achieveGap: Modeling Achievement Gap Trajectories with Hierarchical
Penalized Splines
Implements a hierarchical penalized spline framework for estimating
achievement gap trajectories in longitudinal educational data.
The achievement gap between two groups (e.g., low versus high
socioeconomic status) is modeled directly as a smooth function
of grade while the baseline trajectory is estimated simultaneously
within a mixed-effects model. Smoothing parameters are selected
using restricted maximum likelihood (REML), and simultaneous
confidence bands with correct joint coverage are constructed
using posterior simulation. The package also includes functions
for simulation-based benchmarking, visualization of gap
trajectories, and hypothesis testing for global and
grade-specific differences. The modeling framework builds on
penalized spline methods (Eilers and Marx, 1996,
<doi:10.1214/ss/1038425655>) and generalized additive modeling
approaches (Wood, 2017, <doi:10.1201/9781315370279>), with
uncertainty quantification following Marra and Wood (2012,
<doi:10.1111/j.1467-9469.2011.00760.x>).
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