# glm.scoretest

##### Score Test for Adding a Covariate to a GLM

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

- Keywords
- regression

##### 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.

##### 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.

##### See Also

##### 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
```

*Documentation reproduced from package statmod, version 1.4.14, License: LGPL (>= 2)*