Addressing Heteroscedasticity in Correlated Binary Data: A Bayesian Mixed Effects Location Scale Approach

The mixed effects logistic regression model is a common model for analysing correlated binary data as longitudinal data. The between and within subject variances are typically considered to be homogeneous but longitudinal data often show heterogeneity in these variances. This study proposes a Bayesian mixed effects location scale model to accommodate heteroscedasticity in binary data analysis.

This study was carried out in two stages; first, the simulation study was used to evaluate the accuracy of the proposed model with the Bayesian approach and then the proposed model was applied to a real data. In simulation study, the data were generated from the mixed effects location scale model with different correlations between the random location effect and random scale effect and different sample sizes. In order to evaluate the accuracy of the estimations, the Root Mean Square Error, bias and Coverage Probability were calculated and the deviance information criterion was used to select the appropriate model. At the end we utilized this model to analyse uric acid levels of patients with haematological disorders.

The simulation results show the accuracy of model parameter estimates as well as the correlation between random location and scale effects. They also display that if a random scale effect is present in the data, it should be accounted for in model. Otherwise, the model is forced to assign the within subject variation due to these subject random effects to the error term. The results of real data are also in line with this. The odds of having normal UA levels increases by a factor of 26% per week. Due to the positive value of the covariance parameter, patients with higher mean of UA levels show higher variation in UA levels. Furthermore, the significance of the covariates in the between subject and within subject variances model, as well as the significance of the random scale variance determines the heterogeneity across subjects.

Bayesian mixed effects location scale model provides a useful tool for analysing correlated binary data with heteroscedasticity because it considers data correlation and modelling mean and variance simultaneously. Furthermore, it improves the accuracy of statistical inference in longitudinal studies compared to classic mixed effects models.