mc.est.CMData {CorrBin}

Distribution of the number of responses assuming marginal compatibility.

Description

The mc.est function estimates the distribution of the number of responses in a cluster under the assumption of marginal compatibility: information from all cluster sizes is pooled. The estimation is performed independently for each treatment group.

Usage

## S3 method for class 'CMData'
mc.est(object, eps = 1e-06, ...)

## S3 method for class 'CBData'
mc.est(object, ...)

mc.est(object, ...)

Arguments

object

a CBData or CMData object

eps

numeric; EM iterations proceed until the sum of squared changes fall below eps

...

other potential arguments; not currently used

Details

The EM algorithm given by Stefanescu and Turnbull (2003) is used for the binary data.

Value

For CMData: A data frame giving the estimated pdf for each treatment and clustersize. The probabilities add up to 1 for each Trt/ClusterSize combination. It has the following columns:

Prob

numeric, the probability of NResp responses in a cluster of size ClusterSize in group Trt

Trt

factor, the treatment group

ClusterSize

numeric, the cluster size

NResp.1 - NResp.K

numeric, the number of responses of each type

For CBData: A data frame giving the estimated pdf for each treatment and clustersize. The probabilities add up to 1 for each Trt/ClusterSize combination. It has the following columns:

Prob

numeric, the probability of NResp responses in a cluster of size ClusterSize in group Trt

Trt

factor, the treatment group

ClusterSize

numeric, the cluster size

NResp

numeric, the number of responses

Note

For multinomial data, the implementation is currently written in R, so it is not very fast.

Author(s)

Aniko Szabo

References

George EO, Cheon K, Yuan Y, Szabo A (2016) On Exchangeable Multinomial Distributions. #'Biometrika 103(2), 397-408.

Stefanescu, C. & Turnbull, B. W. (2003) Likelihood inference for exchangeable binary data with varying cluster sizes. Biometrics, 59, 18-24

Examples

data(dehp)
dehp.mc <- mc.est(subset(dehp, Trt=="0"))
subset(dehp.mc, ClusterSize==2)

data(shelltox)
sh.mc <- mc.est(shelltox)

library(lattice)
xyplot(Prob~NResp|factor(ClusterSize), groups=Trt, data=sh.mc, subset=ClusterSize>0, 
   type="l", as.table=TRUE, auto.key=list(columns=4, lines=TRUE, points=FALSE),
   xlab="Number of responses", ylab="Probability P(R=r|N=n)")