Structural Equation Modeling: Introduction & Example

Instructor: Gaines Arnold

Gaines has a Master of Science in Education.

Statistics are necessary for social science study, but most statistical methods cannot be easily used by social scientists. This lesson looks at structural equation modeling, which was designed with social scientists in mind.

Finding a Model that Works

Rob's employer tasked him with finding out how to raise the job satisfaction level of line employees. His boss wasn't worried about the people who had risen to the supervisory and management levels; he was concerned with the rate at which he was starting to lose low-level employees to competitors after he had spent the money to train them. Rob happened to be trained as a social scientist, and he had excelled in statistical analysis as a student. He knew how to use regression analysis, variance and other statistical concepts, but he needed something more to satisfy the needs of this employer. Rob needed to conduct this analysis using a model that would allow him to determine unseen variables like satisfaction, and he needed to understand how satisfaction could be measured as it related to variables that could be seen. He decided to use statistical equation modeling (SEM) because it's a system of statistical inference that allowed him to determine the relative strength of different variables whether or not they could be directly measured.

What Is Structural Equation Modeling?

SEM is a model of statistics used in behavioral sciences because it allows researchers to determine complex relationships between dependent and independent variables. It combines factor analysis and path analysis (also sometimes called regression). An independent variable is one that can stand alone, while a dependent variable is one that's controlled by other variables. In SEM, these are generally called exogenous variables (independent) and endogenous (dependent). The model also defines whether variables are directly or indirectly measured: manifest variables are measured directly and latent variables are measured indirectly.

How Is SEM Used?

Psychology and other social sciences work with constructs, like satisfaction, that are difficult to both define and research. This is why structural equation modeling is a perfect fit for social science research - it can deal with these kinds of latent variables. Rob was given the assignment to measure job satisfaction in some meaningful way, so he used SEM. It's possible to guess why someone may be satisfied with their job, but it is almost impossible to discover a tangible, concrete reason. SEM provides tools with which researchers can ask these difficult questions, like who has the greater job satisfaction, who is more intelligent, or even what causes a particular group to riot. These and many more non-concrete questions can be answered with a greater degree of specificity by using SEM.

An Example of SEM

Remember, Rob is tasked with determining job satisfaction among the employees of a particular factory. Of course, there are tangible factors (manifest variables) that can be used, but there are also underlying factors (latent variables). The questions Rob has to answer are: What is the link between the variables, how do they correlate with each other, and how well do they correlate to the overall question of job satisfaction?

He begins with the idea of job satisfaction and reasons out the factors he believes are associated with it. He then makes variable estimates and constructs a path diagram. Path analysis (from which the diagram is drawn) is used to discover how different variables relate. For example, independent variables like number of work hours and pay are shown with arrows going to the dependent variable of job satisfaction. In general, measurable manifest variables (hours worked and pay) are depicted within rectangles or squares, and latent variables (job satisfaction) are within circles or ovals.

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