validate.Rq
Validation of a Quantile Regression Model
The validate function when used on an object created by
Rq does resampling validation of a quantile regression
model, with or without backward step-down variable deletion. Uses
resampling to estimate the optimism in various measures of predictive
accuracy which include mean absolute prediction error (MAD), Spearman
rho, the \(g\)-index, and the intercept and slope
of an overall
calibration \(a + b\hat{y}\). The "corrected"
slope can be thought of as shrinkage factor that takes into account
overfitting. validate.Rq can also be used when a model for a
continuous response is going to be applied to a binary response. A
Somers' \(D_{xy}\) for this case is computed for each resample by
dichotomizing y. This can be used to obtain an ordinary receiver
operating characteristic curve area using the formula \(0.5(D_{xy} +
1)\). See predab.resample for the list of
resampling methods.
The LaTeX needspace package must be in effect to use the
latex method.
- Keywords
- models, regression
Usage
# fit <- fitting.function(formula=response ~ terms, x=TRUE, y=TRUE)
# S3 method for Rq
validate(fit, method="boot", B=40,
bw=FALSE, rule="aic", type="residual", sls=0.05, aics=0,
force=NULL, estimates=TRUE, pr=FALSE, u=NULL, rel=">",
tolerance=1e-7, …)Arguments
- fit
a fit derived by
Rq. The optionsx=TRUEandy=TRUEmust have been specified. Seevalidatefor a description of argumentsmethod-pr.- method,B,bw,rule,type,sls,aics,force,estimates,pr
see
validateandpredab.resampleandfastbw- u
If specifed,
yis also dichotomized at the cutoffufor the purpose of getting a bias-corrected estimate of \(D_{xy}\).- rel
relationship for dichotomizing predicted
y. Defaults to">"to usey>u.relcan also be"<",">=", and"<=".- tolerance
ignored
- …
other arguments to pass to
predab.resample, such asgroup,cluster, andsubset
Value
matrix with rows corresponding to various indexes, and optionally \(D_{xy}\), and columns for the original index, resample estimates, indexes applied to whole or omitted sample using model derived from resample, average optimism, corrected index, and number of successful resamples.
Side Effects
prints a summary, and optionally statistics for each re-fit
See Also
Examples
# NOT RUN {
set.seed(1)
x1 <- runif(200)
x2 <- sample(0:3, 200, TRUE)
x3 <- rnorm(200)
distance <- (x1 + x2/3 + rnorm(200))^2
f <- Rq(sqrt(distance) ~ rcs(x1,4) + scored(x2) + x3, x=TRUE, y=TRUE)
#Validate full model fit (from all observations) but for x1 < .75
validate(f, B=20, subset=x1 < .75) # normally B=300
#Validate stepwise model with typical (not so good) stopping rule
validate(f, B=20, bw=TRUE, rule="p", sls=.1, type="individual")
# }