{ "_id": "6a105d8dacfb0bcc41ca4d3c", "Package": "mGSFPCA", "Title": "Estimate Functional Principal Components from Sparse Data", "Version": "0.2.2", "Authors@R": "c(person(\"Uche\", \"Mbaka\", , \"uche.mbaka@ucd.ie\", role = c(\"aut\", \"cre\"),\ncomment = c(ORCID = \"0000-0002-1427-6388\")),\nperson(\"Michelle\", \"Carey\", , \"michelle.carey@ucd.ie\", role = \"ctb\",\ncomment = c(ORCID = \"0000-0002-5603-4264\"))\n)", "Description": "Implements functional principal component analysis (FPCA)\nfor univariate and multivariate sparse functional data. The\npackage estimates eigenfunctions, eigenvalues, and error\nvariance simultaneously via maximum likelihood estimation\n(MLE), using a spline basis representation of the\neigenfunctions. Orthonormality of the estimated eigenfunctions\nis enforced through a modified Gram-Schmidt (MGS)\northogonalization procedure applied iteratively during\nestimation, avoiding direct optimization over the Stiefel\nmanifold and improving numerical stability. The optimal number\nof basis functions and principal components is selected via an\nAkaike Information Criterion (AIC)-type criterion, supporting\nboth a full grid-search strategy and a computationally\nefficient sequential selection approach. Principal component\nscores are estimated by conditional expectation, enabling\nreconstruction of individual trajectories over the entire\ndomain from sparse observations. Pointwise confidence intervals\nfor reconstructed trajectories are also provided. 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