F.step.cjs(cap.covars, surv.covars, fit.crit = "qaicc", signif.drop = 0, signif.increase = 0, plot = TRUE, ...)fit.crit the most will be added to the model, assuming that the decrease is greater
than or equal to abs(signif.drop) (see signif.drop for more).
During backward (elimination) looks, the variable that increases fit.crit the most will be removed
from the model, assuming
that the increase is greater than or equal to abs(signif.increase). fit.crit that should be considered "significant" during
forward steps.
This argument controls stopping and is functionally equivalent to the alpha-to-enter
parameter of classical stepwise routines. Stepwise selection stops
when the minimum fit.crit on the current iteration minus the minimum fit.crit
on the previous iteration is greater than or equal to signif.drop.
This means signif.drop should be less than or equal to 0, unless for some odd reason,
steps that add variables without predictive abilities are desired.
If signif.drop = 0 (the default), steps are halted when no variables decrease fit.crit.
Thus, the default method yields the minimum fit.crit model among those considered during
stepwise selection. If signif.drop = -2, steps are halted when fit.crit decreases by less than
2 (or increases) between the
current and previous steps. fit.crit that should be is considered
"significant" during backward looks. This argument controls elimination,
but not stoppage. A variable in the current model is a candidate for removal if,
upon removal, fit.crit
increases by less than or equal to signif.increase. This means signif.increase
should be greater than or equal to 0 to be meaningful, unless no variables should be removed,
in which case set signif.increase = -Inf (or some other negative number). If 2 or more
variables are candidates for removal during a single backward look step, the variable which
increases fit.crit the most will be removed (the other will remain).
If signif.increase = 0 (the default), variables are left in the model if they
increase fit.crit when removed. If signif.increase = 2, variables in the current model
are left in the model if they increase fit.crit by more than 2 units when removed.fit.crit at the end on each forward-backward step should be plotted.
This plot can be useful for assessing which variable(s) cause relatively "big" and which cause
relatively "little" jumps in fit.crit.F.cjs.estim, like histories= , nhat.v.meth=, c.hat=, control=, etc.F.cjs.estim for a
description of the components of this object. Elements of both the cap.covars and surv.covars
arguments can specify the names of single covariates or sets of
covariates to consider as a group to be included or excluded
together. For example, if cap.covars = c("sex",
"ageclass1 + ageclass2 + ageclass3" ), the routine will
include and exclude sex as a single covariate with 1
estimated coefficient and ageclass1 + ageclass2 +
ageclass3 as a set of 3 covariates (with 3 estimated
coefficients) to be included and excluded as a set. This is
useful if factor covariates are pre-coded as indicator variables. In the
example above, specifying ageclass1 + ageclass2 +
ageclass3 would make sense if age of an individual was
classified into 1 of 4 classes, and ageclassX was a
matrix with elements equal to 1 if the individual was in age
class X during a capture occasion, and 0 otherwise.
Specifying a term like a +
b + ab would ensure that main effect matrices (a
and b) are included whenever the interaction matrix
(ab) is included during model selection. However, this way
of including interactions will only be useful if the main effects
are not considered separately. That is, specifying
cap.covars = c("a", "b", "a + b + ab") will not work
because the routine does not know that "a" and "b" are
components of "a + b + ab". Nonsense models like
"a + b + ab + a + b" could result. Thus, this routine is
likely only useful for terms that do not include interactions.
A useful way to proceed in this case may be to use stepwise
to select a model of main effects, then consider interactions.
Time varying and individual varying variables can be specified
using the tvar and ivar functions in the elements
of cap.covars and surv.covars. For example,
specifying "tvar(year,nan=nrow(ch))" as an element of
surv.covars, where year = 1:ncol(ch) and
ch is the capture history matrix, will fit a linear
year effect (1 coefficient) when this element is added during
stepwise selection. Likewise, factors are preserved during
selection. If year in the above example had been a
factor (i.e., year = as.factor(1:ncol(ch))), separate
effects for each year (ncol(ch) - 1 coefficients) would
have been fitted when this effect came up for consideration
during stepwise selection.
The variable to add or eliminate is selected after all variables
in both the capture and survival models are considered. That is, the
variable that decreases (or increases) fit.crit the most over both
models is added.
Selection does not iteratively fix one model and select variables
in the other. For example, on one step, the variable that decreases fit.crit
the most may be a survival covariate, while on the next step
the variable that decreases fit.crit
the most may be a capture covariate.
F.cjs.estim, F.fit.table
# Aquire data and intermediate variables
data(dipper.histories)
data(dipper.males)
ch <- dipper.histories
males <- dipper.males
ns <- ncol(ch)
nan <- nrow(ch)
# Construct covariates
small.t <- as.factor( paste("T",1:ns, sep=""))
post.flood <- as.numeric( 1:ns >= 4 )
year <- 1:ns - (ns / 2)
males.postflood <- outer( c(males), post.flood ) # individual and time varying
print(dim(males.postflood))
# Attach attributes to covariates. For convienence only.
attr(small.t, "nan") <- nan
attr(small.t, "drop") <- c(1,2)
attr(year, "nan") <- nan
attr(post.flood, "nan") <- nan
attr(males, "ns") <- ns
# Define pool of variables to be considered in each model
cap.vars <- c("tvar(small.t)","tvar(year)")
surv.vars <- c("tvar(small.t)","tvar(year)", "tvar(post.flood)", "ivar(males)",
"males.postflood")
# Do stepwise selection
final.fit <- F.step.cjs( cap.vars, surv.vars, histories=ch,
control=mra.control(maxfn=500, cov.meth=2) )
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