Robust bias correction model for estimation of global trend in marine populations

In modeling biological and ecological processes from data, it is essential to deal with data selection bias properly in order to obtain reliable and reasonable predictions. To incorporate the mechanism of selection bias into a statistical analysis, a propensity score (PS) is widely employed as an inverse probability weight in order to obtain a consistent estimation of a binary response variable of interest. However, the estimation performance often becomes unstable due to the mis‐estimation of the PS. In order to obtain a consistent estimation as well as to stabilize the estimation performance, we propose a new regression model that incorporates the PS as an explanatory variable. Moreover, we show that the proposed model has a the property of double robustness, which enables us to obtain a consistent estimation of the response without suffering from selection bias if either the PS model or the proposed model is correctly specified. The robust bias correction model also accommodates heterogeneity of data distributions based on an asymmetric logistic model, which in turn improves model fitting and prediction accuracy. The PS in our regression model enables us to estimate consistently the global fish stock status even if the information of the stock status available is biased.