Graphical models | Latent variable models | Structural equation models | Regression models
Structural equation modeling
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. It is used most in the social and behavioral sciences. A definition of SEM is difficult without reference to highly technical language, but a good starting place is the name itself. 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. The structural aspect of the model implies theoretical associations between variables that represent the phenomenon under investigation. 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 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 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 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. 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. 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). 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. Researchers using SEM employ software programs to estimate the strength and sign of a coefficient for each modeled arrow (the numbers shown in Figure 1 for example), and to provide diagnostic clues suggesting which indicators or model components might produce inconsistency between the model and the data. Criticisms of SEM methods hint at mathematical formulation problems, a tendency to accept models without establishing external validity, and potential philosophical bias. A SEM suggesting that intelligence (as measured by four questions) can predict academic performance (as measured by SAT, ACT, and high school GPA) is shown in Figure 1. The concept of human intelligence cannot be measured directly in the way that one could measure height or weight. Instead, researchers have a theory and conceptualization of intelligence and then design measurement instruments such as a questionnaire or test that provides them with multiple indicators of intelligence. These indicators are then combined in a model to create a plausible way of measuring intelligence as a latent variable (the circle for intelligence in Figure 1) from the indicators (square boxes with scale 1–4 in Figure 1). Figure 1 is presented as a final model, after running it and obtaining all estimates (the numbers on the arrows). There is no consensus on the best symbolic notation to represent SEMs, for example Figure 2 represents a similar model as Figure 1 without as many arrows and in a format that might occur prior to running the model. A great advantage of SEM is that all of these measurements and tests occur simultaneously in one statistical estimation procedure, where the errors throughout the model are calculated using all information from the model. This means the errors are more accurate than if a researcher were to calculate each part of the model separately. (Wikipedia).
