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Structural Equation Modeling Optimization in Python.

Project description


Visit our website for a detailed introduction

semopy is a Python package that includes numerous Structural Equation Modelling (SEM) techniques.


  • Write down a model description in a user-friendly syntax
  • Estimate model's parameters using a variety of objective functions
  • Estimate models with population structure via random effects
  • Restricted Maximum Likelihood
  • Integration with gaussian processes/mixture models to tackle huge variety of phenomena
  • Calculate numerous statistics and fit indices
  • Estimate model's parameters in presence of ordinal variables
  • A vast number of settings to fit a researcher's needs
  • Fast and accurate
  • Automatically create fancy HTML reports


semopy is available at PyPi and can be installed by typing the following line into terminal:

pip install semopy


To specify SEM models, The semopy uses the syntax, which is natural to describe regression models in R. The syntax supports three operator symbols characterising relationships between variables:

  • ~ to specify structural part,
  • =~ to specify measurement part,
  • ~~ to specify common variance between variables.

For example, let a linear equation in the structural part of SEM model take the form:

y = β1 x1 + β2 x2 + ε

Then, in semopy syntax it becomes:

y ~ x1 + x2

Parameters β1, β2 are to be estimated by semopy. In some cases a user might want to fix some of parameters to particular value. For instance, let's assume that we want β1 to stay equal to 2.0 and we are only interested in estimating β2:

y ~ 2*x1 + x2

Likewise, if a latent variable η is explained by manifest variables y1, y2, y3, then in semopy syntax it can be written down this way:

eta =~ y1 + y2 + y3


The pipeline for working with SEM models in semopy consists of three steps:

  1. Specifying a model
  2. Loading a dataset.
  3. Estimating parameters of the model.

Main object required for scpecifying and estimating an SEM model is Model.

Model is responsible for setting up a model from the proposed SEM syntax:

# The first step
from semopy import Model
mod = """ x1 ~ x2 + x3
          x3 ~ x2 + eta1
          eta1 =~ y1 + y2 + y3
          eta1 ~ x1
model = Model(mod)

Then a dataset should be provided:

# The second step
from pandas import read_csv
data = read_csv("my_data_file.csv", index_col=0)

To estimate parameters of the model we run a fit method with the dataset as an argument:

# The third step

The default objective function for estimating parameters is the likelihood function and the optimisation method is SLSQP (Sequential Least-Squares Quadratic Programming). However, the semopy supports a wide range of other objective functions and optimisation schemes being specified as parameters in the fit method.

Finally, user can inspect parameters' estimates:


Would you like to know more?

Tutorial and overview of semopy features are available at the project's website.


numpy, pandas, scipy, sympy, sklearn, statmodels


  • Mescheryakov A. Georgy - Developer - georgy.m - student, SPbPU
  • Igolkina A. Anna - Supervisor - iganna - Engineer, SPbPU


This project is licensed under the MIT License - see the file for details.

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