Consider the matched pairs random effects model (12 3) For given Icirc sup2 0 , let Icirc acute 0 be such that micro Igrave 12 n 12 Icirc acute 0 and micro Igrave 21 n 21 Icirc acute 0 satisfies log( micro Igrave 21 micro Igrave 12 ) Icirc sup2 0 Suppose micro Igrave ij has nonnegative log odds ratio Explain why a The likelihood ratio statistic for testing H 0 Icirc sup2 Icirc sup2 0 in this model equals b The likelihood ratio test of H 0 Icirc sup2 0 is the test of symmetry z log 12 2 12 log 2 60

Question: Consider the matched-pairs random effects model (12.3). For given Î² 0 , let Î´ 0 be such that µÌ 12 = n 12 + Î´

Consider the matched-pairs random effects model (12.3). For given Î²₀, let Î´₀be such that µÌ‚₁₂= n₁₂+ Î´₀and µÌ‚₂₁= n₂₁€“ Î´₀satisfies log(µÌ‚₂₁/µÌ‚₁₂) = Î²₀. Suppose {µÌ‚_ij} has nonnegative log odds ratio. Explain why:

a. The likelihood-ratio statistic for testing H₀ : Î² = Î²₀ in this model equals

Пи + Пz log П — бо П12 2|п12 log П2 + 60

b. The likelihood-ratio test of H₀: Î² = 0 is the test of symmetry.

+ z log 12 2|12 log 2 + 60

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