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Practical approaches to principal component analysis for simultaneously dealing with missing and censored elements in
1Department of Theoretical Chemistry, Institute of Chemistry, The University of Silesia, 9 Szkolna Street, 40-006 Katowice, Poland.
Analytica Chimica Acta
|September 11, 2013
Summary
Handling missing and left-censored chemical data is crucial. Substitution with half the reporting limit works for up to 40% censoring, while the generalized nonlinear iterative partial least squares (NIPALS) algorithm is best for higher percentages.
Area of Science:
- Analytical Chemistry
- Chemometrics
- Data Science
Background:
- Multivariate chemical data frequently contain missing completely at random (MCAR) and left-censored values below a reporting limit.
- Existing methods effectively address MCAR data or data with outliers, but simultaneous processing of missing and left-censored data remains challenging.
Purpose of the Study:
- To compare the suitability of different methods for handling simultaneous missing and left-censored elements in multivariate chemical data.
- To identify the most effective approach for robust data processing in analytical chemistry.
Main Methods:
- Comparison of the generalized nonlinear iterative partial least squares (NIPALS) algorithm, maximum likelihood principal component analysis (MLPCA), and various replacement methods.
- Monte Carlo simulation study using both artificial and real chemical data sets.
Main Results:
- Substitution with half the reporting limit is effective for variables with up to 30-40% left-censored elements.
- The generalized NIPALS algorithm is recommended for higher percentages of left-censored elements per variable, especially when numerous variables are censored.
- The expectation-maximization (EM) approach with half-reporting limit substitution is a viable strategy, with generalized NIPALS as a fallback if EM convergence fails.
Conclusions:
- The choice of method depends on the percentage and number of censored variables in the chemical dataset.
- Generalized NIPALS offers a robust solution for complex censoring scenarios in multivariate chemical data analysis.
- Accurate data imputation is essential for reliable downstream analysis and interpretation of chemical measurements.
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