Structural Equation Modelling
An Introduction (Part 1)
What is Structural Equation Modelling?
• SEM is a general statistical modelling technique used to establish relationship among
• SEM is a confirmatory data analysis technique, i.e.
it tests models that are conceptually derived, beforehand
it tests if the theory fits the data
• SEM can be thought of as a combination of factor analysis and multiple regression
it can simultaneously test measurement and structural relationships
• SEM is a family of related procedures. It is alternately defined by the following terms
Path Analysis, Path Modelling, Causal Modelling, Analysis of Covariance Structures, Latent
Variable Analysis, Linear Structural Relations
Covariance: At the Heart of SEM
• Covariance is a measure of how much two random variables change
together. Alternately, it can be defined as the strength of association
between the two variables and their variabilities.
𝑖=1(𝑋 𝑖 −
𝑋)(𝑌 𝑖 − 𝑌)
𝑐𝑜𝑣 𝑥𝑦 = 𝑟 𝑥𝑦 𝑆𝐷 𝑥 𝑆𝐷 𝑦
• The basic statistic of SEM
Understanding patterns of correlations among a set of variables
Explain as much of their variance as possible with the model specified
Logic of SEM
• Every theory (model) implies a set of correlations
And why variables are correlated
• Necessary (but insufficient) condition for the validity of the theory is
that it should be able to reproduce the correlations that are actually
i.e., the implied covariance matrix should = the actual covariance
Why SEM over Regression?
• Regression allows for only a single dependent variable,
whereas SEM allows for multiple dependent variables.
• SEM allows for variables to correlate, whereas regression
adjusts for other variables in the model.
• Regression assumes perfect measurement, whereas SEM
accounts for measurement error.
USES OF SEM
• Theory testing
Strength of prediction/association in models with multiple DVs
• Mediation/tests of indirect effects
• Group differences
• Longitudinal models
• Multilevel nested models
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