R: Score Test for Adding a Covariate to a GLM

glm.scoretest {statmod} | R Documentation

## 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.

### 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.

### Value

numeric vector containing the z-statistics, one for each covariate.

### Author(s)

Gordon Smyth

### 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

[Package statmod version 1.4.30 Index]