Stepwise Selection Procedure for Multi-Parameter Regression (MPR) Models
Applies a stepwise selection procedure to an object of class “
mpr” to find the best model
in the sense of AIC (or BIC).
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an object of class “
either a single formula defining the
a numeric vector indicating the regression component(s) to which the selection procedure should be
applied. Note that “
the mode of stepwise search, which can be one of
if positive, information is printed during the running of
additional arguments to be passed to internal methods.
stepmpr uses repeated calls to
dropterm and is based on the idea that variable selection should be applied to
each component individually and to all components jointly (when
joint = TRUE). As an example,
consider the case where forward selection (
direction = "forward") will be carried out in components
1 and 2 individually (
comp = 1:2) and jointly (
joint = TRUE). At a given iteration of
the algorithm, the following single-term additions are then carried out:
- individual step
each term currently absent from component 1 will be considered.
- individual step
each term currently absent from component 2 will be considered.
- joint step
each term currently absent from both components 1 and 2 will be considered.
The reason for the joint step is to account for the possibility that a covariate may only appear significant
when it is present simultaneously in both regression components. This situation can arise as the
variance-covariance matrix for the estimated regression coefficients is typically not block diagonal with
respect to the regression components and, in particular, coefficients for the same covariate in
different components are typically highly correlated. Of course, the
stepmpr function has the
flexibility to carry individual steps only, joint steps only or individual steps in a particular component
only as the end user prefers. See “Examples” below.
The set of models searched is determined by the
scope argument which is either a single
upper formula or a list whose elements are
upper formulae. The
upper formula must contain each formula corresponding to the components under
consideration (as indicated by
comp) whereas the
lower formula must be contained
within each of these formulae. For more information on the use of
scope is missing, the
lower model is simply the null model (i.e., a model with no
covariates) and the
upper model is formed using terms from the initial model; specifically,
all terms from the regession components under consideration (as indicated by
comp) are used
A final “best”
mpr model as selected using the stepwise procedure.
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# Veterans' administration lung cancer data data(veteran, package="survival") head(veteran) ####### mod0 <- mpr(Surv(time, status) ~ 1, data=veteran) mod0 # family = "Weibull" by default # the "upper" model formula (by default the lower will be ~ 1) scope <- ~ trt + celltype stepmpr(mod0, scope) stepmpr(mod0, scope, direction="forward", aic=FALSE) # individual steps only stepmpr(mod0, scope, joint=FALSE) # joint steps only stepmpr(mod0, scope, jointonly=TRUE) # component 1 only (and, hence, only individual steps) stepmpr(mod0, scope, comp=1) ####### mod1 <- mpr(Surv(time, status) ~ trt + celltype, data=veteran) mod1 stepmpr(mod1) stepmpr(mod1, scope = ~ .^2) # "lower" model formula forces trt to stay in stepmpr(mod1, scope = list(~trt, ~.))