Constructing bootstrap confidence intervals for principal component loadings in the presence of missing data: a...

Area of Science:

• Statistics
• Data Analysis
• Machine Learning

Background:

• Principal Component Analysis (PCA) is a dimensionality reduction technique.
• Bootstrap confidence intervals are used to estimate the uncertainty of PCA loadings.
• Incomplete datasets require handling missing values before analysis, often using multiple imputation.

Purpose of the Study:

• To address the challenge of calculating accurate bootstrap confidence intervals for principal component loadings with multiply imputed data.
• To propose and evaluate methods for correcting confidence intervals in the presence of missing data.

Main Methods:

• Investigated several methods for correcting bootstrap confidence intervals for principal component loadings.
• Utilized simulation studies to assess the performance of the proposed corrections.
• Compared the coverage of population loadings using corrected intervals against existing methods.

Main Results:

• The proposed corrections for multiply imputed data demonstrated good coverage of population loadings.
• The methods proved effective across various simulated scenarios with incomplete data.
• Validated the utility of bootstrap confidence intervals for PCA loadings in complex datasets.

Conclusions:

• The developed methods provide reliable bootstrap confidence intervals for principal component loadings when dealing with multiply imputed data.
• These corrections are crucial for accurate statistical inference in PCA with missing data.
• The findings support the use of these corrected intervals in practical data analysis involving incomplete datasets.