1\name{score.stat} 2\alias{score.stat} 3\alias{score.stat.vlm} 4%- Also NEED an '\alias' for EACH other topic documented here. 5\title{ Rao's Score Test 6 Statistics Evaluated at the Null Values } 7\description{ 8 Generic function that computes 9 Rao's score test statistics evaluated at the null values. 10} 11% (consequently they 12% may 13% not suffer from the Hauck-Donner effect). 14\usage{ 15score.stat(object, ...) 16score.stat.vlm(object, values0 = 0, subset = NULL, omit1s = TRUE, 17 all.out = FALSE, orig.SE = FALSE, iterate.SE = TRUE, 18 iterate.score = TRUE, trace = FALSE, ...) 19} 20%- maybe also 'usage' for other objects documented here. 21\arguments{ 22\item{object, values0, subset}{ 23 Same as in \code{\link{wald.stat.vlm}}. 24 25 26} 27\item{omit1s, all.out}{ 28 Same as in \code{\link{wald.stat.vlm}}. 29 30 31} 32\item{orig.SE, iterate.SE}{ 33 Same as in \code{\link{wald.stat.vlm}}. 34 35 36} 37\item{iterate.score}{ 38 Logical. The score vector is evaluated at one value of 39 \code{values0} and at other regression coefficient values. 40 These other values may be either the MLE obtained from the original 41 object (\code{FALSE}), else at values obtained by 42 further IRLS iterations---this argument enables that choice. 43 44 45 46} 47\item{trace}{ 48 Same as in \code{\link{wald.stat.vlm}}. 49 50 51} 52\item{\dots}{ 53 Ignored for now. 54 55 56} 57} 58\details{ 59 The (Rao) \emph{score test} 60 (also known as the \emph{Lagrange multiplier test} in econometrics) 61 is a third general method for 62 hypothesis testing under a likelihood-based framework 63 (the others are the likelihood ratio test and 64 Wald test; see \code{\link{lrt.stat}} and 65 \code{\link{wald.stat}}). 66 Asymptotically, the three tests are equivalent. 67 The Wald test is not invariant to parameterization, and 68 the usual Wald test statistics computed at the estimates 69 make it vulnerable to the Hauck-Donner effect 70 (HDE; see \code{\link{hdeff}}). 71 This function is similar to \code{\link{wald.stat}} in that 72 one coefficient is set to 0 (by default) and the \emph{other} 73 coefficients are iterated by IRLS to get their MLE subject to this 74 constraint. 75 The SE is almost always based on the expected information matrix 76 (EIM) rather than the OIM, and for some models 77 the EIM and OIM coincide. 78 79 80 81% It is not permissible to have \code{iterate.SE = TRUE} 82% and \code{orig.SE = TRUE} together. 83 84 85 86 87} 88\value{ 89 By default the 90 signed square root of the 91 Rao score statistics are returned. 92 If \code{all.out = TRUE} then a list is returned with the 93 following components: 94 \code{score.stat} the score statistic, 95 \code{SE0} the standard error of that coefficient, 96 \code{values0} the null values. 97 Approximately, the default score statistics output are 98 standard normal random variates if each null hypothesis is true. 99 100 101 102 Altogether, 103 by the eight combinations of \code{iterate.SE}, \code{iterate.score} 104 and \code{orig.SE}, 105 there are six different variants of the Rao score statistic 106 that can be returned because the score vector has 2 and 107 the SEs have 3 subvariants. 108 109 110 111} 112%\references{ 113% 114%} 115\author{ Thomas W. Yee } 116 117%\note{ 118%} 119 120\section{Warning }{ 121 See \code{\link{wald.stat.vlm}}. 122 123 124} 125 126 127\seealso{ 128 \code{\link{wald.stat}}, 129 \code{\link{lrt.stat}}, 130 \code{\link{summaryvglm}}, 131 \code{\link[stats]{summary.glm}}, 132 \code{\link{anova.vglm}}, 133 \code{\link{vglm}}, 134 \code{\link{hdeff}}. 135 136 137% \code{\link{anova.vglm}}, 138 139 140 141} 142\examples{ 143set.seed(1) 144pneumo <- transform(pneumo, let = log(exposure.time), 145 x3 = rnorm(nrow(pneumo))) 146(pfit <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, pneumo)) 147score.stat(pfit) # No HDE here; should be similar to the next line: 148coef(summary(pfit))[, "z value"] # Wald statistics computed at the MLE 149summary(pfit, score0 = TRUE) 150} 151\keyword{models} 152\keyword{regression} 153 154