score.stat: Rao's Score Test Statistics Evaluated at the Null Values

In VGAM: Vector Generalized Linear and Additive Models

Rao's Score Test Statistics Evaluated at the Null Values

Description

Generic function that computes Rao's score test statistics evaluated at the null values.

Usage

score.stat(object, ...)
score.stat.vlm(object, values0 = 0, subset = NULL, omit1s = TRUE,
          all.out = FALSE, orig.SE = FALSE, iterate.SE = TRUE,
          iterate.score = TRUE, trace = FALSE, ...)

Arguments

object, values0, subset	Same as in wald.stat.vlm.
omit1s, all.out	Same as in wald.stat.vlm.
orig.SE, iterate.SE	Same as in wald.stat.vlm.
iterate.score	Logical. The score vector is evaluated at one value of values0 and at other regression coefficient values. These other values may be either the MLE obtained from the original object (FALSE), else at values obtained by further IRLS iterations—this argument enables that choice.
trace	Same as in wald.stat.vlm.
...	Ignored for now.

Details

The (Rao) score test (also known as the Lagrange multiplier test in econometrics) is a third general method for hypothesis testing under a likelihood-based framework (the others are the likelihood ratio test and Wald test; see lrt.stat and wald.stat). Asymptotically, the three tests are equivalent. The Wald test is not invariant to parameterization, and the usual Wald test statistics computed at the estimates make it vulnerable to the Hauck-Donner effect (HDE; see hdeff). This function is similar to wald.stat in that one coefficient is set to 0 (by default) and the other coefficients are iterated by IRLS to get their MLE subject to this constraint. The SE is almost always based on the expected information matrix (EIM) rather than the OIM, and for some models the EIM and OIM coincide.

Value

By default the signed square root of the Rao score statistics are returned. If all.out = TRUE then a list is returned with the following components: score.stat the score statistic, SE0 the standard error of that coefficient, values0 the null values. Approximately, the default score statistics output are standard normal random variates if each null hypothesis is true.

Altogether, by the eight combinations of iterate.SE, iterate.score and orig.SE, there are six different variants of the Rao score statistic that can be returned because the score vector has 2 and the SEs have 3 subvariants.

Warning

See wald.stat.vlm.

Author(s)

Thomas W. Yee

See Also

wald.stat, lrt.stat, summaryvglm, summary.glm, anova.vglm, vglm, hdeff.

Examples

set.seed(1)
pneumo <- transform(pneumo, let = log(exposure.time),
                            x3 = rnorm(nrow(pneumo)))
(pfit <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, pneumo))
score.stat(pfit)  # No HDE here; should be similar to the next line:
coef(summary(pfit))[, "z value"]  # Wald statistics computed at the MLE
summary(pfit, score0 = TRUE)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.