Random Regression Models Based On The Skew Elliptically Contoured Distribution Assumptions With Applications To...

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Random regression models are crucial for longitudinal data analysis.
• Existing models often assume normal or symmetric distributions, limiting their applicability.
• Handling undetectable values and informative drop-outs remains a challenge.

Purpose of the Study:

• To extend random regression models using multivariate skew elliptical contoured distributions (ECD).
• To assess the performance of skew ECDs in fitting continuous data, especially when symmetry is violated.
• To evaluate model fitness through a simulation study and real data analysis.

Main Methods:

• Construction of random regression models based on multivariate skew ECD.
• Application of models to a real dataset with unimodal continuous data.
• Conducting a simulation study to assess model fit across various skew ECDs.
• Utilizing SAS/STAT V. 9.13 software for analysis.

Main Results:

• Skew ECDs demonstrate superior fitting for certain unimodal continuous data compared to Gaussian or general symmetric distributions.
• The proposed models effectively handle longitudinal data with undetectable values and informative drop-outs.
• The simulation study validates the model's fitness across diverse skew ECD scenarios.

Conclusions:

• Multivariate skew ECDs provide a flexible and robust framework for longitudinal data analysis.
• These distributions are advantageous when the assumption of symmetry is not met.
• The methodology offers a valuable tool for researchers dealing with complex longitudinal data structures.