Structural Equation Modeling

What Is SEM?

SEM is a family of statistical methods for analyzing data. SEMs are considered to be confirmatory, rather than exploratory because the researcher defines the model to be tested and SEMs confirm (or disconfirm) the researcher’s prespecified theoretical model. SEM is based on the analysis of the pattern of relations among the variables included in the analysis (i.e., covariance structures, or the variance–covariance matrix of the variables). In some models, mean structures (e.g., intercepts) are also analyzed. For all SEMs, the researcher defines a theoretical model consisting of relations between the variables of interest, and the implied variance–covariance matrix based on the specified model is compared to the observed variance–covariance matrix based on the data that were collected in the study. This comparison is used to assess the fit of the specified theoretical model to the collected data.[Page 2167]

Figure 1 Three types of hypothetical structural equation models

Source: Author.

Note: A = confirmatory factor analysis; B = Path analysis; C = Latent growth analysis with a predictor of the intercept; SES = socioeconomic status.

[Page 2168]SEM notation varies. Some researchers and computer programs use Greek letters and subscripts to identify the various parts of the model. Other researchers and programs use the Latin alphabet to identify model parts. Regardless of the notation system, all SEMs share some common components. Variables in an SEM can be observed or latent. An observed variable is one for which data were collected, and it is usually noted by a rectangle or square (Figure 1). A latent variable is one that is not observed (e.g., no data were collected) but instead is inferred from the model. Latent variables are usually noted by ovals or circles (Figure 1). A common example of a latent variable is a weighted combination of items that make up a factor (Figure 1A).

Relations between observed and/or latent variables are called paths. Paths are noted by arrows, which can be single-headed, suggesting that one variable predicts another variable, or double-headed, suggesting covariation among the variables that is not directional. The number associated with a path is called a parameter or path/structural coefficient, which is the strength of the association between the two variables. In Figure 1, paths with no associated values are being freely estimated or determined by the model. Paths with an associated value are fixed to that value and not estimated by the model.

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