In Example 3.2 (student attainment), standardize the SATM-score predictor to provide values \(x_{i}^{s}\). Then replace the conventional prior by a CMP prior at values \(\tilde{x}_{1}=\left(1, x_{L}^{s}\right)=\) \((1,-1)\) and \(\tilde{x}_{2}=\left(1, x_{U}^{s}\right)=(1,1)\). Assess sensitivity in the optimal threshold \(\eta_{d}^{T}\) to this alternative prior.

Data from Example 3.2

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To illustrate assessment of a binary logistic regression, consider pass-fail outcomes y; for n = 30 students in relation to centred SAT-Math (SAT-M) scores (Johnson and Albert, 1999, p. 77). To assess any poorly fitted cases, predictive probabilities of correct classification Pr(yrepi yily), and Monte Carlo estimates of conditional predictive ordinates p(yrep.ily[i]) are obtained. To demonstrate assessment of classification accuracy, a set of D = 11 thresholds are set, from = -1 through to n = 1 at intervals of 0.2, and aggregates n11d and =-