rms (version 5.1-2)

# fastbw: Fast Backward Variable Selection

## Description

Performs a slightly inefficient but numerically stable version of fast backward elimination on factors, using a method based on Lawless and Singhal (1978). This method uses the fitted complete model and computes approximate Wald statistics by computing conditional (restricted) maximum likelihood estimates assuming multivariate normality of estimates. `fastbw` deletes factors, not columns of the design matrix. Factors requiring multiple d.f. will be retained or dropped as a group. The function prints the deletion statistics for each variable in turn, and prints approximate parameter estimates for the model after deleting variables. The approximation is better when the number of factors deleted is not large. For `ols`, the approximation is exact for regression coefficients, and standard errors are only off by a factor equal to the ratio of the mean squared error estimate for the reduced model to the original mean squared error estimate for the full model.

If the fit was from `ols`, `fastbw` will compute the usual \(R^2\) statistic for each model.

## Usage

```fastbw(fit, rule=c("aic", "p"),
type=c("residual", "individual", "total"),  sls=.05, aics=0, eps=1e-9,
k.aic=2, force=NULL)# S3 method for fastbw
print(x, digits=4, estimates=TRUE, …)```

## Arguments

fit

fit object with `Varcov(fit)` defined (e.g., from `ols`, `lrm`, `cph`, `psm`, `glmD`)

rule

Stopping rule. Defaults to `"aic"` for Akaike's information criterion. Use `rule="p"` to use \(P\)-values

type

Type of statistic on which to base the stopping rule. Default is `"residual"` for the pooled residual chi-square. Use `type="individual"` to use Wald chi-square of individual factors.

sls

Significance level for staying in a model if `rule="p"`. Default is .05.

aics

For `rule="aic"`, variables are deleted until the chi-square - `k.aic` times d.f. would rise above `aics`. Default `aics` is zero to use the ordinary AIC. Set `aics` to say 10000 to see all variables deleted in order of descending importance.

eps

Singularity criterion, default is `1E-9`.

k.aic

multiplier to compute AIC, default is 2. To use BIC, set `k.aic` equal to \(\log(n)\), where \(n\) is the effective sample size (number of events for survival models).

force

a vector of integers specifying parameters forced to be in the model, not counting intercept(s)

x

result of `fastbw`

digits

number of significant digits to print

estimates

set to `FALSE` to suppress printing table of approximate coefficients, SEs, etc., after variable deletions

ignored

## Value

a list with an attribute `kept` if `bw=TRUE`, and the following components:

result

matrix of statistics with rows in order of deletion.

names.kept

names of factors kept in final model.

factors.kept

the subscripts of factors kept in the final model

factors.deleted

opposite of `factors.kept`.

parms.kept

column numbers in design matrix corresponding to parameters kept in the final model.

parms.deleted

opposite of `parms.kept`.

coefficients

vector of approximate coefficients of reduced model.

var

approximate covariance matrix for reduced model.

Coefficients

matrix of coefficients of all models. Rows correspond to the successive models examined and columns correspond to the coefficients in the full model. For variables not in a particular sub-model (row), the coefficients are zero.

## References

Lawless, J. F. and Singhal, K. (1978): Efficient screening of nonnormal regression models. Biometrics 34:318--327.

`rms`, `ols`, `lrm`, `cph`, `psm`, `validate`, `solvet`, `rmsMisc`

## Examples

Run this code
``````# NOT RUN {
fastbw(fit, optional.arguments)     # print results
z <- fastbw(fit, optional.args)     # typically used in simulations
lm.fit(X[,z\$parms.kept], Y)         # least squares fit of reduced model
# }
``````

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