Skew-normal antedependence models for skewed longitudinal data.

Abstract

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 [Formula: see text]th-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.