speed = s <- as.double(1:5 * 5))
# Prob(dist at speed s > dist at speed 0)
# speed 0 is reference, not a good choice here
PI(m, newdata = nd)
# Prob(dist at speed s > dist at speed 15)
lp15 <- c(predict(m, newdata = data.frame(speed = 15)))
PI(m, newdata = nd, reference = lp15)
PI(m, newdata = nd, reference = nd[3,,drop = FALSE])
# Prob(dist at speed s' > dist at speed s)
PI(m, newdata = nd, reference = nd)
# essentially:
lp <- predict(m, newdata = nd)
PI(object = dist(lp))
# same, with simultaneous confidence intervals
PI(m, newdata = nd, reference = nd, conf.level = .95)
# plot ROC curves + confidence bands
# compare speed 20 and 25 to speed 15
plot(ROC(m, newdata = nd[4:5,,drop = FALSE],
reference = nd[3,,drop = FALSE],
conf.level = 0.95))
# Overlap of conditional densities at speed s' and s
OVL(m, newdata = nd, reference = nd)
### ROC analysis (takes too long for CRAN Windows)
if (require("mlbench") && .Platform$OS.type != "windows") {
layout(matrix(1:4, nrow = 2))
data("PimaIndiansDiabetes2", package = "mlbench")
dia <- sort(unique(PimaIndiansDiabetes2$diabetes))
nd <- data.frame(diabetes = dia,
age = 29, mass = 32) ### median values
### unconditional ROC analysis: glucose tolerance test
m0 <- Colr(glucose ~ diabetes, data = PimaIndiansDiabetes2)
# ROC curve + confidence band
plot(ROC(m0, newdata = nd[2,,drop = FALSE], conf.level = .95))
# Wald interval for AUC
PI(m0, newdata = nd[2,,drop = FALSE], conf.level = .95)
# score interval for AUC
PI(-c(coef(m0), score_test(m0)$conf.int[2:1]))
### adjusted ROC analysis for age and mass
m1 <- Colr(glucose ~ diabetes + age + mass, data = PimaIndiansDiabetes2)
# ROC curve + confidence band (this is the same for all ages /
# masses)
plot(ROC(m1, newdata = nd[2,,drop = FALSE],
reference = nd[1,,drop = FALSE],
conf.level = .95))
# Wald interval for adjusted AUC
PI(m1, newdata = nd[2,,drop = FALSE], reference = nd[1,,drop = FALSE],
conf.level = .95)
# Score interval for adjusted AUC
PI(-c(coef(m1)[1], score_test(m1, names(coef(m1))[1])$conf.int[2:1]))
### conditional ROC analysis: AUC regression ~ age + mass
m2 <- Colr(glucose ~ diabetes * (age + mass), data = PimaIndiansDiabetes2)
# ROC curve for a person with age = 29 and mass = 32
plot(ROC(m2, newdata = nd[2,,drop = FALSE],
reference = nd[1,,drop = FALSE],
conf.level = .95))
# AUC for persons ages 21:81, all with mass = 32
nd1 <- data.frame(diabetes = nd[1,"diabetes"], age = 21:81, mass = 32)
nd2 <- data.frame(diabetes = nd[2,"diabetes"], age = 21:81, mass = 32)
auc <- PI(m2, newdata = nd2, reference = nd1, one2one = TRUE,
conf.level = 0.95)
plot(nd1$age, auc[, "Estimate"], xlab = "Age (in years)", ylab =
"AUC", ylim = c(0, 1), type = "l")
lines(nd1$age, auc[, "lwr"], lty = 3)
lines(nd1$age, auc[, "upr"], lty = 3)
}