A multigroup extension to piecewise path analysis

Abstract

Abstract Path analysis allows one to test the consistency of data to hypothesized causal relationships between variables. Often, interest lies in how the hypothesized dependencies differ between groups. Multigroup comparisons can be made by imposing various constraints: constraints on the topology, the path coefficients, the residual variances, and more. To date, only classical path analysis and structural equation modeling can account for differences between groups. These techniques have assumptions that are often not appropriate for ecological studies. The d‐sep test and the recently developed generalized chi‐squared test relax many of these assumptions for path models that can be represented as directed acyclic graphs (DAGs), but are currently lacking a multigroup test. In this paper, we develop a multigroup extension to the d‐sep test. Furthermore, we show how a recently developed generalized chi‐squared test and AIC for DAGs can be used for multigroup testing. The approaches are illustrated by a worked example and implemented in the commonly used statistical package, R. Practical recommendations for multigroup modeling are made, and advantages and disadvantages of the multigroup d‐sep and the chi‐squared test are discussed.

Keywords

• d‐separation
• equality constraints
• group comparison
• hierarchical designs
• nonnormal data
• path analysis