![]() Although there are not always clear boundaries of what is and what is not SEM, it generally involves path models (see also path analysis) and measurement models (see also factor analysis) and always employs statistical models and computer programs to investigate the structural connections between latent variables underlying the actual variables taken from observed data. Use of SEM is commonly justified because it helps identify latent variables that are believed to exist, but cannot be directly observed (like an attitude, intelligence or mental illness). Variations among the styles of latent causal connections, variations among the observed variables measuring the latent variables, and variations in the statistical estimation strategies result in the SEM toolkit including confirmatory factor analysis, confirmatory composite analysis, path analysis, multi-group modeling, longitudinal modeling, partial least squares path modeling, latent growth modeling and hierarchical or multilevel modeling. The boundary between what is and is not a structural equation model is not always clear but SE models often contain postulated causal connections among a set of latent variables (variables thought to exist but which can’t be directly observed) and causal connections linking the postulated latent variables to variables that can be observed and whose values are available in some data set. The equations in SEM are mathematical and statistical properties that are implied by the model and its structural features, and then estimated with statistical algorithms (usually based on matrix algebra and generalized linear models) run on experimental or observational data. The causal structures imply that specific patterns of connections should appear among the values of the variables, and the observed connections between the variables’ values are used to estimate the magnitudes of the causal effects, and to test whether or not the observed data are consistent with the postulated causal structuring. The postulated causal structuring is often depicted with arrows representing causal connections between variables (as in Figures 1 and 2) but these causal connections can be equivalently represented as equations. The structural aspect of the model implies theoretical associations between variables that represent the phenomenon under investigation. SEM involves the construction of a model, to represent how various aspects of an observable or theoretical phenomenon are thought to be causally structurally related to one another. It is used most in the social and behavioral sciences. ![]() Structural equation modeling ( SEM) is a label for a diverse set of methods used by scientists in both experimental and observational research across the sciences, business, and other fields. ![]() The unlabeled arrow pointing to academic performance acknowledges that things other than intelligence can also influence academic performance. This model postulates that separate measurement errors influence each of the two indicators of latent intelligence, and each indicator of latent achievement. ![]() It is hoped a good indicator has been chosen for each latent, but the 1.0 values do not signal perfect measurement because this model also postulates that there are other unspecified entities causally impacting the observed indicator measurements, thereby introducing measurement error. The 1.0 effect connecting a latent to an indicator specifies that each real unit increase or decrease in the latent variable’s value results in a corresponding unit increase or decrease in the indicator’s value. Because intelligence and academic performance are merely imagined or theory-postulated variables, their precise scale values are unknown, though the model specifies that each latent variable’s values must fall somewhere along the observable scale possessed by one of the indicators. Similar to Figure 1 but without standardized values and fewer items. An example structural equation model before estimation.
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