The iterated score regression estimation algorithm for PCA-based missing data with high correlation

Area of Science:

• Statistics
• Data Science
• Machine Learning

Background:

• Missing data poses challenges in statistical analyses, particularly within Principal Component Analysis (PCA).
• High correlations among variables complicate imputation methods for missing data.
• Existing imputation algorithms may not perform optimally under high correlation scenarios.

Purpose of the Study:

• To propose a novel imputation algorithm, iterated score regression, for handling missing data in PCA with high correlations.
• To evaluate the stability and accuracy of the proposed algorithm.
• To compare the performance of iterated score regression against modified existing algorithms.

Main Methods:

• Development of the iterated score regression algorithm using a transformation matrix to separate missing and observed data.
• Construction of regression equations based on data blocks, score matrix, and PCA model.
• Sensitivity analysis examining effects of standard deviations, correlation coefficients, missing proportions, variable numbers, and sample sizes.
• Modification and comparison with three existing imputation algorithms.

Main Results:

• The iterated score regression algorithm consistently achieved the smallest Mean Squared Error (MSE) values among compared methods.
• The algorithm demonstrated stability and accuracy across various tested conditions.
• Numerical studies and real-world data set illustrations confirmed the algorithm's advantages.

Conclusions:

• Iterated score regression is an effective imputation method for PCA with highly correlated missing data.
• The algorithm offers improved accuracy and stability over existing approaches.
• The proposed method provides a valuable tool for addressing complex missing data scenarios in statistical modeling.