What are the multiple correlations of three sets of predictors and overall state of health? The first set of predictors contains demographic variables (age and years of education). The second….
Find the posterior mean for α and π by using the formula for the total probability P(yi = 1).
Suppose a binary response has true prevalence Pr(Y = 1) = π but that observed responses are subject to misclassification with probabilities α0 = Pr(y = 1|Y = 0), and α1 = Pr(y = 0|Y = 1). Assuming α0 = α1 = α, state the total probability P(yi = 1) in terms of the true prevalence probabilities P(Y = 1) and P(Y = 0) and the conditional probabilities P(y = 1|Y = 1) and p(y = 1|Y = 0). Winkler and Gaba (1990, p. 307) note that high values of α are unlikely and provide observed data on a juvenile survey question ‘have you beaten up on someone’, with r = 21 and n = 104. They assume π ∼ Beta(2, 8) and α ∼ Beta(2, 18) consistent with a prior misclassification rate of 10%. Find the posterior mean for α and π by using the formula for the total probability P(yi = 1).