Exploration of the MCMC Wald test with linear regression

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Traditional likelihood-based Wald tests can violate assumptions in small samples or complex models.
• Asparouhov and Muthén (2021) introduced a novel MCMC Wald test for robust frequentist inference.
• This method bypasses analytic expressions for sampling variation, offering potential improvements.

Purpose of the Study:

• To compare the performance of the new MCMC Wald test against maximum likelihood (ML) counterparts.
• To evaluate type I error rates and statistical power across various conditions.
• To assess the robustness of the MCMC Wald test with nonnormal data.

Main Methods:

• Simulation study comparing MCMC Wald test with ML Wald test.
• Varied sample sizes, effect sizes, and model complexity (degrees of freedom).
• Included analysis of nonnormal data distributions.

Main Results:

• The MCMC Wald test demonstrated superior performance over ML tests.
• Outperformance was particularly evident in small sample sizes (N < 150) and complex models (≥5 predictors).
• Robustness was confirmed with nonnormal data, maintaining superior accuracy.

Conclusions:

• The MCMC Wald test is a more reliable alternative to ML Wald tests, especially in challenging statistical conditions.
• It provides honest significance tests where traditional methods may falter.
• The findings support the adoption of MCMC Wald tests for improved statistical inference.