5. In Example 7.6 apply the known age scores model (using a centred version of the values 6, 8.5, . . . , 14.5) and compare the fitted values and mean G2 with that of the full rowcolumn effects model as estimated in the text. Sample new data from each model and apply a posterior predictive check using a chi square or G2 criterion to assess whether the models are consistent with the data. Next use the Chuang and Agresti (1986) parameterisation of the row and column effects model with ν1 and ν4 preset and with ν3 ≥ ν2; there is no need to apply any normalisation to the column scores in this case though the sum to zero constraint on the age scores still applies. Does this reduced parameterisation improve the fit. Finally re-estimate the full row and column effects model with all νj unknown (so a normalisation constraint is needed again) but without a monotonicity constraint, and assess whether there is a reversal in the rankings.