# validate.ols

From rms v2.0-2
0th

Percentile

##### Validation of an Ordinary Linear Model

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 $n$), 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.

Keywords
models, regression
##### Usage
# fit <- fitting.function(formula=response ~ terms, x=TRUE, y=TRUE)
## S3 method for class 'ols':
validate(fit, method="boot", B=40,
bw=FALSE, rule="aic", type="residual", sls=0.05, aics=0,
pr=FALSE, u=NULL, rel=">", tolerance=1e-7, \dots)
##### Arguments
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
pr
see validate and predab.resample
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 "<"< code="">, ">=", and "<="< code="">.
tolerance
tolerance for singularity; passed to lm.fit.qr.
...
other arguments to pass to predab.resample, such as group, cluster, and subset
##### Value

• matrix with rows corresponding to R-square, MSE, 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.

##### Side Effects

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

##### concept

• model validation
• bootstrap
• predictive accuracy

ols, predab.resample, fastbw, rms, rms.trans, calibrate

• validate.ols
##### Examples
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=150

#Validate stepwise model with typical (not so good) stopping rule
validate(f, B=20, bw=TRUE, rule="p", sls=.1, type="individual")
Documentation reproduced from package rms, version 2.0-2, License: GPL (>= 2)

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