Abstract:Longitudinal associations may vary over time, yet allowing every regression effect to be dynamic can inflate estimation variance and obscure interpretable structure. We develop time-varying-effect selection (TV-Select), a group-sparse smoothing framework that classifies covariate effects as zero, constant, or time varying. Each coefficient is decomposed into a constant mean and a centered temporal deviation represented by a full-rank, L2-normalized effective spline basis. A group penalty identifies varying components, while a roughness penalty controls their curvature. The resulting convex criterion is solved by cyclic block proximal-gradient updates and followed by smooth refitting. Under a full-column-rank unpenalized design and an effective model dimension that is small relative to the total number of observations, we establish prediction and parameter rates, blockwise function-estimation bounds, and exact recovery of the varying set under irrepresentability and beta-min conditions. A stable classification refit further separates zero from constant effects. For fixed-dimensional contrasts, we construct an oracle-equivalent one-step estimator with cluster-robust asymptotic normality and consistent sandwich variance estimation. Simulations demonstrate that TV-Select combines low false-positive rates with accurate function estimation and competitive prediction across a range of longitudinal settings. An application to Sleep-EDF data produces smooth and parsimonious temporal effect estimates with essentially unchanged held-out predictive performance.
From: Mengfei Ran [view email]
[v1]
Sun, 8 Mar 2026 14:39:35 UTC (1,879 KB)
[v2]
Fri, 31 Jul 2026 09:53:52 UTC (1,303 KB)
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