Local influence analysis of structural equation models with continuous and ordinal categorical variables

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Structural Equation Models (SEM) are widely used for analyzing complex relationships between variables.
• Assessing the influence of minor perturbations is crucial for model robustness and valid interpretation.
• Existing methods often struggle with mixed continuous and categorical data.

Purpose of the Study:

• To develop a novel methodology for assessing local influence in SEM with continuous and ordinal categorical variables.
• To provide a computationally efficient and easily implementable diagnostic tool for SEM.
• To enhance the reliability of SEM by identifying influential data points.

Main Methods:

• Treats latent variables as hypothetical missing data.
• Applies Cook's approach to the conditional expectation of the complete-data log-likelihood within an EM algorithm.
• Utilizes Gibbs sampling to generate observations for diagnostic measures, calculating normal and conformal normal curvatures.

Main Results:

• The proposed method is shown to be simple to implement and computationally efficient.
• The methodology is feasible for various perturbation schemes.
• Demonstrated effectiveness through two illustrative real-world examples.

Conclusions:

• The developed method offers a practical and efficient approach to local influence assessment in complex SEM.
• This technique enhances the diagnostic capabilities for SEM with mixed data types.
• The findings contribute to more reliable statistical modeling and data analysis.