Collapsibility of the Conditional Models of CG‐Graphical Models

Abstract The conditional models of CG‐graphical models and their collapsibility property have been continuously attracting researchers' attention. The pioneering work of Didelez & Edwards (2004) derived the equivalent conditions for the conditional models' collapsibility, albeit the result is applicable only to the cases where a specific assumption holds. The subsequent study by B. Liu & Guo (2013) eliminated the assumption requirement in the settings with purely discrete or continuous variables. Via a novel technical approach, this work fully resolves the challenge for the complex scenario with mixed variable types. By examining model interaction preservation after marginalization, we bypass the need to compute intractable conditional densities and gain new insights into the problem. We identify a set of equivalent conditions for the model‐collapsibility in the most general setting without requiring additional assumption. Furthermore, we establish the equivalence between model‐collapsibility and estimate‐collapsibility for the conditional models of CG‐graphical models.