12. Consider three-wave data on a skin treatment trial (Saei and McGilchrist, 1998), with the responses yi t being on a 5-point ordinal scale and a categorical predictor namely clinic Ci

(1–6) – see Exercise 11.12.odc. Treatment (1 = test drug, 2 = placebo) is denoted by Gi .

Apply a constant (but treatment-specific) threshold model with random patient intercepts bi , and fixed clinic effects γCi , namely logit(Pr(yi t ≤ j |Gi ,Ci , bi ) = logit(ωi jt ) = κjGi

− γCi

− bi .

For all the {γk , k = 1, 6} to be identified, only J − 2 = 3 threshold parameters are estimated, while if γ1 = 0 there are four free threshold parameters. Compare this model’s predictive fit (the proportion of observations correctly classified on sampling new responses yi t,new) with a model allowing changing thresholds κjm (m = 1, 2) over the T = 3 periods.