Stratified subsampling for regression analysis of big count response data Available to Purchase

Count frequency data are found in many applications such as traffic accident analysis, car insurance claims, hospital admissions records and adverse vaccine reaction data. In some cases, these data have high zero counts and/or heavy tails due to cases such as no claim or no incidence in insurance and accident data, respectively. In regression modelling, the data size can be formidable due to either large sample size and/or large number of covariates or predictors which leads to computational challenges. Although many computer engineering solutions are available through supercomputers and parallel computing, there exists limitations due to cost and accessibility. As such, statistical solutions have been considered to ameliorate the challenges posed by regression modelling of big data. In general, these statistical solutions are classified as divide and conquer approach, fine-to-coarse method and subsampling methods. To address the problem of large data size in count regression modelling, we propose a stratified subsampling strategy according to frequency classes with shrinkage leveraging for statistical inference. An attractive feature of this strategy is in its ability to preserve the characteristics of data like over dispersion, high zero counts and/or heavy-tailed. A Monte Carlo simulation study is conducted to investigate the performance of the proposed stratified subsampling method in regression modelling with big count data. The regression analysis will be illustrated using a family of mixed Poisson regression models which have been shown to be flexible in its ability to model count data with high zero counts and/or a long tail.