The `validate`

function when used on an object created by
`ols`

does resampling validation of a multiple linear regression
model, with or without backward step-down variable deletion. Uses
resampling to estimate the optimism in various measures of predictive
accuracy which include \(R^2\), \(MSE\) (mean squared error with a
denominator of \(n\)), 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.ols`

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 \(0.5(D_{xy} +
1)\). The Nagelkerke-Maddala \(R^2\) index for the dichotomized
`y`

is also given. See `predab.resample`

for the list of
resampling methods.

The LaTeX needspace package must be in effect to use the `latex`

method.

```
# fit <- fitting.function(formula=response ~ terms, x=TRUE, y=TRUE)
# S3 method for ols
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, …)
```

fit

a fit derived by `ols`

. The options `x=TRUE`

and `y=TRUE`

must have been specified. See `validate`

for a description of
arguments `method`

- `pr`

.

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

see
`validate`

and `predab.resample`

and
`fastbw`

u

If specifed, `y`

is also dichotomized at the cutoff `u`

for
the purpose of getting a bias-corrected estimate of \(D_{xy}\).

rel

relationship for dichotomizing predicted `y`

. Defaults to
`">"`

to use `y>u`

. `rel`

can also be `"<"`

,
`">="`

, and `"<="`

.

tolerance

tolerance for singularity; passed to `lm.fit.qr`

.

…

other arguments to pass to `predab.resample`

, such as `group`

, `cluster`

, and `subset`

matrix with rows corresponding to R-square, MSE, g, intercept, slope, and optionally \(D_{xy}\) and \(R^2\), 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.

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

`ols`

, `predab.resample`

, `fastbw`

,
`rms`

, `rms.trans`

, `calibrate`

,
`gIndex`

# 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 <- ols(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") # }