Out-of-bag Prediction Error: A Cross Validation Index for Generalized Structured Component Analysis

Area of Science:

• Statistics
• Psychometrics
• Machine Learning

Background:

• Cross-validation is crucial for assessing predictive generalizability in structural equation modeling (SEM).
• Existing cross-validation indices are available for factor-based and component-based SEM approaches like Partial Least Squares Path Modeling.
• Generalized Structured Component Analysis (GSCA), a component-based approach, currently lacks a dedicated cross-validation index.

Purpose of the Study:

• To propose a novel cross-validation index for Generalized Structured Component Analysis (GSCA).
• To address the absence of a specific cross-validation measure for GSCA.
• To enhance the evaluation of predictive generalizability for GSCA models.

Main Methods:

• Introduction of the Out-of-bag Prediction Error (OPE) index for GSCA.
• Utilizing bootstrap methods to construct in-bag and out-of-bag samples.
• Integrating OPE calculation with GSCA's standard error and confidence interval estimation procedures.

Main Results:

• The proposed Out-of-bag Prediction Error (OPE) index effectively estimates expected prediction error in GSCA.
• The OPE index is computationally compatible with GSCA's bootstrap-based estimation.
• Empirical evaluations using simulated and real data demonstrate the performance of the OPE index.

Conclusions:

• The Out-of-bag Prediction Error (OPE) provides a valuable tool for cross-validation in GSCA.
• This new index improves the assessment of predictive generalizability for GSCA models.
• The OPE index enhances the utility and reliability of GSCA in structural equation modeling.