Resampling Validation of a Fitted Model's Indexes of Fit

The validate function when used on an object created by one of the rms series does resampling validation of a regression model, with or without backward step-down variable deletion. The print method will call the latex or html method if options(prType=) is set to "latex" or "html". For "latex" printing through print(), the LaTeX table environment is turned off. When using html with Quarto or RMarkdown, results='asis' need not be written in the chunk header.

See predab.resample for information about confidence limits.

Usage

# fit <- fitting.function(formula=response ~ terms, x=TRUE, y=TRUE)
validate(fit, method="boot", B=40,
         bw=FALSE, rule="aic", type="residual", sls=0.05, aics=0, 
         force=NULL, estimates=TRUE, pr=FALSE, ...)
# S3 method for class 'validate'
print(x, digits=4, B=Inf, ...)
# S3 method for class 'validate'
latex(object, digits=4, B=Inf, file='', append=FALSE,
                         title=first.word(deparse(substitute(x))),
                         caption=NULL, table.env=FALSE,
                         size='normalsize', extracolsize=size, ...)
# S3 method for class 'validate'
html(object, digits=4, B=Inf, caption=NULL, ...)

Arguments

fit

a fit derived by e.g. lrm, cph, psm, ols. The options x=TRUE and y=TRUE must have been specified.

method

may be "crossvalidation", "boot" (the default), ".632", or "randomization". See predab.resample for details. Can abbreviate, e.g. "cross", "b", ".6".

B

number of repetitions. For method="crossvalidation", is the number of groups of omitted observations. For print.validate, latex.validate, and html.validate, B is an upper limit on the number of resamples for which information is printed about which variables were selected in each model re-fit. Specify zero to suppress printing. Default is to print all re-samples.

bw

TRUE to do fast step-down using the fastbw function, for both the overall model and for each repetition. fastbw keeps parameters together that represent the same factor.

rule

Applies if bw=TRUE. "aic" to use Akaike's information criterion as a stopping rule (i.e., a factor is deleted if the \(\chi^2\) falls below twice its degrees of freedom), or "p" to use \(P\)-values.

type

"residual" or "individual" - stopping rule is for individual factors or for the residual \(\chi^2\) for all variables deleted

sls

significance level for a factor to be kept in a model, or for judging the residual \(\chi^2\).

aics

cutoff on AIC when rule="aic".

force

see fastbw

estimates

see print.fastbw

pr

TRUE to print results of each repetition

...

parameters for each specific validate function, and parameters to pass to predab.resample (note especially the group, cluster, amd subset parameters). For latex, optional arguments to latex.default. Ignored for html.validate.

For psm, you can pass the maxiter parameter here (passed to survreg.control, default is 15 iterations) as well as a tol parameter for judging matrix singularity in solvet (default is 1e-12) and a rel.tolerance parameter that is passed to survreg.control (default is 1e-5).

For print.validate ... is ignored.

x,object

an object produced by one of the validate functions

digits

number of decimal places to print

file

file to write LaTeX output. Default is standard output.

append

set to TRUE to append LaTeX output to an existing file

title, caption, table.env, extracolsize

see latex.default. If table.env is FALSE and caption is given, the character string contained in caption will be placed before the table, centered.

size

size of LaTeX output. Default is 'normalsize'. Must be a defined LaTeX size when prepended by double slash.

Details

It provides bias-corrected indexes that are specific to each type of model. For validate.cph and validate.psm, see validate.lrm, which is similar.
For validate.cph and validate.psm, there is an extra argument dxy, which if TRUE causes the dxy.cens function to be invoked to compute the Somers' \(D_{xy}\) rank correlation to be computed at each resample. The values corresponding to the row \(D_{xy}\) are equal to \(2 * (C - 0.5)\) where C is the C-index or concordance probability.

For validate.cph with dxy=TRUE, you must specify an argument u if the model is stratified, since survival curves can then cross and \(X\beta\) is not 1-1 with predicted survival.
There is also validate method for tree, which only does cross-validation and which has a different list of arguments.

Value

a matrix with rows corresponding to the statistical indexes and columns for columns for the original index, resample estimates, indexes applied to the whole or omitted sample using the model derived from the resample, average optimism, corrected index, and number of successful re-samples.

Side Effects

prints a summary, and optionally statistics for each re-fit

Author

Frank Harrell
Department of Biostatistics, Vanderbilt University
fh@fharrell.com

Examples

# See examples for validate.cph, validate.lrm, validate.ols
# Example of validating a parametric survival model:

require(survival)
n <- 1000
set.seed(731)
age <- 50 + 12*rnorm(n)
label(age) <- "Age"
sex <- factor(sample(c('Male','Female'), n, TRUE))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
dt <- -log(runif(n))/h
e <- ifelse(dt <= cens,1,0)
dt <- pmin(dt, cens)
units(dt) <- "Year"
S <- Surv(dt,e)


f <- psm(S ~ age*sex, x=TRUE, y=TRUE)  # Weibull model
# Validate full model fit
validate(f, B=10)                # usually B=150
#>           index.orig training    test optimism index.corrected   Lower  Upper
#> Dxy           0.3854   0.3937  0.3789   0.0148          0.3706  0.2846 0.4076
#> R2            0.0918   0.1032  0.0881   0.0152          0.0766  0.0388 0.0896
#> Intercept     0.0000   0.0000  0.3467  -0.3467          0.3467 -0.3214 0.9523
#> Slope         1.0000   1.0000  0.9015   0.0985          0.9015  0.6851 1.0844
#> D             0.0449   0.0503  0.0430   0.0073          0.0376  0.0164 0.0447
#> U            -0.0012  -0.0011 -0.0017   0.0005         -0.0017 -0.0110 0.0008
#> Q             0.0461   0.0515  0.0447   0.0068          0.0393  0.0243 0.0452
#> g             0.7377   0.8071  0.7236   0.0835          0.6542  0.4520 0.7634
#>            n
#> Dxy       10
#> R2        10
#> Intercept 10
#> Slope     10
#> D         10
#> U         10
#> Q         10
#> g         10


# Validate stepwise model with typical (not so good) stopping rule
# bw=TRUE does not preserve hierarchy of terms at present
validate(f, B=10, bw=TRUE, rule="p", sls=.1, type="individual")
#> 
#> 		Backwards Step-down - Original Model
#> 
#>  Deleted   Chi-Sq d.f. P      Residual d.f. P      AIC  
#>  age * sex 0.98   1    0.3217 0.98     1    0.3217 -1.02
#> 
#> Approximate Estimates after Deleting Factors
#> 
#>                 Coef    S.E. Wald Z         P
#> (Intercept)  5.40012 0.37320 14.470 0.000e+00
#> age         -0.04254 0.00598 -7.114 1.127e-12
#> sex=Male     0.58686 0.14850  3.952 7.750e-05
#> 
#> Factors in Final Model
#> 
#> [1] age sex
#>           index.orig training    test optimism index.corrected   Lower  Upper
#> Dxy           0.3858   0.3942  0.3805   0.0137          0.3721  0.3078 0.4571
#> R2            0.0907   0.0981  0.0894   0.0087          0.0820  0.0301 0.1157
#> Intercept     0.0000   0.0000  0.0759  -0.0759          0.0759 -0.7556 0.9171
#> Slope         1.0000   1.0000  0.9799   0.0201          0.9799  0.7395 1.2519
#> D             0.0443   0.0481  0.0437   0.0044          0.0399  0.0134 0.0575
#> U            -0.0012  -0.0012 -0.0010  -0.0002         -0.0010 -0.0047 0.0012
#> Q             0.0455   0.0493  0.0447   0.0046          0.0409  0.0172 0.0583
#> g             0.6888   0.7217  0.6996   0.0220          0.6668  0.5233 0.8190
#>            n
#> Dxy       10
#> R2        10
#> Intercept 10
#> Slope     10
#> D         10
#> U         10
#> Q         10
#> g         10
#> 
#> Factors Retained in Backwards Elimination
#> 
#>  age sex age * sex
#>  *   *            
#>  *   *   *        
#>  *   *            
#>  *   *            
#>  *   *            
#>  *   *            
#>  *   *            
#>  *       *        
#>  *   *   *        
#>  *   *            
#> 
#> Frequencies of Numbers of Factors Retained
#> 
#> 2 3 
#> 8 2