Structural Equation Modelling(SEM)

An Introduction (Part 2)

SEM: Basic Concepts

• Measured Variable or Indicator Variable

• Latent Variable

• Measurement Model

• Structural Model

Basic Concepts: Measured Variable/Indicator• Measured variable(s) are the variables that are actually measured in the

study.

Latent Variable

Measured Variable 1 Measured Variable 2 Measured Variable 3

Basic Concepts: Latent Variable• Intangible constructs that are measured by a variety of indicators

(more is better!)

Latent Variable

Measured Variable 1 Measured Variable 2 Measured Variable 3

Basic Concepts: Measurement Model• The measurement model can be described as follows. It shows the

relationship between a latent variable and its measureditems(variables).

Latent Variable

Measured Variable 1 Measured Variable 2 Measured Variable 3

Basic Concepts: Structural Models

• Often used to specify models in SEM

Causal flow is from left to right; top to bottom

• Straight arrows represent direct effects

• Curved arrows represent bidirectional “correlational”relationships

• Ellipses represent latent variables

• Boxes/rectangles represent observed variables

Example: Structural Models

Variants of Structural Equation Modelling

•Confirmatory Factor Analysis (CFA)

•Path Analysis with observed variables

•Path analysis with latent variables

Confirmatory Factor Analysis “Measurement Model”

• Tests model that specifies relationships between variables (items) andfactors

And relationships among factors

• Confirmatory

Because model is specified a priori

Example: Oblique CFA Model

Confirmatory vs. Exploratory Factor Analysis

• In CFA the model is specified a priori

Based on theory

• EFA is not a member of the SEM family

Includes a class of procedures involving centroids, principal components, andprincipal axis factor analysis

Does not require a priori hypothesis about relationships within your model

Inductive vs. deductive approach

More restrictions on the relationships between indicators and latent factors

Example: Oblique EFA Model

Observed Variable Path Analysis (OVPA)

• Tests only a structural model

Relationships among constructs represented by direct measured(observed variables)

i.e., each “box” in model is an idem, subscale, or scale

• Analogous to a series of multiple regressions

But, with MR, we would need k different analyses, where k is # ofDVs

With SEM, can test entire model at once

Example: OVPA

Latent Variable Path Analysis (LVPA)

• Simultaneous test of measurement and structural parameters

• CFA and OVPA at same time

• LVPA models incorporate….

• Relationships between observed and latent variables (i.e., measures and factors)

• Relationships between latent variables

• Error & disturbances/residuals

Example: LVPA

Data Considerations

Sample Size

• SEM is a large-sample technique

• The required Sample size needed depends on….

Complexity of model

Ratios of sample size to estimated parameters ranging from5:1 to 20:1 (Bentler & Chou, 1987; Kline, 2005)

Data Quality

Larger samples for non-normal data

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