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.