fastbw {Design} | R Documentation

## 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="aic", type="residual", sls=.05, aics=0, eps=1e-9, k.aic=2)

    ## S3 method for class 'fastbw':
    print(x, digits=4, ...)

### Arguments

`fit` | fit object with `Varcov(fit)` defined (e.g., from `ols`, `lrm`, `cph`, `psm`, `lm`, `glm`)
`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. falls below `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).
`x` | result of `fastbw`
`digits` | number of significant digits to print
`...` | ignored

### Value

a list with 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.

### Author(s)

Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu

### References

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

### See Also

`Design`, `ols`, `lrm`, `cph`, `psm`, `validate`, `solvet`, `Design.Misc`

### Examples

    ## 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
    ## End(Not run)

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