Statistics Blog

An Overview Of Structural Equation Modeling (SEM) For Marketing Researchers

What is SEM?

Structural Equation Modeling (SEM) is a statistical methodology that combines both regression and factor analysis. More specifically, it is a system of equations based on a priori hypotheses that are modeled simultaneously. In other words, the model’s configuration is based on assumed relationships between variables derived in advance.

What kind of models are examined using SEM?

Many types of models can be conducted using SEM. Path Models are regression models using observed variables (variables measured directly in a survey or experiment). When examining path models with SEM, the results produced are identical to those derived from conducting regression in another statistical software, such as SPSS.

Measurement Models are factor analytic models where observed variables are caused by a latent variable (a variable that cannot be directly measured itself, but is assumed to be made up of specific observed variables). Intelligence is a good example of a latent variable because it cannot be directly measured. However, intelligence is indirectly measured by questions involving math, logic, verbal skills, and spatial skills. In this way, the answers to the observed variables from math, logic, verbal skills, and spatial skills are thought to be caused by the latent variable - intelligence. In this example, the questions regarding math, logic, verbal skills, and spatial skills make up a factor that we call “intelligence.”

Measurement models are typically referred to as Confirmatory Factor Analyses (CFA) because they are intended to confirm (or deny) the a priori factor structure that has been hypothesized. In best practices, exploratory factor analyses are conducted first to determine factor structure and then CFA is applied to confirm factor structure. Measurement models allow for specifications, such as which variables load onto which factors and whether factors are correlated with one another.

Combining path models with measurement models creates Structural Models. Structural models investigate the relationships between latent variables and observed variables, all while taking into account error. These models can be used to examine simple regression, multiple regression, moderation, multiple moderation, mediation, serial mediation, and longitudinal analyses (among others).

How does SEM differ from regression or factor analysis?

SEM is more flexible than regression and factor analysis and is known for being able to manage very complex models. Unlike regression or factor analysis, SEM tests hypotheses on observed variables and latent constructs. It smoothly handles many equations at the same time, allows for reciprocal relationships and multiple dependent variables. Furthermore, it analyzes both regression models and factor models simultaneously. Lastly, one of SEM’s most important features is that it accounts for measurement error. This type of error can be found in poorly worded survey questions, overly complex questions, excessively lengthy questions and surveys, location of the questions in the survey, and in data collection methods (in person, over the phone, online, etc.). Respondent effects—such as tendency to acquiesce, ability to interpret questions, and ability to recall events—can also create the potential for measurement error.

How can we use SEM in marketing research?

Some reasons for using SEM in marketing research are to find key drivers of an outcome, to create custom brand equity scores, to examine ‘laddering’ models, and to investigate ‘domino’ effects.

SEM is a great tool for calculating derived importance for Key Drivers. Key driver analysis reveals the importance of attributes to an outcome (such as likelihood to purchase, likelihood to recommend, likelihood to consider, and overall satisfaction, etc.). Using SEM for key drivers is recommended when there are many attributes that could be grouped into factors and/or the outcome variable is believed to be measured by several variables. A key driver analysis conducted using SEM returns information on which attribute grouping (factor) is most important to the outcome and which individual attributes are most important within each factor.

SEM works well to create weights to be used in the formation of Brand Equity Scores. Brand equity scores are custom score calculations that show how well a brand is doing overall and in comparison to other brands.

SEM can also be used to investigate Laddering Models. Laddering models assume that there is a hierarchical structure between variables. At the lowest level are variables that “ladder” up to or contribute to mid-level variables. The mid-level variables “ladder” up to, or contribute to, top-level variables. Laddering models can have many levels. One example of a laddering model may include company initiatives at the lowest level, which contribute to company platforms that then contribute to the company’s overall strategy. This type of modeling reveals which lower-level variables contribute/are important to mid- and top-level variables, as well as which mid-level variables contribute to top-level variables.

SEM is the perfect tool to analyze a Domino Effect (also known as serial mediation). A domino effect is when one thing influences another, which then impacts something else, which then influences another thing. An example of a simple domino effect might include a product interaction that influences a respondent’s opinion of the company, which then impacts future intent to purchase, which then influences future recommendations of the product.

Lastly, researchers must be careful not to assume that SEM models are causal models; they are not. SEM models are only causal when the data collected is done so using an experimental method (e.g., actively manipulating which products or attributes are shown to respondents). Traditional survey data asks respondents to report on their thoughts, feelings, and behaviors and, thus, is not experimental. Therefore, using regular survey data in a complex modeling system does not equal a causal model.

Conclusion

Structural Equation Modeling is a flexible multi-use tool in the marketing researcher’s pocket. Researchers benefit from using SEM due to its multi-functional capabilities. It handles not only the typical regressions (path models) and factor analyses (measurement models) researchers often conduct, but also the complex structural models, such as time series analyses or serial mediation. Furthermore, SEM’s benefits are many, such as managing many independent and dependent variables, examining different types of models, accounting for measurement error, and analyzing all relationships simultaneously.

Audrey Guinn

Statistical Consultant, Advanced Analytics Group

Audrey utilizes her knowledge in both inferential and Bayesian statistics to solve real-world marketing problems. She has experience in research design, statistical methods, data analysis, and reporting. As a Statistical Consultant, she specializes in market segmentation, SEM, MaxDiff, GG, TURF, and Key Driver analysis. Audrey earned a Ph.D. and Master of Science in Experimental Psychology with an emphasis on emotional decision-making from The University of Texas at Arlington.

• 
•