Acyclic directed mixed graphs (ADMGs) are the graphs used by Pearl (Causality: models, reasoning, and inference. Cambridge University Press, Cambridge, 2009) for causal effect identification. Recently, alternative acyclic directed mixed graphs (aADMGs) have been proposed by Peña (Proceedings of the 32nd conference on uncertainty in artificial intelligence, 577–586, 2016) for causal effect identification in domains with additive noise. Since the ADMG and the aADMG of the domain at hand may encode different model assumptions, it may be that the causal effect of interest is identifiable in one but not in the other. Causal effect identification in ADMGs is well understood. In this paper, we introduce a sound algorithm for identifying arbitrary causal effects from aADMGs. We show that the algorithm follows from a calculus similar to Pearl’s do-calculus. Then, we turn our attention to Andersson–Madigan–Perlman chain graphs, which are a subclass of aADMGs, and propose a factorization for the positive discrete probability distributions that are Markovian with respect to these chain graphs. We also develop an algorithm to perform maximum likelihood estimation of the factors in the factorization.