Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts*

Summary This paper makes three contributions. Firstly, it uses copula functions to obtain a flexible bivariate parametric model for non‐negative integer‐valued data (counts). Secondly, it recovers the distribution of the difference in the two counts from a specified bivariate count distribution. Thirdly, the methods are applied to counts that are measured with error. Specifically, we model the determinants of the difference between the self‐reported number of doctor visits (measured with error) and true number of doctor visits (also available in the data used).