4.4 Relation between age and the D-score
Figure 4.3 shows that the relation between D-score and age is nonlinear. Development in the first year is more rapid than in the second year. During the first year, infants gain about 40\(D\), whereas in the second year they gain about 20\(D\). A similar change in growth rate occurs in length (first year: 23 cm, second year: 12 cm, for Dutch children).
Figure 4.4 shows the mutual relations between age, percentage of milestone passing and the D-score. There are three main orientations.
- In the default orientation (age on the horizontal axis, D-score on the vertical axis), we see a curvilinear relation between the age and item difficulty.
- Rotate the graph (age on the horizontal axis, passing percentage on the vertical axis). Observe that this is the same pattern as in Figure 4.1 (with unequal slopes). Curves are coloured by domain.
- Rotate the graph (D-score on the horizontal axis, passing percentage on the vertical axis). Observe that this pattern is the same as in Figure 4.2 (with equal slopes).
All patterns can co-exist because of the curvature in the relation between D-score and age. The curvature is never explicitly modelled or defined, but a consequence of the equal-slopes assumption in the relation between the D-score and the passing percentage of a milestone.