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High dimensional correlated binary data arise in many areas, such as observedgenetic variations in biomedical research. Data simulation can help researchersevaluate efficiency and explore properties of different computational andstatistical methods. Also, some statistical methods, such as Monte-Carlomethods, rely on data simulation. Lunn and Davies (1998) proposed linear timecomplexity methods to generate correlated binary variables with three commoncorrelation structures. However, it is infeasible to specify unequalprobabilities in their methods. In this manuscript, we introduce severalcomputationally efficient algorithms that generate high-dimensional binary datawith specified correlation structures and unequal probabilities. Our algorithmshave linear time complexity with respect to the dimension for three commonlystudied correlation structures, namely exchangeable, decaying-product andK-dependent correlation structures. In addition, we extend our algorithms togenerate binary data of general non-negative correlation matrices withquadratic time complexity. We provide an R package, CorBin, to implement oursimulation methods. Compared to the existing packages for binary datageneration, the time cost to generate a 100-dimensional binary vector with thecommon correlation structures and general correlation matrices can be reducedup to $10^5$ folds and $10^3$ folds, respectively, and the efficiency can befurther improved with the increase of dimensions. The R package CorBin isavailable on CRAN at https://cran.r-project.org/.

A set of efficient methods to generate high-dimensional binary data with specified correlation structures