DEFFbinary: Compute the design effect for correlated binary data
In DEFFbinary: Compute the design effect for correlated binary data

Description Usage Arguments Details Value Author(s) References Examples

This package computes the intraclass correlation, the design effect, and standard errors for the intercept for a binary-valued model with a group-level random effect, when the number of groups and number of observations per group are specified.

1	DEFFbinary(logitMean, sigma, NperGroup = NULL, Ngroups = NULL, Nsim = 1000)

`logitMean`	The mean response, on the logit scale
`sigma`	The standard deviation of the group-level random effect
`NperGroup`	Number of observations per group, if unspecified only the ICC is computed
`Ngroups`	Number of groups, if unspecified standard errors are not computed.
`Nsim`	Number of simulations for computing the moments of the logistic-normal distribution.

Consider the following model, where Y_ij is the jth observation from the ith group:

Y_ij|P_i ~ Bernoulli(P_i)

logit(P_i) = mu+ U_i

U_i ~ N(0, sigma^2)

logitMean is mu, the conditional mean on the logit scale. The sigma argument is sigma above.

A vector with the following elements

`ICC`	The correlation cor(Y_ij,Y_ik))
`DEFF`	The design effect, (the total sample size divided by the effective sample size)
`SE`	The standard error of the estimate of mu

The first and second moments of P_i are returned as an attribute

Patrick Brown

Brown and Jiang (2009), "Intraclass Correlation and the Design Effect for Binary Random Effects Models", unpublished.

# Design effect with conditional mean 0.5, standard deviation 1,
# 10 groups and 10 observations per group
DEFFbinary(0, 1, NperGroup=10, Ngroups = 10, Nsim=10000)

# the same with conditional mean 0.1
DEFFbinary(log(0.1/0.9), 1, NperGroup=10, Ngroups = 10, Nsim=10000)