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Quantitative Analysis Using Structural Equation Modeling

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


About this Site and How to Use

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.More...

What's New?

Currently, these web pages represent the intial public launch of education materials. Updates that follow will be logged here.More...

Feature: Causal networks clarify productivity-richness interrelations, bivariate plots do not

Bogong subalpine grassland in Australia
Photo: Bogong subalpine grassland in Australia, a participating site in the Nutrient Network Global Cooperative. Photo credit: Eric Land, Nutrient Network.

Lay summary from Functional Ecology:

Species diversity and productivity are among the most fundamental characteristics of ecosystems. While the importance of these ecological properties is universally agreed upon, the mechanisms connecting these two variables have been debated for decades without resolution. In an attempt to achieve a synthetic understanding of the collective effects of proposed mechanisms, some ecologists have turned to the examination of bivariate plots to see if particular patterns are consistently observed in nature.



A number of projects involving USGS scientists at the National Wetlands Research Center apply SEM to basic and applied science issues.More...


  • Grace, J.B., Scheiner, S.M., Schoolmaster, D.R. Jr. 2015. Structural equation modeling: building and evaluating causal models. Chapter 8 In: Fox, G.A., Negrete-Yanlelevich, S., and Sosa, V.J. (eds.) Ecological Statistics: Contemporary Theory and Application. Oxford University Press.
  • Grace, J.B., Adler, P.B., Harpole, W.S., Borer, E.T., and Seabloom, E.W. 2014 Causal networks clarify productivity–richness interrelations, bivariate plots do not. Functional Ecology, DOI: 10.1111/1365-2435 (early online) (


View a list of applications using SEM. More...
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    
Categorical Predictors (SEM.1.7) pdf code data
Doing SEM in R      
Introduction to Lavaan (SEM.2.1) pdf code data
Local Estimation of Equations (SEM.2.2) pdf code data
Model Evaluation (SEM.3) 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) 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 - Comparing Specifications (SEM.10.4) pdf    
IV. Additional Topics      
Additional lavaan Options pdf    
Modeling Interactions pdf code data
Spatial Autocorrelation Procedures pdf code data
Spatial Autocorrelation Exercise pdf code data
Reciprocal Effects Overview pdf    
Adjusting for Nested Data using lavaan.survey pdf code data


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Page Last Modified: Friday, 16-Oct-2015 19:07:50 EDT