A Monte Carlo simulation study comparing linear regression, beta regression, variable-dispersion beta regression and...

Area of Science:

• Biostatistics
• Statistical Modeling
• Biomedical Research

Background:

• Biomedical data frequently involves response variables with support on the (0,1) interval.
• Traditional linear regression is often used, but alternative models like beta regression exist.
• This study compares linear regression with beta regression, variable-dispersion beta regression, and fractional logit regression.

Purpose of the Study:

• To compare the statistical properties of linear regression and novel beta regression models.
• To evaluate model performance under various conditions, including differing dispersion parameters and sample sizes.
• To assess bias, variance, type-1 error, and power of the compared models.

Main Methods:

• A Monte Carlo simulation design was employed.
• Data were simulated from probability models emulating proportion/percentage/rate differences.
• Estimators were compared based on bias, variance, type-1 error, and power, with Monte Carlo error estimates provided.

Main Results:

• All models performed well with constant dispersion parameters.
• Beta regression models showed bias when dispersion parameters differed between samples.
• Linear regression exhibited superior type-1 error rates in small samples, which could be improved in beta models via bias correction.
• Variable-dispersion beta regression and fractional logit regression showed slightly higher power.

Conclusions:

• Linear, variable-dispersion beta, and fractional logit regression models performed well overall.
• Proper specification of the dispersion sub-model is crucial for accurate inference in beta regression for (0,1) data.
• Misspecification can lead to inferential errors.