Cause and Correlation in BiologyA User's Guide to Path Analysis, Structural Equations and Causal Inference with R
Book contents
- Cause and Correlation in Biology
- Cause and Correlation in Biology
- Copyright page
- Dedication
- Contents
- Preface
- 1Cause from Correlation?
- 2From Cause to Correlation and Back
- 3Sewall Wright, Path Analysis, and d-Separation
- 4Covariance-Based SEM without Explicit Latent Variables
- 5Statistical Power, AIC Statistics, and Equivalent Models
- 6Piecewise SEM with Implicit Latent Variables
- 7Modelling Explicit Latent Variables in Covariance-Based SEM
- 8Multigroup and Multilevel Structural Equation Models
- 9Exploratory Structural Equation Modelling
- 10A Cheat Sheet of Important R Functions
- References
- Index
6 - Piecewise SEM with Implicit Latent Variables
Published online by Cambridge University Press: 18 July 2026
Book contents
- Cause and Correlation in Biology
- Cause and Correlation in Biology
- Copyright page
- Dedication
- Contents
- Preface
- 1Cause from Correlation?
- 2From Cause to Correlation and Back
- 3Sewall Wright, Path Analysis, and d-Separation
- 4Covariance-Based SEM without Explicit Latent Variables
- 5Statistical Power, AIC Statistics, and Equivalent Models
- 6Piecewise SEM with Implicit Latent Variables
- 7Modelling Explicit Latent Variables in Covariance-Based SEM
- 8Multigroup and Multilevel Structural Equation Models
- 9Exploratory Structural Equation Modelling
- 10A Cheat Sheet of Important R Functions
- References
- Index
Summary
A variable that is part of a hypothesized causal graph but for which no observations are available is called a ‘latent’ variable. If this latent variable is part of the resulting structural equations, then it is ‘explicit’. If it is not part of the structural equations, then it is ‘implicit’. This chapter explains how one can convert a DAG with explicit latent variables into an equivalent causal graph (a mixed acyclic graph (MAG)) that does not include the latent variables. The notion of ‘m-separation’ in a MAG is a generalization of ‘d-separation’ of a DAG. One can generalize the dsep test to include MAGs, and this generalization is included in the pwSEM package.
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- Cause and Correlation in BiologyA User's Guide to Path Analysis, Structural Equations and Causal Inference with R, pp. 177 - 210Publisher: Cambridge University PressPrint publication year: 2026
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