Trajectory clustering with adjustment for time-varying covariate effects

In this paper, we propose a penalized regression method to detect subgroups of trajectories while accounting for the time-varying effects of given covariates. Specifically, we allow both the latent heterogeneous trajectories and the covariate effects to be nonlinear which can be approximated by B-splines. We then identify subgroups by applying a pairwise-fusion penalization on coefficients and estimate the functional effects of covariates simultaneously without prespecifying the number of subgroups and the underlying distribution. In theory, we establish consistency properties for estimated trajectories, subgrouping memberships and functional effects under suitable conditions. The efficiency of the proposed method in identifying subgroups and estimating the nonparametric functions is illustrated through extensive simulations. To demonstrate the effectiveness of the proposed trajectory clustering method with adjustment for time-varying effects, we analyze CO2 emissions trajectories while controlling the effects of GDP per capita.