Determining the number of components in PLS regression on incomplete data set

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Partial least squares regression (PLS) is a multivariate statistical method widely used in applied research.
• PLS regression effectively analyzes relationships between an outcome and multiple components.
• The NIPALS algorithm can estimate parameters even with incomplete datasets, but component selection with missing data is debated.

Purpose of the Study:

• To investigate the performance of the NIPALS algorithm in Partial Least Squares (PLS) regression with varying proportions and types of missing data.
• To compare different criteria for selecting the number of components in PLS regression when dealing with incomplete datasets.
• To evaluate the effectiveness of imputation methods prior to component selection in PLS regression.

Main Methods:

• The NIPALS algorithm was used to fit PLS regression models to datasets with simulated missing data (5% to 50%).
• Component selection was assessed using Q2-leave-one-out, AIC, and BIC criteria.
• Three imputation methods were compared: multiple imputation by chained equations, k-nearest neighbour imputation, and singular value decomposition imputation.

Main Results:

• The NIPALS algorithm's behavior was studied under various missing data scenarios.
• Q2-leave-one-out component selection demonstrated more reliable results compared to AIC and BIC criteria when applied to both incomplete and imputed datasets.
• The performance of imputation methods varied, impacting the subsequent component selection.

Conclusions:

• Q2-leave-one-out is a more robust criterion for selecting the number of components in PLS regression with missing data.
• Imputation strategies can influence the choice of components, highlighting the importance of method selection.
• Further research is needed to optimize imputation and component selection strategies for PLS regression in the presence of missing data.