Quantitative Analysis Using Structural Equation Modeling

Science Center Objects

USGS scientists have been involved for a number of years in the development and use of Structural Equation Modeling (SEM). This methodology represents an approach to statistical modeling that focuses on the study of complex cause-effect hypotheses about the mechanisms operating in systems. SEM is increasingly used in ecological and environmental studies and this site seeks to provide educational materials related to that enterprise. This site serves up tutorials, exercises, and examples designed to help researchers learn and apply SEM. Please click on the “Science” tab to learn more.

Disentangling the mechanisms regulating coastal wetland sustainability in the face of rising sea levels
One of our applications of SEM has been to uncover how human activities are linked to ecological integrity in National Parks.​​​​​​​

How to Use This Site

This site provides tutorials, examples, and exercises for those wishing to learn basic or specialized structural equation modeling methods. A description of what has been added and when can be found in the document What’s New


Comments on existing tutorials and suggestions for additional tutorials can be sent to sem@usgs.gov. Please note that while emails to this address will be read, we cannot provide individual replies given time constraints. For this we apologize, but we do hope the materials provided will be helpful.

To Receive Update Notices

We will maintain a mailing list for sending out updates to those interested in following the development of new materials. Just let us know of your interest by sending a message to sem@usgs.gov.

Site Contents     pdf

Prelude -  What is Structural Equation Modeling (SEM)?     pdf     video

Example SEM-based Study (SEM.0a)     pdf

I. Introduction and Background

     SEM Essentials
          Summary Points (SEM.1.1)     pdf
          Anatomy of SE Models (SEM.1.2)     pdf
          Model Specifications (SEM.1.3)     pdf
          Estimation (SEM.1.4)     pdf
          Path Rules (SEM.1.5)     pdf
          Interpreting Coefficients (SEM.1.6)     pdf
          Interpreting Effects of Categorical Predictors (SEM.1.7)     pdf     code     data
          Coefficients Involving Logged Variables (SEM.1.8)     pdf

     Doing SEM in R
          Introduction to Lavaan (SEM.2.1)     pdf     code     data
          Lavaan Syntax Reference (SEM.2.1a)     pdf
          Local Estimation of Equations (SEM.2.2)     pdf     code     data

     Model Evaluation (SEM.3)     pdf     code     data
          Model Evaluation Exercise     pdf     code     data


II. Basic Elements of Modeling

     Overview of the Modeling Process (SEM.4)     pdf
     The Test of Mediation (SEM.5)     pdf     code     data
           Test of Mediation Exercise     pdf     code     data
     SEM versus Multiple Regression (SEM.6)     pdf     code     data
     Causal Modeling Principles Revisited (SEM.7)     pdf
     SEM versus ANOVA and ANCOVA (SEM.8)     pdf


III. Modeling with Latent and Composite Variables

     Modeling with Latent Variables (SEM.9.1)     pdf     code     data
     Confirmatory Factor Analysis (SEM.9.2)     pdf     code     data
          Confirmatory Factor Analysis Exercise     pdf     code     data
     Composites and Formative Indicators (SEM.10.1)     pdf     code
     Composites and Endogenous Nonlinearities (SEM.10.2)     pdf
     Composites with Multiple Effects (SEM.10.3)     pdf
          Composites with Multiple Effects Exercise     pdf     code     data
     Composites - Comparing Specifications (SEM.10.4)     pdf


IV. Additional Topics

     Additional Lavaan Options (SEM.11.1)     pdf
     Multi-Group Modeling (SEM.11.2)     pdf
     Modeling Interactions (SEM.11.3)     pdf     code     data
     Spatial Autocorrelation Procedures (SEM.11.4)     pdf     code     data
          Spatial Autocorrelation Exercise     pdf     code     data
     Reciprocal Effects Overview (SEM.11.5)     pdf
     Adjusting for Nested Data using lavaan.survey (SEM.11.6)     pdf     code     data
​​​​​​​     Latent Trajectory Modeling in lavaan (SEM.11.7)     pdf     code     data


Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.