Missing data imputation via the expectation-maximization algorithm can improve principal component analysis aimed at...

Area of Science:

• Nutritional science
• Biostatistics
• Data science

Background:

• Principal Component Analysis (PCA) is widely used for analyzing complex datasets, including biomarker profiles and dietary patterns.
• A common limitation in PCA is the presence of missing data, which can lead to biased results.
• The practice of imputing missing data before PCA is not consistently applied.

Purpose of the Study:

• To evaluate the effectiveness of the expectation-maximization (EM) algorithm for imputing missing data prior to PCA.
• To determine if EM imputation improves the derivation of biomarker profiles and dietary patterns.
• To assess the impact of missing data on PCA eigenvalues in nutritional research.

Main Methods:

• Numerical simulations were conducted to mimic real-world nutritional data with varying amounts of missing values.
• The expectation-maximization (EM) algorithm was used for missing data imputation.
• Principal Component Analysis (PCA) was applied to both original datasets (without missing values) and datasets with imputed missing values.
• Real-world data from the US National Health and Nutrition Examination Survey (NHANES) were analyzed.

Main Results:

• PCA applied to data with missing values resulted in biased eigenvalues compared to complete datasets.
• The bias in eigenvalues increased with a higher percentage of missing data.
• Imputing missing data using the EM algorithm before PCA led to eigenvalues that closely matched those from the complete dataset.
• These findings were validated using real-world NHANES data.

Conclusions:

• The EM algorithm is a reliable and advantageous method for imputing missing data before applying PCA in nutritional research.
• EM imputation effectively corrects eigenvalue bias caused by missing data, leading to more accurate biomarker profiles and dietary patterns.
• This technique is particularly beneficial for analyses involving smaller sample sizes.