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Influence curves for factor loadings.

C W Kwan1, W K Fung

  • 1Clinical Trials Centre, The University of Hong Kong, and Clinical Pathology Building, Queen Mary Hospital, Hong Kong. cwkwan@hku.hk

The British Journal of Mathematical and Statistical Psychology
|November 19, 2005
PubMed
Summary
This summary is machine-generated.

Influence curves help identify influential observations in maximum likelihood factor analysis (MLFA). While large distances may not alter factor patterns, they can change factor order and cause switching.

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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.