SO.trend.test: Likelihood ratio test of stochastic ordering
In CorrBin: Nonparametrics with Clustered Binary and Multinomial Data

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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

`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.

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.

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 H0 and Ha 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.

Aniko Szabo, aszabo@mcw.edu

Szabo A, George EO. (2009) On the Use of Stochastic Ordering to Test for Trend with Clustered Binary Data.

SO.LRT for calculating only the test statistic, soControl

data(shelltox)
set.seed(45742)
sh.test <- SO.trend.test(shelltox, R=5, 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)