CorrBin (version 1.6.2)

multi.corr: Extract correlation coefficients from joint probability arrays

Description

Calculates the within- and between-outcome correlation coefficients for exchangeable correlated multinomial data based on joint probability estimates calculated by the jointprobs function. These determine the variance inflation due the cluster structure.

Usage

multi.corr(jp, type = attr(jp, "type"))

Value

a list of estimated correlation matrices by treatment group. If cluster-size specific estimates were requested ((type="cluster")), then each list elements are a list of these matrices for each cluster size.

Arguments

jp

the output of jointprobs - a list of joint probability arrays by treatment

type

one of c("averaged","cluster","mc") - the type of joint probability. By default, the type attribute of jp is used.

Details

If \(R_i\) and \(R_j\) is the number of events of type \(i\) and \(j\), respectively, in a cluster of size \(n\), then $$Var(R_i)= n p_i (1-p_i)(1 + (n-1)\phi_{ii})$$ $$Cov(R_i,R_j)= -n p_i p_j (1 + (n-1)\phi_{ij})$$ where \(p_i\) and \(p_j\) are the marginal event probabilities and \(\phi_{ij}\) are the correlation coefficients computed by multi.corr.

See Also

jointprobs for calculating the joint probability arrays

Examples

data(dehp)
tau <- jointprobs(dehp, type="averaged")
multi.corr(tau)