Inference from stratified samples: Study design, bias and graphical model representations

Stratification is a widely used strategy in empirical research to improve efficiency of the sampling design. One concern of stratification is that ignoring it on analysis may bias the relationship between variables. A weighted analysis can only be carried out when sampling weights are known. When these are unknown, valid inference on the relationship between variables then depends on the ignorability of the design, which may be difficult to establish. Here, graphical representations of multivariate dependencies and independencies are used to find necessary conditions for ignorability of stratified sampling designs for inference on conditional and marginal relationships between variables.