The `validate`

function when used on an object created by
`lrm`

or `orm`

does resampling validation of a logistic
regression model,
with or without backward step-down variable deletion. It provides
bias-corrected Somers' \(D_{xy}\) rank correlation, R-squared index,
the intercept and slope of an overall logistic calibration equation, the
maximum absolute difference in predicted and calibrated probabilities
\(E_{max}\), the discrimination index \(D\) (model L.R. \((\chi^2
- 1)/n\)), the unreliability index \(U\) =
difference in -2 log likelihood between un-calibrated \(X\beta\) and \(X\beta\) with overall intercept and slope
calibrated to test sample / n, the overall quality index (logarithmic
probability score) \(Q = D - U\), and the Brier or quadratic
probability score, \(B\) (the last 3 are not computed for ordinal
models), the \(g\)-index, and `gp`

, the \(g\)-index on the
probability scale. The corrected slope can be thought of as shrinkage
factor that takes into account overfitting. For `orm`

fits, a
subset of the above indexes is provided, Spearman's \(\rho\) is
substituted for \(D_{xy}\), and a new index is reported: `pdm`

, the mean
absolute difference between 0.5 and the predicted probability that
\(Y\geq\) the marginal median of \(Y\).

```
# fit <- lrm(formula=response ~ terms, x=TRUE, y=TRUE) or orm
# S3 method for lrm
validate(fit, method="boot", B=40,
bw=FALSE, rule="aic", type="residual", sls=0.05, aics=0,
force=NULL, estimates=TRUE,
pr=FALSE, kint, Dxy.method=if(k==1) 'somers2' else 'lrm',
emax.lim=c(0,1), …)
# S3 method for orm
validate(fit, method="boot", B=40, bw=FALSE, rule="aic",
type="residual", sls=.05, aics=0, force=NULL, estimates=TRUE,
pr=FALSE, ...)
```

fit

a fit derived by `lrm`

or `orm`

. The options `x=TRUE`

and
`y=TRUE`

must have been specified.

method,B,bw,rule,type,sls,aics,force,estimates,pr

see `validate`

and `predab.resample`

kint

In the case of an ordinal model, specify which intercept to validate.
Default is the middle intercept. For `validate.orm`

,
intercept-specific quantities are not validated so this does not matter.

Dxy.method

`"lrm"`

to use `lrm`

s computation of \(D_{xy}\) correlation,
which rounds predicted probabilities to nearest .002. Use
`Dxy.method="somers2"`

(the default) to instead use the more
accurate but slower `somers2`

function. This will matter most when
the model is extremely predictive. The default is `"lrm"`

for
ordinal models, since `somers2`

only handles binary response
variables.

emax.lim

range of predicted probabilities over which to compute the maximum error. Default is entire range.

…

other arguments to pass to `lrm.fit`

(now only `maxit`

and
`tol`

are allowed) and to `predab.resample`

(note especially
the `group`

, `cluster`

, and `subset`

parameters)

a matrix with rows corresponding to \(D_{xy}\),
\(R^2\), `Intercept`

, `Slope`

, \(E_{max}\), \(D\),
\(U\), \(Q\), \(B\), \(g\), \(gp\), and
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.
For `validate.orm`

not all columns are provided, Spearman's rho
is returned instead of \(D_{xy}\), and `pdm`

is reported.

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

If the original fit was created using penalized maximum likelihood estimation,
the same `penalty.matrix`

used with the original
fit are used during validation.

Miller ME, Hui SL, Tierney WM (1991): Validation techniques for logistic regression models. Stat in Med 10:1213--1226.

Harrell FE, Lee KL (1985): A comparison of the
*discrimination*
of discriminant analysis and logistic regression under multivariate
normality. In Biostatistics: Statistics in Biomedical, Public Health,
and Environmental Sciences. The Bernard G. Greenberg Volume, ed. PK
Sen. New York: North-Holland, p. 333--343.

`predab.resample`

, `fastbw`

, `lrm`

,
`rms`

, `rms.trans`

, `calibrate`

,
`somers2`

, `cr.setup`

,
`gIndex`

, `orm`

# NOT RUN { n <- 1000 # define sample size age <- rnorm(n, 50, 10) blood.pressure <- rnorm(n, 120, 15) cholesterol <- rnorm(n, 200, 25) sex <- factor(sample(c('female','male'), n,TRUE)) # Specify population model for log odds that Y=1 L <- .4*(sex=='male') + .045*(age-50) + (log(cholesterol - 10)-5.2)*(-2*(sex=='female') + 2*(sex=='male')) # Simulate binary y to have Prob(y=1) = 1/[1+exp(-L)] y <- ifelse(runif(n) < plogis(L), 1, 0) f <- lrm(y ~ sex*rcs(cholesterol)+pol(age,2)+blood.pressure, x=TRUE, y=TRUE) #Validate full model fit validate(f, B=10) # normally B=300 validate(f, B=10, group=y) # two-sample validation: make resamples have same numbers of # successes and failures as original sample #Validate stepwise model with typical (not so good) stopping rule validate(f, B=10, bw=TRUE, rule="p", sls=.1, type="individual") # } # NOT RUN { #Fit a continuation ratio model and validate it for the predicted #probability that y=0 u <- cr.setup(y) Y <- u$y cohort <- u$cohort attach(mydataframe[u$subs,]) f <- lrm(Y ~ cohort+rcs(age,4)*sex, penalty=list(interaction=2)) validate(f, cluster=u$subs, subset=cohort=='all') #see predab.resample for cluster and subset # }