  The variability of structure in a finite Markov equivalence class of causally
sufficient models represented by directed acyclic graphs has been fully
characterized. Without causal sufficiency, an infinite semi-Markov equivalence
class of models has only been characterized by the fact that each model in the
equivalence class entails the same marginal statistical dependencies. In this
paper, we study the variability of structure of causal models within a
semi-Markov equivalence class and propose a systematic approach to construct
models entailing any specific marginal statistical dependencies.
