Random-effects, fixed-effects and the within-between specification for clustered data in observational health...

Area of Science:

• Econometrics
• Biostatistics
• Health Services Research

Background:

• Unaccounted group-level characteristics can bias traditional linear regression.
• Random-effects (RE) and fixed-effects (FE) estimators address these issues but rely on different assumptions.
• The within-between (WB) method, proposed by Mundlak, is an underutilized alternative.

Purpose of the Study:

• Compare the performance of RE, FE, and WB estimators.
• Evaluate estimator appropriateness across diverse simulation scenarios.
• Identify the most efficient and least biased estimation method.

Main Methods:

• Conducted a large-scale simulation study (16,200 scenarios).
• Varied factors include group number, group size, within-group variation, model fit, and model specification.
• Performance assessed by mean squared error of marginal effects and root mean squared error of fitted values.

Main Results:

• The WB approach demonstrated superior performance over RE and FE in finite samples.
• Traditional RE estimation was found to be optimal in fewer scenarios compared to FE and WB.
• The Hausman test's guidance for estimator selection was only accurate 61% of the time.

Conclusions:

• The WB approach is underutilized and particularly beneficial for marginal effects inference in small samples.
• Data characteristics and analysis objectives should guide estimator selection.
• Avoid blind application of any single estimator to prevent bias and flawed inference.