Misturas finitas de modelos parcialmente lineares: uma abordagem via P-splines para estimação das componentes não paramétricas

Abstract

Regression models, well-established in statistical development, remain a primary tool for investigating relationships between predictors and outcomes. In their classical formulation, these models assume that observations come from a single homogeneous population. However, in practice, unobserved characteristics may lead to distinct behaviors among observation subgroups. In such circumstances, we can employ regression mixture models to incorporate this heterogeneity, estimating not only the specific parameters of each mixture component (subgroup) but also the posterior probabilities of each observation belonging to each component - which can be used in classification and clustering contexts, in the framework of supervised and unsupervised learning, respectively. In this work, we study mixtures of partially linear models using P-splines for estimating the nonparametric components. Our configuration allows different linear and nonlinear covariates to composse the semiparametric structure of each group. The penalized maximum likelihood estimators were obtained through an EM-type algorithm, while standard errors were calculated via the empirical information matrix. For selecting the curve smoothing parameters and the number of groups, we used the Bayesian Information Criterion (BIC). The proposed methodology was evaluated through simulation studies and real data applications. Furthermore, in the application, the goodness-of-fit was verified by constructing simulated envelopes based on randomized quantile residuals.