jointprobs {CorrBin}  R Documentation 
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}^{K1}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 
type 
character string describing the desired type of estimate:

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
clustersize specific estimates (type="cluster"
) or pooled estimates
(type="averaged"
or type="mc"
) are requested. For the clustersize specific estimates
the first dimension is the clustersize. 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 withinmultinomial correlations from the joint probabilities.
Examples
data(dehp)
# averaged over clustersizes
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 type1, and one type2 outcome
#plot P(X1=O1)  the marginal probability of a type1 event over clustersizes
tau < jointprobs(dehp, type="cluster")
ests < as.data.frame(lapply(tau, function(x)x[,"1","0"]))
matplot(ests, type="b")