Piecewise Growth Mixture Model with More than One Unknown Knot: An Application in Reading Development.

The present study explored the potential growth pattern of reading development from kindergarten to high school using the publicly available dataset from the Early Childhood Longitudinal Study-Kindergarten cohort (ECLS-K). We extended the piecewise growth mixture model (PGMM) with a single unknown knot into the situation with more than one knot. The results showed that the PGMM with more than one knot could be used to study reading development. Students' reading development had fast growth before entering elementary school, but development slowed after. The turning point appears differently for a heterogeneous population. For the normal group, the knot was at Grade 2 (y =2.01), while the faster group transferred into the second period much earlier than the normal group around Grade 1 (y = 0.87). However, both groups reached similar ability levels in later school years. Moreover, teachers should pay special attention to the slower group, which had not only slower growth (y = 2.69) than but also difficulty catching up with the normal-level children.