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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Skew-normal antedependence models for skewed longitudinal data.

Shu-Ching Chang1, Dale L Zimmerman2

  • 1Clinical Program Services Research, Providence St. Vincent Medical Center, Portland, Oregon 97225, U.S.A.

Biometrika
|June 10, 2016
PubMed
Summary
This summary is machine-generated.

We introduce skew-normal antedependence models for analyzing skewed longitudinal data with time-varying correlations. These models extend normal antedependence methods, offering better analysis for complex datasets.

Keywords:
AntedependenceMultivariate skew-normal distributionPenalized maximum likelihood estimationSkew selectionTransition model

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Area of Science:

  • Statistics
  • Longitudinal Data Analysis
  • Time Series Analysis

Background:

  • Antedependence (transition) models are effective for longitudinal data with serial correlation, particularly when variances or correlations change over time.
  • Standard normal antedependence models lack applicability for longitudinal data exhibiting significant skewness.
  • Existing statistical inference procedures for normal antedependence models are well-developed but unsuitable for skewed data.

Purpose of the Study:

  • To propose two novel extensions of normal antedependence models to skew-normal antedependence models.
  • To address the limitations of normal antedependence models when applied to skewed longitudinal data.
  • To develop statistical inference procedures for these new skew-normal models.

Main Methods:

  • Imposing antedependence on a multivariate skew-normal distribution.
  • Developing a sequential autoregressive model with skew-normal innovations.
  • Establishing conditions for [Formula: see text]th-order antedependence and developing likelihood-based estimation and testing procedures.

Main Results:

  • Two distinct skew-normal antedependence models were successfully formulated.
  • Necessary and sufficient conditions for [Formula: see text]th-order antedependence were derived for both proposed models.
  • Likelihood-based estimation and testing procedures were developed and validated using simulated and real cattle growth data.

Conclusions:

  • The proposed skew-normal antedependence models provide a viable statistical framework for analyzing skewed longitudinal data.
  • These models effectively handle time-varying variances and correlations in skewed longitudinal datasets.
  • The developed methods are applicable to both simulated and real-world longitudinal studies, such as the cattle growth example.