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

View source: R/DEFFbinary.R

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Brown and Jiang (2009), "Intraclass Correlation and the Design Effect for Binary Random Effects Models", unpublished.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