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
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
fastbw will compute the usual $R^2$
statistic for each model.
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
- 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.
rule="aic", variables are deleted until the chi-square -
k.aictimes d.f. falls below
aicsis zero to use the ordinary AIC. Set
aicsto say 10000 to see all variables dele
- Singularity criterion, default is
- multiplier to compute AIC, default is 2. To use BIC, set
k.aicequal to $\log(n)$, where $n$ is the effective sample size (number of events for survival models).
- result of
- number of significant digits to print
- 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
parms.kept column numbers in design matrix corresponding to parameters kept in the final model. parms.deleted opposite of
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.
- variable selection
Lawless, J. F. and Singhal, K. (1978): Efficient screening of nonnormal regression models. Biometrics 34:318--327.
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