Applying structural equation modeling (SEM) to a research

By Riya Jain and Priya Chetty on February 9, 2022

Structural equation modeling (SEM) is a century-old statistical method that witnessed progression over time. Initially, the model focused only on path analysis. However, with the growth in usage of SEM in social science, the factor analysis technique was integrated into it. Presently SEM is a powerful multivariate technique applicable in scientific investigations to evaluate and test the multivariate casual relationships. The challenge today is that research problems are of different kinds and there are multiple models. Therefore, it is essential to understand the basics before applying structural equation modeling in research.

The previous article focused on five main models:

  • Confirmatory factor analysis
  • Confirmatory composite analysis
  • Path analysis
  • Partial least square path modeling
  • Latent growth modeling.

This article focuses on differentiating all the models and identifies the usage and applicability of each model.

Applicability of different structural equation modeling (SEM) types

SEM helps to draw a linkage between two or more variables by defining them as measures, observed, explanatory and predicted patterns. However, different types of SEM tests are applied in different cases. The table below shows how the tests differ from each other and how to apply them.

NatureConfirmatory factor analysis (CFA)Confirmatory composite analysis (CCA)Path analysisPartial least square path modeling (PLS)Latent growth modeling
PurposeHelps to build the linkage between latent variables.To build the linkage between linearly interrelated components (composites).To explain the causal relationship among variables.To explain the causal relationship combining multiple composites (observed variables connected with weighted sum)Helps to examine the changes in the longitudinal data.
SuitabilitySuitable for identifying the factor loading or weightage of statement for its construct.Suitable for datasets whose model is theoretically identified and could be used for assessing the factor loading of constructs.Suitable for datasets having dependent and independent variables.Useful for the dataset with a small sample size and less theoretical verification for causal relationships.Suitable for interpreting that changes over time i.e. required for assessing time-varying effects, especially for ecological research.
BenefitsAllows the assessment of formal statistical tests for examining the efficiency of the model, provides detailed information on model misfit degree and source, removes measurement error-based bias, and handles data uncertainty.Construct validity and content coverage improve by retaining a higher number of items, formative measurement models are applied, and determinant construct scores are available.Provides the opportunity of having a simultaneous analysis of complex models and decomposition of correlations for measuring the direct and indirect effects.Contributes to formulating and supporting more complicated non-theoretically verified models. Even nonrequirement of a large sample size, non-normal data, and formative measurement are benefits of the model.The flexibility is available for researchers in model formulation i.e. free to choose a range of parameters with one variable and single growth trajectory to complex progression. A researcher can also implement time-specific measurement errors in regression ensuring reliability and heteroscedasticity.
LimitationCFA fails to help assess models validity systematically due to the nonexistence of a rigorous test for the composite models. It also requires a large sample size for reliable results.  Proper conceptualization and construct dimensions identification is critical and measurement of confirmatory composite analysis cannot be operationalized.There are various assumptions in path analysis like relation among variables must be linear/ causal/ additive, residual not correlated with other variables, one-way casual flow, and measurement at interval scale which are hard to be satisfied. Collinearity issues prevent the detection of significant effects, understanding the meaning of model fitness, and the requirement of a large sample size. Lastly, categorical variables are major problems with the model.The model could not be used for the dataset to simply build casual relationships. A specifically linear linkage between the composites is required. Even inconsistent and biased estimation, model testing problems, and measuring quality problems are some other methodological limitations.Requires technique and language usage needing expertise and advanced training for analyzing and designing. Even missing observations and the presence of unequally spaced observations over time need to be treated as a model that can’t be formulated without it.
PopularityPopular for examining the simple contribution of variablesNot popular among researchers due to limited applicability.Widely used and applicable majorly for all types of research.Popular majorly in social research studiesLess popular and only applicable are time-based studies such as a 40-year analysis of economic growth.
Example6 statements are used for identifying time management and 6 statements for measuring the cost management status of the company. To examine the linkage between project management practices i.e. time management and scope management and their statements loading, CFA is used.The confirmatory compose analysis model is applied for examining the privacy concerns (awareness, information management, and interaction management) effect on providing personal data willingness by considering two contexts online retail services and airport digital services.Path analysis could be used for examining the impact of exercise on illness by considering fitness as a mediating variable.A model needs to be built for examining the impact of social executive behaviour and social employee behaviour on business process performance with each of the constructs dependent on different statements using the simulated dataset of 300 observationsA latent growth modeling model could be built for investigating the impact of child gender on the log reading trajectory
Table 1: Structural equation modeling applicability in research (Benitez et al., 2020; Columbia Public Health, 2017; Jeon, 2015; Lahey et al., 2012; Mwesiumo et al., 2021; R€onkk€o et al., 2016; Trninić et al., 2013; Willett & Bub, 2005)

Case-based examination of structural equation modeling (SEM) applicability in a research

Case 1

A study aims to measure depression levels in 961 sampled populations. For this, the researcher used the scale developed by the National Institute of Mental Health and developed a questionnaire containing 5 statements. Herein, the model needs to be built for measuring depression (Zimmer, 2019). Since this study does not intend to check the linkage or relationship or impact, and instead just requires the measurement of a construct based on the respective statements, the CFA model is suitable for analysis.

Case 2

A psychological study aims to find out the link between anxiety and online shopping behaviour of 400 consumers. The researcher in this study identified attention-seeking behaviour as a mediating variable. Therefore, the model needs to be built such that attention-seeking is regarded as a mediator between anxiety and online shopping behaviour. Since the main aim is to establish the relationship or the impact, a path analysis model will be applied.

Case 3

A study aims to develop a European customer satisfaction index model to assess the perception of 100 consumers on one product, service, and brand. The model should take into consideration the different linkages among constructs i.e.:

  • dependence of perceived value on expectation and perceived quality,
  • satisfaction on perceived value, expectation, perceived quality, and image,
  • loyalty on satisfaction, image and complaints,
  • complaints on satisfaction and,
  • the expectation on the image.

Each of these constructs is further measured on Likert scale statements of 1 to 5. Since this case involves complex relationships with small sample size, partial least square path modeling will be applied.

Figure 1: PLS-PM model from structural equation modelling
Figure 1: PLS-PM model (Russolillo, 2019)

Case 4

A clinical study focused on assessing and comparing the treatment effect among 62 female patients with bulimia nervosa. The researcher randomly assigned patients to a guided self-change treatment with a self-care manual and 16 weekly sessions for cognitive behavioural therapy. Since the model needs to be built by considering two periods involved i.e. treatment and post-treatment, latent growth modeling is a suitable method.

References

  • Benitez, J., Henseler, J., Castillo, A., & Schuberth, F. (2020). Information & Management How to perform and report an impactful analysis using partial least squares : Guidelines for confirmatory and explanatory IS research. Information & Management, 57(2), 103168. https://doi.org/10.1016/j.im.2019.05.003
  • Columbia Public Health. (2017). Latent Growth Curve Analysis.
  • Fan, Y., Chen, J., Shirkey, G., John, R., Wu, S. R., Park, H., & Shao, C. (2016). Applications of structural equation modeling (SEM) in ecological studies: an updated review. Ecological Processes, 5(1). https://doi.org/10.1186/s13717-016-0063-3
  • Hardy, S. A., & Thiels, C. (2009). Using latent growth curve modeling in clinical treatment research: An example comparing guided self-change and cognitive behavioral therapy treatments for bulimia nervosa. International Journal of Clinical and Health Psychology, 9(1), 51–71. https://doi.org/10.1016/j.eurpsy.2007.01.590
  • Jeon, J. (2015). The Strengths and Limitations of the Statistical Modeling of Complex Social Phenomenon : Focusing on SEM, Path Analysis, or Multiple Regression Models. International Journal of Economics and Management Engineering, 9(5), 1634–1642.
  • Lahey, B. B., McNealy, K., Knodt, A., Zald, D. H., Sporns, O., Manuck, S. B., Flory, J. D., Applegate, B., Rathouz, P. J., & Hariri, A. R. (2012). NIH Public Access. Neuroimage, 60(4), 1982–1991. https://doi.org/10.1016/j.neuroimage.2012.02.002.Using
  • Mwesiumo, D., Halpern, N., Budd, T., Suau-sanchez, P., & Bråthen, S. (2021). An exploratory and confirmatory composite analysis of a scale for measuring privacy concerns. Journal of Business Research, 136(February), 63–75. https://doi.org/10.1016/j.jbusres.2021.07.027
  • R€onkk€o, M., McIntosh, C. N., Antonakis, J., & Edwards, J. R. (2016). Partial least squares path modeling : Time for some serious second thoughts € nkk o. Journal of Operations Management. https://doi.org/10.1016/j.jom.2016.05.002
  • Russolillo, G. (2019). An introduction to partial least squares path modeling. STA201 – Analyse Multivariée Approfondie AN.
  • Trninić, V., IgorJelaska, & Štalec, J. (2013). Appropriateness and limitations of factor analysis methods utilised in psychology and kinesiology. 67(1), 5–17.
  • Willett, B. J. B., & Bub, K. L. (2005). Structural Equation Modeling : Latent Growth Curve Analysis. John Wiley & Sons, 1–15.
  • Zimmer, C. (2019). Learn to Perform Path Analysis in Stata With Data From the General Social Survey (2016). Sage Publications. https://doi.org/10.4135/9781529700114
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