## 5.5 Quality of equate groups

Figure 5.4 shows how the passing percentage depends on the child’s D-score as calculated under four models. All models include the same 1339 milestones, but differ in the number of active equates. The grey curve corresponds to the estimate made under the assumption that milestones are equally difficult. Good milestones for bridging instruments will have a tight bundle of curves. For example, equate EXP26 has tight bundles especially in models 1339_11 and 1339_33. By comparison, the curves of the two extreme models vary considerably: the model without any bridges (1339_0) or the model with all bridges (1339_184) are thus less than ideal. The shallow grey curve of model 1339_184 indicates a poorer overall fit.

Outfit and infit statistics measure the residual deviation of the items to the grey curve. High values (e.g. above 1.4) are undesirable and indicate lack of fit to the model. For example, the fit statistics for EXP26 in model 1339_184 (1.70 and 1.25) indicate a mediocre fit, whereas EXP26 in models 1339_33 and 1339_11 fits well. Sometimes the individual item curves are steeper than the grey curve. This indicates that these milestones are more discriminative than the combined item. Model 1339_0 lacks a grey curve and has no fit statistics for equate groups, because in that model, the combined item is not activated.

The probability curves provide a quick visual method for spotting promising and problematic equate groups. Examples of promising equate groups include COG36, FM31, GM26 and GM42. A little more weak are FM26 (has more variability), FM52 (looks promising, but has a problem with the item grigcd402 from the GCDG_JAM_STUNTED cohort), and GM35 (does not align cohort GCDG-ZAF). In such cases, one may wish to move an item out of an equate group, combine equate groups, or inactivate troublesome links.

Until now we only looked at models that include all 1339 items. In practice, we may improve upon the model by selecting the subset of milestones that fit the Rasch model. The next section looks in this modelling step in more detail.