Skew-normal antedependence models for skewed longitudinal data. (28th March 2016)

• Record Type: Journal Article
• Authors: Chang, Shu-Ching; Zimmerman, Dale L.
• Is Part Of: Biometrika. Volume 103:Number 2(2016:Jun.)
• Page Start: 363
• Page End: 376
• Publication Date: 2016-03-28
• Subjects: Antedependence -- Multivariate skew-normal distribution -- Penalized maximum likelihood estimation -- Skew selection -- Transition model; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asw006
• Languages: English
• ISSNs: 0006-3444

Abstract

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 $p$ 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.