Modeling Achievement Gap Trajectories with Hierarchical Penalized Splines R package achieveGap version 0.1.0 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>). Software Depends: R (>= 4.1.0) Imports: mgcv (>= 1.9-0), lme4 (>= 1.1-0), MASS (>= 7.3-0), ggplot2 (>= 3.4.0) Suggests: knitr (>= 1.36), rmarkdown (>= 2.11), testthat (>= 3.0.0) Subir Hait <haitsubi@msu.edu> Comprehensive R Archive Network (CRAN) Subir Hait [aut, cre] (ORCID: <https://orcid.org/0009-0004-9871-9677>) GPL (>= 3) 2026-03-19 application/tgz https://CRAN.R-project.org/package=achieveGap doi:10.32614/CRAN.package.achieveGap