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Path Analysis With Mixed-Scale Variables: Categorical ML, Least Squares, and Bayesian Estimations.

Xinya Liang1, Paula Castro1, Chunhua Cao2

  • 1University of Arkansas, Fayetteville, USA.

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Summary
This summary is machine-generated.

For mixed-scale path analyses predicting binary outcomes, weighted least squares (WLSMV) and Bayesian methods with weakly informative priors (Bayes-WI) offer the most accurate estimators, especially with smaller samples.

Keywords:
Bayesian estimationcategorical MLRleast squaresmixed-scale datapath analysis

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Area of Science:

  • Statistics
  • Social and Behavioral Sciences
  • Medicine
  • Education

Background:

  • Path models commonly integrate continuous and ordinal variables to predict binary outcomes in applied research.
  • Selecting appropriate statistical estimators is crucial for reliable results in these complex models.

Purpose of the Study:

  • To evaluate the performance of six different statistical estimators for path models with mixed-scale data predicting binary outcomes.
  • To provide practical guidance on choosing the most accurate and stable estimators.

Main Methods:

  • Monte Carlo simulations were used to compare six estimators: robust maximum likelihood (MLR-probit, MLR-logit), weighted and unweighted least squares (WLSMV, ULSMV), and Bayesian methods (Bayes-NI, Bayes-WI).
  • Simulations varied sample sizes, variable scales, and effect sizes.

Main Results:

  • Weighted least squares with mean and variance adjustment (WLSMV) and Bayesian methods with weakly informative priors (Bayes-WI) demonstrated consistently low bias and Root Mean Square Error (RMSE).
  • These preferred estimators performed particularly well in small samples or when predictor variables had few categories.
  • Categorical robust maximum likelihood (MLR) estimators showed unstable results for moderate effect sizes.

Conclusions:

  • WLSMV and Bayes-WI are recommended for mixed-scale path analyses predicting binary outcomes due to their stability and accuracy.
  • The choice of estimator significantly impacts the reliability of findings in applied research across various disciplines.
  • This study offers crucial insights for researchers seeking robust inference in complex statistical modeling.