A multigroup extension to piecewise path analysis

Jacob C Douma,Bill Shipley

doi:10.1002/ecs2.3502

Abstract

AbstractPath 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.

Highlights

Ecological studies often involve many measured variables that are interrelated in one way or another
One can test, identical to classical structural equation modeling (SEM), the consistency of multigroup path models by constraining some coefficients to be equal across groups, and a saturated model that assumes that all estimated coefficients to be group-specific
This paper presents two methods for multigroup analysis for piecewise path models that can be represented by directed acyclic graphs

Summary

Introduction

Ecological studies often involve many measured variables that are interrelated in one way or another. When this assumption does not hold, or when we wish to statistically test this assumption in order to determine whether (and where) the causal structure might differ between groups of observations, one must conduct a multigroup path analysis.

Results

Conclusion