Modeling longitudinal skewed functional data.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Longitudinal functional data analysis often struggles with complex dependencies and pointwise variations.
• Existing models may not adequately capture skewness, which is common in real-world data.
• Accurate modeling is crucial for reliable prediction and estimation in dynamic datasets.

Purpose of the Study:

• To introduce a novel statistical model for longitudinal functional data analysis.
• To explicitly account for and model pointwise skewness.
• To provide a unified framework for quantile estimation and trajectory prediction.

Main Methods:

• Utilized copula methodology to decouple marginal pointwise variation from longitudinal and functional dependence.
• Employed parametric distribution functions to describe time- and function-varying skewness.
• Quantified joint dependence using a Gaussian copula with low-rank covariance approximation.
• Developed an R package (sLFDA) for practical implementation.

Main Results:

• The proposed model successfully accounts for pointwise skewness in longitudinal functional data.
• The copula approach effectively captures complex dependencies.
• The model enables accurate pointwise quantile estimation and prediction of future data trajectories.
• Demonstrated applicability through simulations and a diffusion tensor imaging study.

Conclusions:

• The developed statistical model offers a robust approach to longitudinal functional data analysis with skewness.
• The method provides a flexible and unifying framework for various analytical tasks.
• The publicly available R package facilitates the application of this advanced statistical technique.