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

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.