Structural equation modeling (SEM) is a statistical technique used to establish relationships between variables that can simultaneously test measurement and structural relationships. SEM combines factor analysis and multiple regression to test if a conceptual model fits the data. It is defined by terms like path analysis, path modeling, and causal modeling. At the heart of SEM is covariance, which measures how variables change together, and SEM aims to explain as much variance in a set of variables as possible with a specified model by reproducing the actual covariance matrix. SEM has advantages over regression like allowing for multiple dependent variables, accounting for correlations between variables, and accounting for measurement error. Key uses of SEM include theory testing, mediation analysis, group comparisons, longitudinal modeling, and multilevel

1. Structural Equation Modelling
(SEM)
An Introduction (Part 1)

2. What is Structural Equation Modelling?
• SEM is a general statistical modelling technique used to establish relationship among
variables.
• 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

3. 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.
𝑛
𝑖=1(𝑋 𝑖 −
𝑋)(𝑌 𝑖 − 𝑌)
𝑁−1
OR
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

4. 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
observed
 i.e., the implied covariance matrix should = the actual covariance
matrix

5. 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.

6. USES OF SEM
• Theory testing
 Strength of prediction/association in models with multiple DVs
 Model fit
• Mediation/tests of indirect effects
• Group differences
 Multiple-sample analysis
• Longitudinal models
• Multilevel nested models

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Training?
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