Generic function that computes Wald test statistics evaluated at the null values (consequently they do not suffer from the Hauck-Donner effect).
wald.stat(object, ...)
wald.stat.vlm(object, values0 = 0, subset = NULL, omit1s = TRUE,
all.out = FALSE, orig.SE = FALSE, iterate.SE = TRUE,
trace = FALSE, ...)By default the signed square root of the Wald statistics
whose SEs are computed at one each of the null values.
If all.out = TRUE then a list is returned with the
following components:
wald.stat the Wald statistic,
SE0 the standard error of that coefficient,
values0 the null values.
Approximately, the default Wald statistics output are standard
normal random variates if each null hypothesis is true.
Altogether,
by the four combinations of iterate.SE and orig.SE,
there are three different variants of the Wald statistic
that can be returned.
A vglm fit.
Numeric vector. The null values corresponding to the null hypotheses. Recycled if necessary.
Same as in hdeff.
Logical. Does one omit the intercepts? Because the default would be to test that each intercept is equal to 0, which often does not make sense or is unimportant, the intercepts are not tested by default. If they are tested then each linear predictor must have at least one coefficient (from another variable) to be estimated.
Logical. If TRUE then a list is returned containing
various quantities such as the SEs,
instead of just the Wald statistics.
Logical. If TRUE then
the standard errors are computed at the MLE
(of the original object).
In practice, the (usual or unmodified)
Wald statistics etc. are extracted from summary(object)
because it was computed there.
These may suffer from the HDE since
all the SEs are evaluated
at the MLE of the original object.
If TRUE then argument iterate.SE may
be ignored or overwritten.
If orig.SE = FALSE then the \(k\)th SE uses
the \(k\)th value of values0 in its computation and
iterate.SE specifies the choice of the other coefficients.
This argument was previously called as.summary because
if TRUE then the Wald statistics are the same
as summary(glm()).
For one-parameter models setting
orig.SE = FALSE results in what is called the
null Wald (NW) statistic by some people,
e.g., Laskar and King (1997) and Goh and King (1999).
The NW statistic does not suffer from the HDE.
Logical, for the standard error computations.
If TRUE then IRLS iterations are performed to
get MLEs of the other regression coefficients, subject
to one coefficient being equal to the appropriate
values0 value.
If FALSE then the other regression coefficients have
values obtained at the original fit.
It is recommended that a TRUE be used as the answer
tends to be more accurate.
If the large (VLM) model matrix only has one column and
iterate.SE = TRUE then an error will occur because
there are no other regression coefficients to estimate.
Logical. If TRUE then some output is produced as
the IRLS iterations proceed.
The value NULL means to use the trace
value of the fitted object;
see vglm.control.
Ignored for now.
Thomas W. Yee
This function has been tested but not thoroughly.
Convergence failure is possible for some models applied to
certain data sets; it is a good idea to set trace = TRUE
to monitor convergence.
For example, for a particular explanatory variable,
the estimated regression coefficients
of a non-parallel cumulative logit model
(see cumulative) are ordered,
and perturbing one coefficient might disrupt the order
and create numerical problems.
By default, summaryvglm and most regression
modelling functions such as summary.glm
compute all the standard errors (SEs) of the estimates at
the MLE and not at 0.
This corresponds to orig.SE = TRUE and
it is vulnerable to the Hauck-Donner effect (HDE;
see hdeff).
One solution is to compute the SEs
at 0 (or more generally, at the values of
the argument values0).
This function does that.
The two variants of Wald statistics are asymptotically equivalent;
however in small samples there can be an appreciable difference,
and the difference can be large if the estimates are near
to the boundary of the parameter space.
None of the tests here are joint,
hence the degrees of freedom is always unity.
For a factor with more than 2 levels one can use
anova.vglm to test for the significance of the factor.
If orig.SE = FALSE and iterate.SE = FALSE then
one retains the MLEs of the original fit for the values of
the other coefficients, and replaces one coefficient at a
time by the value 0 (or whatever specified by values0).
One alternative would be to recompute the MLEs of the other
coefficients after replacing one of the values;
this is the default because iterate.SE = TRUE
and orig.SE = FALSE.
Just like with the original IRLS iterations,
the iterations here are not guaranteed to converge.
Almost all VGAM family functions use the EIM and not
the OIM; this affects the resulting standard errors.
Also, regularity conditions are assumed for the Wald,
likelihood ratio and score tests; some VGAM family functions
such as alaplace1 are experimental and
do not satisfy such conditions, therefore naive inference is
hazardous.
The default output of this function can be seen by
setting wald0.arg = TRUE in summaryvglm.
Laskar, M. R. and M. L. King (1997). Modified Wald test for regression disturbances. Economics Letters, 56, 5--11.
Goh, K.-L. and M. L. King (1999). A correction for local biasedness of the Wald and null Wald tests. Oxford Bulletin of Economics and Statistics 61, 435--450.
lrt.stat,
score.stat,
summaryvglm,
summary.glm,
anova.vglm,
vglm,
hdeff,
hdeffsev.
set.seed(1)
pneumo <- transform(pneumo, let = log(exposure.time),
x3 = rnorm(nrow(pneumo)))
(fit <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, pneumo))
wald.stat(fit) # No HDE here
summary(fit, wald0 = TRUE) # See them here
coef(summary(fit)) # Usual Wald statistics evaluated at the MLE
wald.stat(fit, orig.SE = TRUE) # Same as previous line
Run the code above in your browser using DataLab