Fixing a Quantile Regression having Crossing
Returns a similar object fitted with columns of the constraint matrices amalgamated so it is a partially parallel VGLM object. The columns combined correspond to certain crossing quantiles. This applies especially to an extlogF1() VGLM object.
fix.crossing.vglm(object, maxit = 100, trace = FALSE, ...)
object |
an object such as
a |
maxit, trace |
values for overwriting components in |
... |
additional optional arguments. Currently unused. |
The quantile crossing problem has been described as
disturbing and embarrassing.
This function was specifically written for
a vglm with family function extlogF1.
It examines the fitted quantiles of object to see if any cross.
If so, then a pair of columns is combined to make those
two quantiles parallel.
After fitting the submodel it then repeats testing for
crossing quantiles and repairing them, until there is
no more quantile crossing detected.
Note that it is possible that the quantiles cross in
some subset of the covariate space not covered by the
data—see is.crossing.
This function is fragile and likely to change in the future.
For extlogF1 models, it is assumed
that argument data has been assigned a data frame,
and
that the default values of the argument parallel
has been used; this means that the second constraint
matrix is diag(M).
The constraint matrix of the intercept term remains unchanged
as diag(M).
An object very similar to the original object, but with possibly different constraint matrices (partially parallel) so as to remove any quantile crossing.
## Not run: ooo <- with(bmi.nz, order(age))
bmi.nz <- bmi.nz[ooo, ] # Sort by age
with(bmi.nz, plot(age, BMI, col = "blue"))
mytau <- c(50, 93, 95, 97) / 100 # Some quantiles are quite close
fit1 <- vglm(BMI ~ ns(age, 7), extlogF1(mytau), bmi.nz, trace = TRUE)
plot(BMI ~ age, bmi.nz, col = "blue", las = 1,
main = "Partially parallel (darkgreen) & nonparallel quantiles",
sub = "Crossing quantiles are orange")
fix.crossing(fit1)
matlines(with(bmi.nz, age), fitted(fit1), lty = 1, col = "orange")
fit2 <- fix.crossing(fit1) # Some quantiles have been fixed
constraints(fit2)
matlines(with(bmi.nz, age), fitted(fit2), lty = "dashed",
col = "darkgreen", lwd = 2)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.