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

Area of Science:

• Educational Psychology
• Developmental Psychology
• Quantitative Research Methods

Background:

• Understanding reading development trajectories is crucial for effective educational interventions.
• Previous models often assume a single turning point, potentially oversimplifying complex developmental patterns.
• The Early Childhood Longitudinal Study-Kindergarten cohort (ECLS-K) provides a rich dataset for longitudinal analysis.

Purpose of the Study:

• To explore heterogeneous reading development patterns from kindergarten to high school.
• To extend piecewise growth mixture models (PGMM) to accommodate multiple change points in reading ability.
• To identify distinct growth trajectories and their characteristics within a large student population.

Main Methods:

• Utilized the ECLS-K dataset for longitudinal analysis of reading development.
• Extended the piecewise growth mixture model (PGMM) to include multiple knots (change points).
• Analyzed reading growth patterns across different student subgroups.

Main Results:

• Reading development exhibits fast initial growth followed by a slowdown, with varying turning points across individuals.
• Identified distinct groups: a 'normal' group with a turning point around Grade 2, and a 'faster' group around Grade 1.
• A 'slower' group demonstrated significantly slower growth and difficulty catching up, despite reaching similar later ability levels as the normal group.

Conclusions:

• The extended PGMM effectively models complex, multi-knot reading development patterns.
• Student reading development is heterogeneous, with different groups experiencing distinct growth phases.
• Early identification and targeted support for slower-developing readers are essential for academic success.