A Monte Carlo simulation study comparing linear regression, beta regression, variable-dispersion beta regression and fractional logit regression at recovering average difference measures in a two sample design

BMC Medical Research Methodology

Rahim Moineddin¹  Christopher Meaney¹ 

[1] Department of Family and Community Medicine, University of Toronto, 500 University Avenue, Toronto M5G1V7, ON, Canada

关键词: Monte Carlo simulation;    Multinomial distribution;    Beta distribution;    Fractional Logit regression;    Variable-dispersion beta regression;    Beta regression;    Linear regression;    Regression modelling;   

Others  :  1229875
DOI  :  10.1186/1471-2288-14-14

 received in 2013-08-30, accepted in 2014-01-21,  发布年份 2014

【 摘 要 】

Background

In biomedical research, response variables are often encountered which have bounded support on the open unit interval - (0,1). Traditionally, researchers have attempted to estimate covariate effects on these types of response data using linear regression. Alternative modelling strategies may include: beta regression, variable-dispersion beta regression, and fractional logit regression models. This study employs a Monte Carlo simulation design to compare the statistical properties of the linear regression model to that of the more novel beta regression, variable-dispersion beta regression, and fractional logit regression models.

Methods

In the Monte Carlo experiment we assume a simple two sample design. We assume observations are realizations of independent draws from their respective probability models. The randomly simulated draws from the various probability models are chosen to emulate average proportion/percentage/rate differences of pre-specified magnitudes. Following simulation of the experimental data we estimate average proportion/percentage/rate differences. We compare the estimators in terms of bias, variance, type-1 error and power. Estimates of Monte Carlo error associated with these quantities are provided.

Results

If response data are beta distributed with constant dispersion parameters across the two samples, then all models are unbiased and have reasonable type-1 error rates and power profiles. If the response data in the two samples have different dispersion parameters, then the simple beta regression model is biased. When the sample size is small (N₀ = N₁ = 25) linear regression has superior type-1 error rates compared to the other models. Small sample type-1 error rates can be improved in beta regression models using bias correction/reduction methods. In the power experiments, variable-dispersion beta regression and fractional logit regression models have slightly elevated power compared to linear regression models. Similar results were observed if the response data are generated from a discrete multinomial distribution with support on (0,1).

Conclusions

The linear regression model, the variable-dispersion beta regression model and the fractional logit regression model all perform well across the simulation experiments under consideration. When employing beta regression to estimate covariate effects on (0,1) response data, researchers should ensure their dispersion sub-model is properly specified, else inferential errors could arise.

【 授权许可】

   
2014 Meaney and Moineddin; licensee BioMed Central Ltd.

【 图 表 】

Figure 1.

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