# Understanding the application of Structural Equation Modeling (SEM)

By Riya Jain & Priya Chetty on August 3, 2021

Data is present everywhere in the digital world today. It has become complex to manage vast amounts of data. Today, there exists almost 100 zettabytes of digital data in the world. If used well, this data can produce valuable insights which can help companies and governments to predict future trends. Consequently, many statistical models have been developed to identify patterns of relationship between different parameters of data. Some of the most popularly used ones are regression and classification models. Among these, structural equation modeling (SEM) has emerged as a popular one today.

Structural equation modeling establishes the relationship between two or more variables. It also determines the efficiency of the model created in the process. Due to its versatility, it is being used widely by academicians today. However, there are some challenges in its application. It is more technical and complex as compared to regression models.

## What is structural equation modeling (SEM)?

Structural equation modeling is a multivariate statistical methodology for analysing structural and causal correlations between two or more variables. SEM is used for multivariate processes such as factor analysis, regression analysis, discriminant analysis, and canonical correlation (DeVault, 2018). This technique is defined as a combination of multiple regressions. It consists of multiple dependent and independent variables. SEM analysis is used by researchers for estimating the interrelated and multiple dependence in a single analysis (Lee, 2007).

### Case example of a structural equation modeling

Suppose there are various factors that affect an organisation’s skills with respect to time management and job stress, such as:

• Time management factors: goal setting, operational planning, communication management and meeting management.
• Job stress factors: submission, targeting and meetings.

In order to determine how these factors affect organisational skills, SEM can be used.

## Difference between traditional statistical analysis and structural equation modeling

Structural equation modeling is a more comprehensive and flexible method as compared to traditional analysis methods. It is suitable for investigating economic trends, achievements, family and peer dynamics, health issues, self-efficacy, self-concept, depression, exercise, and psychotherapy. Furthermore, traditional approaches are more of a default model-based practice while SEM offers a formulation of model based on requirements and no such default methodology (Suhr, 2006).

Moreover, structural equation modeling is a multivariate analysis technique. This means it allows to find the relationship between measured and unobserved variables. Here, ‘unobserved variables’ refer to the variable that needs to be computed based on other variables.

On the other hand, traditional approaches are suitable only for measured or observed variables. SEM even recognizes these measures’ imperfect nature by including measurement error in the model. However, traditional approaches do not have any such provision. Lastly, the traditional approach provides a straightforward methodology of model fitness. Therefore, multicollinearity problems can exist with these models. Contrarily, SEM offers model fitness examination and the ability to resolve multicollinearity (Suhr, 2006).

## Relevance of SEM in statistics

SEM is a technique for examining complex interactions between variables and reducing them to visual representations. Its key benefit is that it allows us to assess the model’s efficiency. The postulated associations between variables are acceptable if the fit is satisfactory (Hillman & Neustaedter, 2003). There are two types of variables employed in this analysis, endogenous variables and exogenous variables.

Endogenous variables are dependent variables that are the same as the independent variable. Thus, the techniques of SEM help in building the relationship among variables. It helps present multiple and interconnected dependencies in a single analysis.

Using SEM techniques like path models would allow for a shift in perspective i.e. move towards model-based reasoning, cumulative knowledge building, and big-picture thinking, all of which appear to be lacking in the field to varying degrees (Larsson et al., 2020). The application of SEM to research allows for greater research design flexibility, hence making a distinction between what can and cannot be concluded using statistical approaches. Even if the statistics behind the data are somewhat complex, SEM provides a neat visual depiction that is straightforward to interpret.

SEM is most commonly applied in studies that are intended to validate a research study design rather than to analyse or explain a phenomenon. If a researcher is interested in the strength of the relationship between variables in a hypothesis, structural equation modeling offers a means to investigate those correlations without committing to a costly research effort.

## Advantages of structural equation modeling (SEM)

• It is a collection of statistical procedures for testing hypotheses based on numerous constructs that may be related indirectly or directly in both linear and nonlinear models. It differs from other types of analyses in that it may evaluate a large number of associations while also identifying measurement errors.
• SEM offers a notable advantage over traditional multiple regression studies in that it has more statistical power. ‘Statistical power’ here refers to the likelihood of rejecting a false null hypothesis).
• SEM allows for the examination of latent variables and their relationships, allowing for the examination of psychological construct dependencies without measurement errors.
• It can also examine correlated measurement error to see how unknown causes influence shared error between variables. This could change the model’s predicted parameters and can also handle missing data effectively by fitting raw data rather than summary statistics.

## Limitations of SEM

The issue of causal interpretation is the first, and perhaps the biggest limitation of structural equation modeling. The majority of SEM applications are based on non-experimental data. Despite this, many SEM applications perceive the final model as a causal model. Although this may be valid, structural equation modeling does not magically transform correlational data into causative conclusions. Thus, researchers need to be more cautious while interpreting SEM results which leads to making the model more error-prone (Hillman & Neustaedter, 2003).

The other disadvantage of SEM is that the benefit of concurrent investigation of many variables may be outweighed by the need for bigger sample sizes for more variables in order to develop a solution to the calculations (Beran, 2010). Furthermore, this model cannot compensate for the problems inherent in any sort of investigation. Even poor research design, unreliable data and over the interpretation of causal links can lead to false conclusions. Hence, associated technicality and the need for more caution are some of the major limitations of SEM analysis.

SEM is a powerful multivariate analytical tool with a lot of potential in ecological research, especially as data becomes more accessible. Despite SEM’s important addition to research methodology, there are a few things to keep in mind when creating a legal model. These include using the right research design, the right sample size, and the right measurements.

#### References

• Beran, T. N. (2010). Structural equation modeling in medical research: a primer. BMC Research Notes.
• DeVault, G. (2018). Structural Equation Modeling (SEM). Market Research.
• Hillman, S., & Neustaedter, C. (2003). (Why) Should We Use SEM? Methods of Psychological Research, 8(2), 1–22.
• Larsson, T., Plonsky, L., & Hancock, G. R. (2020). On the benefits of structural equation modeling for corpus linguists. Corpus Linguistics and Linguistic Theory. https://doi.org/10.1515/cllt-2020-0051
• Lee, S.-Y. (2007). Structural Equation Modeling : A Bayesian Approach. In New York: John Wiley & Sons.
• Suhr, D. (2006). The Basics of Structural Equation Modeling. In University of Northern Colorado. https://doi.org/10.1007/s007840050036

I am a management graduate with specialisation in Marketing and Finance. I have over 12 years' experience in research and analysis. This includes fundamental and applied research in the domains of management and social sciences. I am well versed with academic research principles. Over the years i have developed a mastery in different types of data analysis on different applications like SPSS, Amos, and NVIVO. My expertise lies in inferring the findings and creating actionable strategies based on them.

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