Structural Equation Modeling

Model Specification

Based on a theory and/or prior research, researchers specify the parameters and relationships among variables in a hypothesized model. In SEM, researchers hypothesize the relationships between the latent variable and the observed variables. For example, as is shown in Figure 1, parental control as a latent variable (represented as oval shape) is composed of three observed variables (i.e., “parental control too harsh,” “parents force children to do things,” and “parents scold and beat children”). Similarly, parental concern is measured by three observed variables (i.e., “parents love their children,” “parents take care of their children,” and “parents do not care about their children”). The six observed variables were loaded on two latent variables, which were correlated with each other (i.e., covariance).

Figure 1 A hypothesized two-factor model of confirmatory factor analysis

Figure 1 depicts this hypothesized model. Parental control (presented as an oval) has a direct effect (presented as a single-headed arrow) on observed variables from A1 to A3 (presented as rectangles). Similar to “parental concern” with three observed variables (i.e., A4 to A6) were loaded on this latent variable. The relationship between parental concern and parental control was represented by a two-headed arrow. These arrows only indicate the directionality, but no causal relationship is implied.

For each observed variable, a single-headed arrow representing an error is presented. In this model, there are (a) six factor loadings between the latent variable and six observed variables; (b) one covariance between the two latent variables; and (c) six errors are associated with six observed variables, thereby suggesting a total of 13 parameters being estimated.

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