rms: validate.ols – R documentation

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validate.ols

Validation of an Ordinary Linear Model

Description

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 * (predicted 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.

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, 
         force=NULL, estimates=TRUE, pr=FALSE, u=NULL, rel=">",
         tolerance=1e-7, ...)

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,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`

Value

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.

Side Effects

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

Author(s)

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

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=300

#Validate stepwise model with typical (not so good) stopping rule
validate(f, B=20, bw=TRUE, rule="p", sls=.1, type="individual")

rms

Regression Modeling Strategies

v6.2-0

GPL (>= 2)

Authors

Frank E Harrell Jr <fh@fharrell.com>

Initial release

2021-03-17