Question: How does positive correlation affect the SE for between-cluster effects with binary data? Let y11,, y1d be Bernoulli trials with E(y1j) = ????1 and let

How does positive correlation affect the SE for between-cluster effects with binary data? Let y11,…, y1d be Bernoulli trials with E(y1j) = ????1 and let y21,…, y2d be Bernoulli trials with E(y2j) = ????2. Suppose corr(yij, yik) = ???? for i = 1, 2 and corr(y1j, y2k) = 0 for all j and k. Find the SE of ̂????1 − ̂????2. Show it is larger when ???? > 0 than when ???? = 0.

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