predab.resample is a general-purpose
function that is used by functions for specific models.
It computes estimates of optimism of, and bias-corrected estimates of a vector
of indexes of predictive accuracy, for a model with a specified
design matrix, with or without fast backward step-down of predictors. If
bw=TRUE, the design
matrix
x must have been created by
ols,
lrm, or
cph.
If
bw=TRUE,
predab.resample prints a matrix of asterisks showing which
factors were selected at each repetition, along with a frequency distribution
of the number of factors retained across re-samples.
predab.resample(fit.orig, fit, measure,
method=c("boot","crossvalidation",".632","randomization"),
bw=FALSE, B=50, pr=FALSE,
rule="aic", type="residual", sls=.05, aics=0,
strata=FALSE, tol=1e-12, non.slopes.in.x=TRUE, kint=1,
cluster, subset, group=NULL, ...)
x=TRUE and
y=TRUE options specified to the model fitting function. This model
should be the FULL model including all candidate variables ever excluded
because of poor associations with the response.
x,
y,
iter,
penalty,
penalty.matrix,
xcol, and other arguments passed to
predab.resample.
If you don't want
iter
as an argument inside the definition of
fit, add ... to the end of its
argument list.
iter is passed to
fit to inform the function of the
sampling repetition number (0=original sample). If
bw=TRUE,
fit should
allow for the possibility of selecting no predictors, i.e., it should fit an
intercept-only model if the model has intercept(s).
fit must return
objects
coef and
fail (
fail=TRUE if
fit failed due to singularity or
non-convergence - these cases are excluded from summary statistics).
fit
must add design attributes to the returned object if
bw=TRUE.
The
penalty.matrix parameter is not used if
penalty=0. The
xcol
vector is a vector of columns of
X to be used in the current model fit.
For
ols and
psm it includes a
1 for the intercept position.
xcol is not defined if
iter=0 unless the initial fit had been from
a backward step-down.
xcol is used to select the correct rows and columns
of
penalty.matrix for the current variables selected, for example.
method=".632" or
method="crossval", it will make the most sense for
measure to compute only indexes that are independent of sample size. The
measure function should take the following arguments or use ...:
xbeta
(X beta for
current fit),
y,
evalfit,
fit,
iter, and
fit.orig.
iter is as in
fit.
evalfit is set to
TRUE
by
predab.resample if the fit is being evaluated on the sample used to make the
fit,
FALSE otherwise;
fit.orig is the fit object returned by the original fit on the whole
sample. Using
evalfit will sometimes save computations. For example, in
bootstrapping the area under an ROC curve for a logistic regression model,
lrm already computes the area if the fit is on the training sample.
fit.orig
is used to pass computed configuration parameters from the original fit such as
quantiles of predicted probabilities that are used as cut points in other samples.
The vector created by measure should have
names() associated with it.
"boot" for ordinary bootstrapping (Efron, 1983, Eq. 2.10).
Use
".632" for Efron's
.632 method (Efron, 1983, Section 6 and Eq. 6.10),
"crossvalidation"
for grouped cross–validation,
"randomization" for the randomization method. May
be abbreviated down to any level, e.g.
"b",
".",
"cross",
"rand".
TRUE to do fast backward step-down for each training sample. Default is
FALSE.
method="crossvalidation", this is also
the number of groups the original sample is split into.
TRUE to print results for each sample. Default is
FALSE.
"aic" or
"p". Default is
"aic" to use Akaike's
information criterion.
"residual" (the default) or
"individual".
rule="p". Default is
.05.
rule="aic". Stops deleting factors when
chi-square - 2 times d.f. falls below
aics. Default is
0.
TRUE if
fit.orig has an
x
element that contains a
"strata" attribute which is a vector
that should be sampled the same way as the observations in
x
and
y
fit and
fastbw.
FALSE if the design matrix
x
does not have columns for intercepts and these columns are needed
kint. This affects the linear
predictor that is passed to
measure.
method="boot". If it is present, the bootstrap is done using sampling
with replacement from the clusters rather than from the original records.
If this vector is not the same length as the number of rows in the data
matrix used in the fit, an attempt will be made to use
naresid on
fit.orig to conform
cluster to the data.
See
bootcov for more about this.
measure function compute measures of accuracy on
a subset of the data. The whole dataset is still used for all model development.
For example, you may want to
validate or
calibrate a model by
assessing the predictions on females when the fit was based on males and
females. When you use
cr.setup to build extra observations for fitting the
continuation ratio ordinal logistic model, you can use
subset to specify
which
cohort or observations to use for deriving indexes of predictive
accuracy. For example, specify
subset=cohort=="all" to validate the
model for the first layer of the continuation ratio model (Prob(Y=0)).
fit and
measure.
For
method=".632", the program stops with an error if every observation
is not omitted at least once from a bootstrap sample. Efron's ".632" method
was developed for measures that are formulated in terms on per-observation
contributions. In general, error measures (e.g., ROC areas) cannot be
written in this way, so this function uses a heuristic extension to
Efron's formulation in which it is assumed that the average error measure
omitting the
ith observation is the same as the average error measure
omitting any other observation. Then weights are derived
for each bootstrap repetition and weighted averages over the
B repetitions
can easily be computed.
measure, and the following columns:
training-test except for
method=".632" - is .632 times
(index.orig - test)
index.orig-optimism
Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu
Efron B, Tibshirani R (1997). Improvements on cross-validation: The .632+ bootstrap method. JASA 92:548–560.
# See the code for validate.ols for an example of the use of # predab.resample