CB-SEM using #SmartPLS4 - 3 - Understanding Basic Concepts in Structural Equation Modeling (SEM)

Structural equation modeling (SEM) is built to test relationships among theoretical constructs by modeling both the constructs and the measurement items that represent them—along with error. Instead of treating variables as directly observed scores only, SEM uses a schematic framework where constructs are linked by hypothesized paths, and each construct is measured through a set of questionnaire items. That combination matters because it lets researchers evaluate whether the items reliably and validly represent the underlying concepts before assessing how those concepts influence one another.

A key clarification is that SEM—especially covariance-based SEM (CB-SEM)—does not establish causation by itself. CB-SEM takes a covariance matrix as input, meaning the analysis is driven by correlations among variables to estimate how constructs are associated. High correlation does not automatically mean one construct causes another; demonstrating causality typically requires experimental design. Still, SEM remains a strong tool for assessing how constructs influence one another in observational data, and it can also be applied to experimental datasets.

SEM distinguishes between variables and constructs. Variables are directly measured quantities such as age, exam score, height, or income. Constructs are indirectly measured, often hypothetical concepts like job satisfaction, perceived usefulness, loyalty, servant leadership, or organizational culture—typically captured through multiple questionnaire items. These constructs are often latent, meaning they are not observed directly; instead, they are inferred from patterns in responses to item sets. For example, “organizational learning” might be treated as a latent construct measured by eight questionnaire items.

Because latent constructs cannot be handled by ordinary least squares (OLS) in a straightforward way—such as by averaging items and running a basic regression—SEM analyzes measurement and structural relationships simultaneously. In SEM, at least two components appear: the measurement model and the structural model. The measurement model focuses on validity and reliability: whether the indicators (items) actually reflect the underlying latent constructs and how well the model fits the measurement side. Once that foundation is supported, the structural model evaluates the influence and significance between constructs—capturing hypothesized directional links (e.g., construct A influencing construct B).

A “full structural model” includes both measurement and structural relationships, tying together items, latent constructs, and their interconnections. SEM also estimates parameters that describe the size and nature of relationships. Parameters can be fixed or freely estimated from data, and they appear not only in the links between constructs but also in how latent constructs map onto their indicators, including error terms.

Sample size guidance for SEM is debated, but one commonly cited rule-of-thumb (Hair et al., 2010) ties minimum sample size to the number of latent constructs and the number of items per construct. For instance, with five or fewer constructs (each with more than three measuring items), 100 cases are suggested; with seven or fewer constructs (each with more than three items), 150 cases; and when constructs have fewer than three items, the guidance increases to 300 or even 500 cases when there are more than seven constructs.

Overall, SEM—particularly CB-SEM—offers a structured way to test theory-driven relationships among latent constructs while explicitly accounting for measurement quality and error, but it relies on covariance patterns rather than experimental control to infer causality.