Abstract

Handling longitudinal data makes data analysis difficult since classical analysis procedures commonly fail to capture the autocorrelation between observations from the same subject. Moreover, an extra challenge for researchers is added when observations are nonstationary. In this context, antedependence modeling is a powerful approach to analyzing longitudinal data since there are no restrictions in variances or same-lag correlations behavior along the time points. Furthermore, this parametric class of models allows for more flexible variance-covariance matrix parametrization while enabling the implementation of well-known covariance structures, thereby reducing the number of parameters to estimate. In most investigations considering these models, the data is generally assumed to be normally distributed, although this assumption is not reasonable in cases of skewness, heavy tails, or multimodality. So, in this study, we propose to overcome these intricacies by extending antedependence modeling to nonstationary longitudinal data, assuming more general classes of distributions to the residuals, such as skew-normal and skew-t ones, in their centered versions. An advantage of using these distributions is that they are in the Scale Mixture Skew Normal (SMSN) family and can be written in a hierarchical form, which is convenient for their computational implementation and estimation procedures. Concerning the estimation, we adopted a Bayesian approach via Hamiltonian Monte Carlo using the STAN software due to its helpful convergence efficiency and user-friendly syntax. Simulation studies were conducted to investigate key aspects of Bayesian analysis, such as Markov chain convergences, parameter recovery, and the choice of priors presenting promising results. Regarding the potential applications, the flexibility to generalize scenarios for longitudinal analysis makes antedependence models highly promising for environmental data research.