Covariate selection for identifying the effects of a particular type of conditional plan using causal networks

Suppose that cause-effect relationships between variables can be described by a causal network with a linear structural equation model. Kuroki and Miyakawa proposed a graphical criterion for selecting covariates to identify the effect of a conditional plan with one control variable J. Roy. Statist. Soc. Ser. B, 2003, 65: 209–222]. In this paper, we study a particular type of conditional plan with more than one control variable and propose a graphical criterion for selecting covariates to identify the effect of a conditional plan of the studied type.