Fast Backward Variable Selection

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.

models, regression, htest
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, \dots)

fit object with Varcov(fit) defined (e.g., from ols, lrm, cph, psm, glmD)
Stopping rule. Defaults to "aic" for Akaike's information criterion. Use rule="p" to use $P$-values
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.
Significance level for staying in a model if rule="p". Default is .05.
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 dele
Singularity criterion, default is 1E-9.
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).
result of fastbw
number of significant digits to print

  • a list with the following components:
  • resultmatrix of statistics with rows in order of deletion.
  • names.keptnames of factors kept in final model.
  • factors.keptthe subscripts of factors kept in the final model
  • factors.deletedopposite of factors.kept.
  • parms.keptcolumn numbers in design matrix corresponding to parameters kept in the final model.
  • parms.deletedopposite of parms.kept.
  • coefficientsvector of approximate coefficients of reduced model.
  • varapproximate covariance matrix for reduced model.
  • Coefficientsmatrix 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.


  • stepwise
  • variable selection


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

See Also

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

  • fastbw
  • print.fastbw
fastbw(fit, optional.arguments)     # print results
z <- fastbw(fit, optional.args)     # typically used in simulations[,z$parms.kept], Y)         # least squares fit of reduced model
Documentation reproduced from package rms, version 2.0-2, License: GPL (>= 2)

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