Data is generated to ensure inter-cluster correlation 0, intra-cluster
correlation in expectation ICC. Algorithm taken from Hossein,
Akhtar. "ICCbin: An R Package Facilitating Clustered Binary Data
Generation, and Estimation of Intracluster Correlation Coefficient (ICC)
for Binary Data".

draw_binary_icc(prob = 0.5, N = NULL, clusters, ICC = 0)

## Arguments

prob |
A number or vector of numbers, one probability per cluster. If none
is provided, will default to 0.5. |

N |
(Optional) A number indicating the number of observations to be
generated. Must be equal to length(clusters) if provided. |

clusters |
A vector of factors or items that can be coerced to
clusters; the length will determine the length of the generated data. |

ICC |
A number indicating the desired `ICC` , if none is provided
the default ICC will be 0. |

## Value

A vector of binary numbers corresponding to the observations from
the supplied cluster IDs.

## Examples

# Divide units into clusters
clusters = rep(1:5, 10)
# Default probability 0.5, default ICC 0
draw_binary_icc(clusters = clusters)

#> [1] 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0
#> [39] 1 0 0 0 1 0 1 0 1 0 0 1

# Specify probability or ICC
corr_draw = draw_binary_icc(prob = 0.5, clusters = clusters, ICC = 0.5)
# Verify ICC of data.
summary(lm(corr_draw ~ as.factor(clusters)))$r.squared

#> [1] 0.3402778