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On the performance of L2E estimation in modelling heterogeneous count responses with extreme values

In healthcare studies, count data sets measured with covariates often exhibit heterogeneity and contain extreme values. To analyse such count data sets, we use a finite mixture of regression model framework and investigate a robust estimation approach, called the L2E [D.W. Scott, On fitting and adapting of density estimates, Comput. Sci. Stat. 30 (1998), pp. 124–133], to estimate the parameters. The L2E is based on an integrated L2 distance between parametric conditional and true conditional mass functions. In addition to studying the theoretical properties of the L2E estimator, we compare the performance of L2E with the maximum likelihood (ML) estimator and a minimum Hellinger distance (MHD) estimator via Monte Carlo simulations for correctly specified and gross-error contaminated mixture of Poisson regression models. These show that the L2E is a viable robust alternative to the ML and MHD estimators. More importantly, we use the L2E to perform a comprehensive analysis of a Western Australia hospital inpatient obstetrical length of stay (LOS) (in days) data that contains extreme values. It is shown that the L2E provides a two-component Poisson mixture regression fit to the LOS data which is better than those based on the ML and MHD estimators. The L2E fit identifies admission type as a significant covariate that profiles the predominant subpopulation of normal-stayers as planned patients and the small subpopulation of long-stayers as emergency patients.