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

## Description

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.

## Usage

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

## Arguments

 `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.

## Details

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.

## Value

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

## References

Brown and Jiang (2009), "Intraclass Correlation and the Design Effect for Binary Random Effects Models", unpublished.

## Examples

 ```1 2 3 4 5 6``` ```# 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) ```

DEFFbinary documentation built on May 31, 2017, 4:29 a.m.