Regression in a copula model for bivariate count data

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Multivariate Frequency-Severity Regression Models in Insurance (2016, background): “In a regression context, this non-identifiability is less likely to be a concern, as noted in [25,29,30,32].”
Copula-Based Models for Multivariate Discrete Response Data (2013, methodology): “[44, 47]); this is not the case for the FGM and elliptical copulas in (11.”