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  "Title": "Modeling Achievement Gap Trajectories with Hierarchical\nPenalized Splines",
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  "Description": "Implements a hierarchical penalized spline framework for\nestimating achievement gap trajectories in longitudinal\neducational data. The achievement gap between two groups (e.g.,\nlow versus high socioeconomic status) is modeled directly as a\nsmooth function of grade while the baseline trajectory is\nestimated simultaneously within a mixed-effects model.\nSmoothing parameters are selected using restricted maximum\nlikelihood (REML), and simultaneous confidence bands with\ncorrect joint coverage are constructed using posterior\nsimulation. The package also includes functions for\nsimulation-based benchmarking, visualization of gap\ntrajectories, and hypothesis testing for global and\ngrade-specific differences. The modeling framework builds on\npenalized spline methods (Eilers and Marx, 1996,\n<doi:10.1214/ss/1038425655>) and generalized additive modeling\napproaches (Wood, 2017, <doi:10.1201/9781315370279>), with\nuncertainty quantification following Marra and Wood (2012,\n<doi:10.1111/j.1467-9469.2011.00760.x>).",
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