SO.trend.test {CorrBin}

Likelihood ratio test of stochastic ordering

Description

Performs a likelihood ratio test of stochastic ordering versus equality using permutations to estimate the null-distribution and the p-value. If only the value of the test statistic is needed, use SO.LRT instead.

Usage

SO.trend.test(cbdata, R = 100, control = soControl())

Arguments

cbdata

a CBData object.

R

an integer – the number of random permutations for estimating the null distribution.

control

an optional list of control settings, usually a call to soControl. See there for the names of the settable control values and their effect.

Details

The test is valid only under the assumption that the cluster-size distribution does not depend on group. During the estimation of the null-distribution the group assignments of the clusters are permuted keeping the group sizes constant; the within-group distribution of the cluster-sizes will vary randomly during the permutation test.

The default value of R is probably too low for the final data analysis, and should be increased.

Value

A list with the following components

LRT

the value of the likelihood ratio test statistic. It has two attributes: ll0 and ll1 - the values of the log-likelihood under H_0 and H_a respectively.

p.val

the estimated one-sided p-value.

boot.res

an object of class "boot" with the detailed results of the permutations. See boot for details.

Author(s)

Aniko Szabo, [e-mail]

References

Szabo A, George EO. (2010) On the Use of Stochastic Ordering to Test for Trend with Clustered Binary Data. Biometrika 97(1), 95-108.

See Also

SO.LRT for calculating only the test statistic, soControl

Examples

data(shelltox)
set.seed(45742)
sh.test <- SO.trend.test(shelltox, R=10, control=soControl(eps=0.1, max.directions=25)) 
sh.test

#a plot of the resampled LRT values
#would look better with a reasonable value of R
null.vals <- sh.test$boot.res$t[,1]
hist(null.vals, breaks=10,  freq=FALSE, xlab="Test statistic", ylab="Density", 
     main="Simulated null-distribution", xlim=range(c(0,20,null.vals)))
points(sh.test$LRT, 0, pch="*",col="red", cex=3)