jointprobs {CorrBin}

Estimate joint event probabilities for multinomial data

Description

An exchangeable multinomial distribution with K+1 categories O_1,\ldots,O_{K+1}, can be parameterized by the joint probabilities of events

\tau_{r_1,\ldots,r_{K}|n} = P\big[X_1=\cdots=X_{r_1}=O_1,\ldots, X_{\sum_{i=1}^{K-1}r_i+1} =\cdots=X_{\sum_{i=1}^{K}r_i}=O_K\big]

where r_i \geq 0 and r_1+\cdots +r_K\leq n. The jointprobs function estimates these probabilities under various settings. Note that when some of the r_i's equal zero, then no restriction on the number of outcomes of the corresponding type are imposed, so the resulting probabilities are marginal.

Usage

jointprobs(cmdata, type = c("averaged", "cluster", "mc"))

Arguments

cmdata

a CMData object

type

character string describing the desired type of estimate:

• "averaged" - averaged over the observed cluster-size distribution within each treatment

• "cluster" - separately for each cluster size within each treatment

• "mc" - assuming marginal compatibility, ie that \tau does not depend on the cluster-size

Value

a list with an array of estimates for each treatment. For a multinomial distribution with K+1 categories the arrays will have either K+1 or K dimensions, depending on whether cluster-size specific estimates (type="cluster") or pooled estimates (type="averaged" or type="mc") are requested. For the cluster-size specific estimates the first dimension is the cluster-size. Each additional dimension is a possible outcome.

See Also

mc.est for estimating the distribution under marginal compatibility, uniprobs and multi.corr for extracting the univariate marginal event probabilities, and the within-multinomial correlations from the joint probabilities.

Examples

data(dehp)
# averaged over cluster-sizes
tau.ave <- jointprobs(dehp, type="ave")
# averaged P(X1=X2=O1, X3=O2) in the 1500 dose group
tau.ave[["1500"]]["2","1"]  # there are two type-1, and one type-2 outcome

#plot P(X1=O1) - the marginal probability of a type-1 event over cluster-sizes
tau <- jointprobs(dehp, type="cluster")
ests <- as.data.frame(lapply(tau, function(x)x[,"1","0"]))
matplot(ests, type="b")