Influence curves for factor loadings

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Maximum likelihood factor analysis (MLFA) is a statistical method used to identify underlying latent variables.
• Identifying influential observations is crucial for robust factor analysis results.
• Existing methods may not fully capture the impact of observations on factor loadings and order.

Purpose of the Study:

• To derive influence curves for initial and rotated factor loadings in MLFA.
• To propose Cook's distances based on empirical influence curves for identifying influential observations.
• To investigate the impact of influential observations on factor loadings, factor order, and factor switching.

Main Methods:

• Derivation of influence curves for factor loadings in MLFA.
• Calculation of Cook's distances using empirical influence curves.
• Analysis of the invariance properties of Cook's distances under scale transformation and factor rotation.
• Examination of factor switching using empirical influence curves and factor scores.

Main Results:

• Influence curves for MLFA factor loadings were successfully derived.
• Cook's distances were proposed and shown to be invariant under scale transformation and factor rotation.
• A large Cook's distance does not always imply excessive influence on the factor loading pattern.
• Influential observations can alter the ordering of factors and lead to factor switching.

Conclusions:

• The proposed Cook's distances provide a valuable tool for identifying influential observations in MLFA.
• Understanding the impact of influential observations on factor order and switching is essential for accurate interpretation of MLFA results.
• The invariance properties of Cook's distances enhance their reliability in various MLFA scenarios.