Skew-normal antedependence models for skewed longitudinal data.

Antedependence models, also known as transition models, have proven to be useful for longitudinal data exhibiting serial correlation, especially when the variances and/or same-lag correlations are time-varying. Statistical inference procedures associated with normal antedependence models are well-developed and have many nice properties, but they are not appropriate for longitudinal data that exhibit considerable skewness. We propose two direct extensions of normal antedependence models to skew-normal antedependence models. The first is obtained by imposing antedependence on a multivariate skew-normal distribution, and the second is a sequential autoregressive model with skew-normal innovations. For both models, necessary and sufficient conditions for pth-order antedependence are established, and likelihood-based estimation and testing procedures for models satisfying those conditions are developed. The procedures are applied to simulated data and to real data from a study of cattle growth.