Abstract

This study proposes an environment-invariant varying-coefficient hybrid factor model for heterogeneous multi-study data. The model decomposes regional white matter measurements into common age-varying covariate effects, environment-specific baseline functions, and latent low-dimensional nuisance components. The covariate effects of primary interest are assumed to be invariant across study environments. We develop a local-polynomial invariance criterion for the common coefficient functions and combine it with a latent-hybrid factor adjustment, yielding the varying-coefficient latent-hybrid environment-invariant local kernel smoothing estimator. The procedure combines local polynomial smoothing, cross-environment invariance, and latent factor adjustment to estimate stable lifespan association functions over partially overlapping age supports. We establish estimation theory and illustrate the proposed approach through simulations and an application to multi-study white matter data.