A fast and flexible Structural Equation Modelling Framework
33 Stars
Updated Last
1 Year Ago
Started In
December 2019


Documentation Build Status Citation
Stable Dev Project Status: Active – The project has reached a stable, usable state and is being actively developed. Github Action CI codecov DOI

This is a package for Structural Equation Modeling. It is still in development. Models you can fit include

  • Linear SEM that can be specified in RAM (or LISREL) notation
  • ML, GLS and FIML estimation
  • Ridge Regularization
  • Multigroup SEM
  • Sums of arbitrary loss functions (everything the optimizer can handle).

We provide fast objective functions, gradients, and for some cases hessians as well as approximations thereof. As a user, you can easily define custom loss functions. For those, you can decide to provide analytical gradients or use finite difference approximation / automatic differentiation. You can choose to mix and match loss functions natively found in this package and those you provide. In such cases, you optimize over a sum of different objectives (e.g. ML + Ridge). This mix and match strategy also applies to gradients, where you may supply analytic gradients or opt for automatic differentiation or mix analytical and automatic differentiation.

You may consider using this package if:

  • you want to extend SEM (e.g. add a new objective function) and need an extendable framework
  • you want to extend SEM, and your implementation needs to be fast (because you want to do a simulation, for example)
  • you want to fit the same model(s) to many datasets (bootstrapping, simulation studies)
  • you are planning a study and would like to do power simulations

The package makes use of

  • Symbolics.jl for symbolically precomputing parts of the objective and gradients to generate fast, specialized functions.
  • SparseArrays.jl to speed up symbolic computations.
  • Optim.jl and NLopt.jl to provide a range of different Optimizers/Linesearches.
  • FiniteDiff.jl and ForwardDiff.jl to provide gradients for user-defined loss functions.

At the moment, we are still working on

  • optimizing performance for big models (with hundreds of parameters)


If you have questions you may ask them here in the issues. Please observe our code of conduct.