lm and glm functions have
been fixed properly. Note that the sm.bs(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE,
Boundary.knots = range(x))
sm.ns(x, df = NULL, knots = NULL, intercept = FALSE,
Boundary.knots = range(x))
sm.poly(x, ..., degree = 1, coefs = NULL, raw = FALSE)
sm.scale(x, center = TRUE, scale = TRUE)x argument is actually common to them all.poly.scale..max.smart,
.smart.prediction and
.smart.prediction.counter
are created while the model is being fitted.
They are created in a new environment called smartpredenv.
These variables are deleted after the model has been fitted.
However,
if there is an error in the model fitting function or the fitting
model is killed (e.g., by typing control-C) then these variables will
be left in smartpredenv. At the beginning of model fitting,
these variables are deleted if present in smartpredenv.
During prediction, the variables
.smart.prediction and
.smart.prediction.counter
are reconstructed and read by the smart functions when the model
frame is re-evaluated.
After prediction, these variables are deleted.
If the modelling function is used with argument smart = FALSE
(e.g., vglm(..., smart = FALSE)) then smart prediction will not
be used, and the results should match with the original Rfunctions.
bs,
ns,
poly and
scale
are now left alone (from 2014-05 onwards) and no longer smart.
They work via safe prediction.
The smart versions of these functions have been renamed and
they begin with "sm.".
The functions
predict.bs and
predict.ns
are not smart.
That is because they operate on objects that contain attributes only
and do not have list components or slots.
The function
predict.poly is not smart.
I(poly(x, 3)),
poly(c(scale(x)), 3),
bs(scale(x), 3),
scale(scale(x)).
See the examples below.
Smart prediction, however, will always work. The basic idea is that the functions in the formula are now smart, and the
modelling functions make use of these smart functions. Smart prediction
works in two ways: using smart.expression, or using a
combination of put.smart and get.smart.
get.smart.prediction,
get.smart,
put.smart,
smart.expression,
smart.mode.is,
setup.smart,
wrapup.smart.
Commonly used data-dependent functions include
scale,
poly,
bs,
ns.
In R,
the functions bs
and ns are in the
bs and ns call. The functions vglm,
vgam,
rrvglm
and
cqo
in T. W. Yee's
# Create some data first
n <- 20
set.seed(86) # For reproducibility of the random numbers
ldata <- data.frame(x2 = sort(runif(n)), y = sort(runif(n)))
library("splines") # To get ns() in R
# This will work for R 1.6.0 and later
fit <- lm(y ~ ns(x2, df = 5), data = ldata)
plot(y ~ x2, data = ldata)
lines(fitted(fit) ~ x2, data = ldata)
new.ldata <- data.frame(x2 = seq(0, 1, len = n))
points(predict(fit, new.ldata) ~ x2, new.ldata, type = "b", col = 2, err = -1)
# The following fails for R 1.6.x and later. It can be
# made to work with smart prediction provided
# ns is changed to sm.ns and scale is changed to sm.scale:
fit1 <- lm(y ~ ns(scale(x2), df = 5), data = ldata)
plot(y ~ x2, data = ldata, main = "Safe prediction fails")
lines(fitted(fit1) ~ x2, data = ldata)
points(predict(fit1, new.ldata) ~ x2, new.ldata, type = "b", col = 2, err = -1)
# Fit the above using smart prediction
library("VGAM") # The following requires the VGAM package to be loaded
fit2 <- vglm(y ~ sm.ns(sm.scale(x2), df = 5), uninormal, data = ldata)
fit2@smart.prediction
plot(y ~ x2, data = ldata, main = "Smart prediction")
lines(fitted(fit2) ~ x2, data = ldata)
points(predict(fit2, new.ldata, type = "response") ~ x2, data = new.ldata,
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