hdeffsev {VGAM} | R Documentation |
Hauck-Donner Effects: Severity Measures
Description
Computes the severity of the Hauck-Donner effect for each regression coefficient of a VGLM regression.
Usage
hdeffsev(x, y, dy, ddy, allofit = FALSE, eta0 = 0, COPS0 = eta0,
severity.table = c("None", "Faint", "Weak",
"Moderate", "Strong", "Extreme", "Undetermined"))
Arguments
x , y |
Numeric vectors;
|
dy , ddy |
Numeric vectors;
the first and second derivatives of the Wald statistics.
They can be computed by |
allofit |
Logical. If |
severity.table |
Character vector with 6 values. The last value is used for initialization. Usually users should not assign anything to this argument. |
eta0 |
Numeric. The hypothesized value. The default is appropriate for most symmetric binomial links,and also for Poisson regression with the natural parameter. |
COPS0 |
Numeric. See Yee (2021). |
Details
Note: This function has a bug or two in it but they should be fixed later this year (2024).
This function is rough-and-ready.
It is possible to use the first two derivatives obtained
from hdeff
to categorize the severity of the
the Hauck-Donner effect (HDE).
It is effectively assumed that, starting at
the origin
and going right,
the curve is made up of a convex segment followed by
a concave segment and then the convex segment.
Midway in the concave segment the derivative is 0, and
beyond that the HDE is really manifest because the
derivative is negative.
For "none"
the estimate lies on the convex
part of the curve near the origin, hence there is
very little HDE at all.
For "weak"
the estimate lies on the
concave part of the curve but the Wald statistic is still
increasing as estimate gets away from 0, hence it is only
a mild form of the HDE.
Previously "faint"
was used but now it has
been omitted.
For "moderate"
,
"strong"
and "extreme"
the Wald statistic is
decreasing as the estimate gets away from eta0
,
hence it
really does exhibit the HDE.
It is recommended that lrt.stat
be used
to compute
LRT p-values, as they do not suffer from the HDE.
Value
By default this function returns a labelled vector with
elements selected from
severity.table
.
If allofit = TRUE
then Yee (2022) gives details
about some of the other list components,
e.g., a quantity called
zeta
is the normal line projected onto the x-axis,
and its first derivative gives additional
information about the position
of the estimate along the curve.
Note
This function is likely to change in the short future because it is experimental and far from complete. Improvements are intended.
Currently,
in order for "Strong"
to be assigned correctly,
at least one such value is needed on the
LHS and/or RHS each. From those, two other boundary
points are obtained so that it creates two intervals.
Author(s)
Thomas W. Yee.
References
Yee, T. W. (2022). On the Hauck-Donner effect in Wald tests: Detection, tipping points and parameter space characterization, Journal of the American Statistical Association, 117, 1763–1774. doi:10.1080/01621459.2021.1886936.
Yee, T. W. (2022). Some new results concerning the Wald tests and the parameter space. In review.
See Also
Examples
deg <- 4 # myfun is a function that approximates the HDE
myfun <- function(x, deriv = 0) switch(as.character(deriv),
'0' = x^deg * exp(-x),
'1' = (deg * x^(deg-1) - x^deg) * exp(-x),
'2' = (deg*(deg-1)*x^(deg-2) - 2*deg*x^(deg-1) + x^deg)*exp(-x))
xgrid <- seq(0, 10, length = 101)
ansm <- hdeffsev(xgrid, myfun(xgrid), myfun(xgrid, deriv = 1),
myfun(xgrid, deriv = 2), allofit = TRUE)
digg <- 4
cbind(severity = ansm$sev,
fun = round(myfun(xgrid), digg),
deriv1 = round(myfun(xgrid, deriv = 1), digg),
deriv2 = round(myfun(xgrid, deriv = 2), digg),
zderiv1 = round(1 + (myfun(xgrid, deriv = 1))^2 +
myfun(xgrid, deriv = 2) * myfun(xgrid), digg))