5.3 Impact of number of active equate groups

Figure 5.2: D-score by age of four models with all 1339 items using 0, 11, 33 and 184 active equate groups. The number of equate groups has a substantial effect on the D-score distribution. Use the arrows to see other cohorts (https://d-score.org/dbook-apps/models1339/).

Figure 5.2 is a display of the D-score by age for all 16 cohorts under four models. As a rough reference to compare, the grey curves in the back represent the Dutch model as calculated from the SMOCC study. In order to speed up the calculations, the figure shows a random subsample of 25% of all points. Manipulate the plot controls to switch cohorts.

All models contain 1339 items, but differ in the number of active equate groups. The most salient features per model are:

  • 1339_0: No equate groups, so different instruments in different cohorts are fitted independently;
  • 1339_11: Connects all cohorts through one or more equated items using 11 equate groups in total;
  • 1339_33: There are 33 equate groups that bridge cohort and instruments;
  • 1339_184: Maximally connects instruments and cohort by all equate groups.

Comparison of the D-score distribution by age across these models yields various insights:

  • The location of cohorts on the vertical scale depends on the number of active equate groups. For example, for Madagascar (MDG) the points are located around 52 when no equate groups are activated, whereas if all are activated it is about 68.

  • The age trend depends on the number of active equate groups. For example, for Colombia (COL) or Ethiopia (ETH), the model without equate groups has a shallow age trend, whereas it is steep for the 1339_184 model.

  • The vertical spread depends on the number of equate groups. For example, the spread in the Chile-2 (CHL-2) cohort substantially increases with the number of active equates.

  • Model 1339_0 for the Dutch NLD-SMOCC cohort is equivalent to the model fitted to the SMOCC study alone. Introducing equate groups compresses the range of scores, especially at the higher end.

We have now seen that the number of active equate groups has a large effect on the model. The next sections look into the equate groups in more detail.