statmod (version 1.4.26)

glm.scoretest: Score Test for Adding a Covariate to a GLM

Description

Computes score test statistics (z-statistics) for adding covariates to a generalized linear model.

Usage

glm.scoretest(fit, x2, dispersion=NULL)

Arguments

fit

generalized linear model fit object, of class glm.

x2

vector or matrix with each column a covariate to be added.

dispersion

the dispersion for the generalized linear model family.

Value

Details

Rao's score statistic. Is the locally most powerful test for testing vs a one-sided alternative. Asympotically equivalent to likelihood ratio tests, but convenient for one-sided tests.

This function computes a score test statistics for adding each covariate individually.

The dispersion parameter is treated as for summary.glm. If NULL, the Pearson estimator is used, except for the binomial and Poisson families, for which the dispersion is one.

References

Lovison, G (2005). On Rao score and Pearson $X^2$ statistics in generalized linear models. Statistical Papers, 46, 555-574.

Pregibon, D (1982). Score tests in GLIM with applications. In GLIM82: Proceedings of the International Conference on Generalized Linear Models, R Gilchrist (ed.), Lecture Notes in Statistics, Volume 14, Springer, New York, pages 87-97.

Smyth, G. K. (2003). Pearson's goodness of fit statistic as a score test statistic. In: Science and Statistics: A Festschrift for Terry Speed, D. R. Goldstein (ed.), IMS Lecture Notes - Monograph Series, Volume 40, Institute of Mathematical Statistics, Beachwood, Ohio, pages 115-126. http://www.statsci.org/smyth/pubs/goodness.pdf

See Also

glm, add1

Examples

#  Pearson's chisquare test for independence
#  in a contingency table is a score test.

#  First the usual test

y <- c(20,40,40,30)
chisq.test(matrix(y,2,2),correct=FALSE)

#  Now same test using glm.scoretest

a <- gl(2,1,4)
b <- gl(2,2,4)
fit <- glm(y~a+b,family=poisson)
x2 <- c(0,0,0,1)
z <- glm.scoretest(fit,x2)
z^2