StructuralEquationModels.jl: a Julia Package for Extensible and Efficient Structural Equation Modeling

Maximilian S. Ernst, Alexey Stukalov, Andreas M Brandmaier, Aaron Peikert

Abstract: We introduce StructuralEquationModels.jl, a novel Structural Equation Modeling (SEM) software designed with extensibility as its core principle. Since theintroduction of SEM, the range of problems it is applied to is rapidly expand-ing. However, SEM software implementations did not anticipate such expansion,so software flexibility has become one major factor limiting the adoption of in-novations in the field of SEM. StructuralEquationModels.jl is designed to bemodular and extensible to remove that bottleneck. This approach not onlyspeeds up innovation in SEM but also ensures the integrity and reliability ofexisting functionality. We leverage the Julia programming language’s ecosystem to achieve efficient implementations of loss functions and gradients andsupport modern optimization backends. The versatility of StructuralEquation-Models.jl is demonstrated on a set of examples (e.g., adding support for regular-ized SEM) and simulations (e.g., sensitivity of the RMSEA to misspecificationof large factor analysis models). Using these simulations as a benchmark, weshow that StructuralEquationModels.jl is computationally more efficient thanexisting SEM implementations.