Correlated Binary Data Clause Samples

Correlated Binary Data. A variety of approaches have been proposed for generating longitudinally corre- lated binary data (see [29] for a summary). One such approach was proposed by ▇▇▇▇▇▇(2003) [67], who introduced a multivariate binary distribution to easily and ef- ficiently simulate correlated binary variables with a given marginal mean vector and correlation matrix. Let Y = (Y1, . . . , YT )T denote a sequence of T binary responses. Further, let the marginal mean of Yt be E (Yt) = Pr (Yt = 1) = µt. The proposed approach is then implemented by generating a binary sequence using the conditional distribution for Yt given (Y1, . . . , Yt−1), where t = 2, . . . , n. Specifically, ▇▇▇▇▇▇ defines ∑ t−1 λt = P (Yt = 1|Y1, . . . , Yt−1) = µt + bjt (Yj − µj) , where bjt reflects the generic correlation structure. ▇▇▇▇▇▇’▇ approach is computation- ally efficient for large T, while offering the flexibility to accommodate non-stationary data and unpatterned correlation. In addition, when compared to other methods for common stationary processes, the proposed approach allows for a wider range of correlation parameters.