Structural equation Modeling

Principal Concepts

Essentially, SEM statistically tests hypotheses of multiple relations among measured variables. As depicted in Figure 1, the conceptual variables or constructs are denominated latent variables. Hence, SEM models these qualitative relations among the latent variables and then tests the extent to which these relations explain the data according to a fit criterion. In many cases, the latent variables cannot be directly observed and are further specified and estimated through the measurements of underlying variables (the Xs and Ys in Figure 1). Besides, through the model's latent variables and their underlying measured variables, SEM can explicitly account for measurement errors.

In general, two distinct but interconnected models lie within a single SEM analysis: a measurement model, aimed to evaluate the extent to which the measured (underlying) variables effectively capture the concepts (or constructs) in the model; and a structural model, aimed to simultaneously test all the causal relations (i.e., the links among the constructs) found in the overall SEM model. It should be noted that the consistency of the causal relations among the latent variables does not rely on the confirmatory testing but on the theoretical support of the model proposed.

SEM has its origins from several different multivariate methods. On one side, the measurement model originates from a much broader category of factor analysis. This statistical technique is often used to study patterns within a set of variables, with the objective to identify their underlying structure. These groupings of variables are known as factors. Initial development of factor analysis came from Charles E. Spearman in 1904 by his work on the identification of underlying structure of mental abilities.

Factor analysis is generally considered an exploratory technique. On the contrary, confirmatory factor analysis (CFA) requires a priori assumptions about the structure of the variables and serves the a purpose similar to that of the measurement model in SEM framework.

The second constituent, path analysis, corresponds to the structural model within SEM analysis. It allows a researcher to model complex relationships among various variables and visually represents them in a path diagram. Path analysis compares the regression weights obtained from a proposed causal model to the correlations obtained from the data, and estimates the fit of the data to the proposed model.

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