In the health and social sciences, two types of mixture model have been widely used by researchers to identify heterogeneous trajectories of participants within a population: latent class growth analysis (LCGA) and the growth mixture model (GMM). Both methods parametrically model trajectories of individuals, and capture latent trajectory classes, by using an expectation-maximization (E-M) algorithm. However, parametric modeling of trajectories using polynomial functions or monotonic spline

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... ions results in limited flexibility for modelling trajectories; as a result, group membership may not be classified accurately due to model misspecification. In this paper, we propose a mixture model (SMM) allowing for smoothing functions of trajectories using a modified E-M algorithm. In the E step, participants are reassigned to only one group for which the estimated trajectory is the most similar to the observed one; in the M step, trajectories are fitted using generalized additive mixed models (GAMM) with smoothing functions of time. This modified E-M algorithm is straightforward to implement using the recently released gamm4 macro in R. The SMM can incorporate time-varying covariates and be applied to longitudinal data with normal, Bernoulli, and Poisson distributions. Simulation results show favorable performance of the SMM in terms of classification of group membership. The proposed method is illustrated by its application to body mass index data of individuals followed from adolescence to young adulthood and the relationship with incidence of cardiometabolic disease.