Incompletely Observed Nonparametric Factorial Designs With Repeated Measurements: A Wild Bootstrap Approach

Area of Science:

• Statistics
• Biostatistics
• Life Sciences

Background:

• Multivariate data analysis in life sciences often uses MANOVA or mixed models.
• These methods require complete data and specific distributional assumptions (e.g., continuity, covariance structure).
• Discrete or ordered categorical data present challenges for traditional parametric methods.

Purpose of the Study:

• Develop statistically sound procedures for analyzing multivariate data with missing values.
• Extend rank-based methods to handle ordinal or ordered categorical data.
• Address limitations of existing methods regarding complete data and distributional assumptions.

Main Methods:

• Utilized nonparametric rank-based approaches.
• Applied a wild bootstrap procedure.
• Employed quadratic form-type test statistics for analysis.

Main Results:

• Developed asymptotically correct procedures for handling missing data and singular covariance matrices.
• Demonstrated applicability to ordinal and ordered categorical data.
• Validated procedure performance through extensive simulation studies, including small samples.

Conclusions:

• The new methods offer robust alternatives for complex data structures in life science research.
• The wild bootstrap and rank-based statistics provide reliable analysis for incomplete and categorical multivariate data.
• The procedures are validated for practical use in real-world data examples.