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This study introduces adjusted Partial Least Squares (PLS) estimators, denoted PLSc, offering consistent and asymptotically normal (CAN) estimates for latent variable models. PLSc corrects inconsistencies in standard PLS, improving parameter estimation accuracy.

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Area of Science:

  • Statistics
  • Econometrics
  • Psychometrics

Background:

  • Partial Least Squares (PLS) is widely used for modeling latent variables measured indirectly by indicators.
  • Standard PLS estimators are known to be inconsistent because the linear compounds used do not accurately represent latent variables.
  • This inconsistency affects the reliability of parameter estimates in complex structural models.

Purpose of the Study:

  • To propose simple, non-iterative corrections to Partial Least Squares (PLS) to achieve consistent and asymptotically normal (CAN) estimators.
  • To develop methods for obtaining CAN-estimators for loadings and latent variable correlations.
  • To extend the approach to estimate parameters in structural recursive systems, including interaction terms.

Main Methods:

  • Development of a novel adjustment to the standard PLS procedure, termed PLSc.
  • Derivation of analytical corrections for loadings and latent variable correlations.
  • Application of the adjusted method to structural recursive models with linear, interaction, and higher-order terms.

Main Results:

  • The proposed adjusted PLS (PLSc) yields consistent and asymptotically normal (CAN) estimators for loadings and latent variable correlations.
  • PLSc provides CAN-estimators for structural parameters in recursive systems, irrespective of the joint distribution of variables.
  • The method also produces CAN-estimators for models with quadratic and higher-order terms under joint normality assumptions.

Conclusions:

  • The adjusted Partial Least Squares (PLSc) offers a statistically sound alternative to standard PLS for latent variable modeling.
  • PLSc addresses the well-known inconsistency issues of traditional PLS, providing more reliable parameter estimates.
  • The study demonstrates the efficacy of PLSc through Monte Carlo simulations and an empirical application, comparing it with Latent Moderated Structural Equations (LMS).