Different types of structural equation modelling analysis

By Riya Jain and Priya Chetty on October 20, 2021

Structural equation modelling (SEM) is a statistical test that helps to evaluate a set of regression equations at the same time. The goal of SEM is to explore relationships between one or more independent variables and one or more dependent variables. It is popularly used in SPSS Amos and LISREL software. SEM is more sophisticated than traditional statistical analysis models such as regression. SEM is the combination of diverse computer algorithms, mathematical models, and statistical methods fitted in a dataset. There are five major types of structural equation modelling analysis. Each of them helps to build a relationship between variables.

Different types of structural equation modelling analysis
Figure 1: Different types of structural equation modelling analysis

Moreover, structural equation modelling analysis can be presented with different models.

  1. Measurement model
  2. Structural model

This article explains the characteristics of each type of analysis and its presentation for constructing a relationship between two or more variables.

Reducing observed variables with confirmatory factor analysis

Structural equation modelling (SEM) is a term used to describe models that study causal links between latent or unobserved variables that do not have a value. SEM identifies the contribution of different statements in this valuation of a latent variable (Holtzman, 2011). In this process, confirmatory factor analysis is a technique to examine the impact of each statement in measuring the respective construct or the main variable. It thus enables the selection of only relevant constructs for the model. Confirmatory factor analysis can decrease data dimensions and standardize the scale of various indicators. In other words, if a model has many latent variables then Confirmatory factor analysis will help to reduce them so that only the relevant ones are visible (Fan, 2016)

Confirmatory Factor analysis in structural equation modelling analysis
Figure 2: Confirmatory Factor analysis (Escobar, 2019)

The confirmatory factor analysis model is the initial step of structural equation modelling analysis. It identifies the relevance of any statement in the computation of the impact. For the above figure 4, the model determines how are factors i.e. ε1 and ε2 measured by indicators i.e. x1 to x8.

Testing composite models that have observed variables

Composite models are defined as a collection of interconnected components that arise as linear combinations of observable variables. It is the variable measured by more than one measured variable. The confirmatory composite analysis is used to test composite models consisting of observed or measured variables. The confirmatory composite analysis makes it easier to operationalize and evaluate the efficiency of the model. Thus, researchers need to choose the model which is already defined theoretically i.e. existing researches or studies have already mentioned the linkage (Schuberth et al., 2018).

For example; the effect of information management and interaction management among the passengers on the sharing of personal information. Herein, as two statements are used for measuring personal information, thus, confirmatory composite analysis can be used.  

Confirmatory composite analysis in structural equation modelling analysis
Figure 3: Confirmatory composite analysis (Schuberth et al., 2018)

Visually, figure 3 shows the confirmatory composite analysis wherein c is a composite variable like personal information, while x1 and x2, y, and z are observed variables. Herein, x1 and x2 is information management and interaction management variable. Observable variables y and z could be some other variable having linkage with personal information sharing that does not have a direct impact on the personal information sharing behaviour.

Examining linkages with path analysis

Path analysis is a type of multiple regression statistical analysis that examines the linkages between a dependent variable and two or more independent variables to test a hypothesis. Path analysis helps to understand the causal relationships between variables (Ashley Crossman, 2019).

For example; a model can be built to examine the impact of exercise and hardiness on illness by considering the mediating effect of fitness and stress.

path analysis in structural equation modelling analysis
Figure 4: A path analysis

While path analysis helps to evaluate the relationship that exists between variables, the direction of linkage is completed based on the model (Ashley Crossman, 2019).

Partial least square path modelling

Partial least square path modelling is used to test and validate exploratory models that are not yet proven or tested. It is the combination of various models from confirmatory composite analyses. There are two types of partial least square path models:

  1. inner models and,
  2. outer models.

The inner model defines the main construct linkage or only latent variables association to present the relationship between main variables (structural model). The outer model consists of one construct linkage with its observed statements (measurement model) (Henseler et al., 2009).

For example; it can be used to build a model to understand the impact of 5 project management practices on project performance. Wherein, each management practice and project performance is dependent on some other statements.

Figure 5: Partial least square path modelling (Henseler et al., 2016)

The Partial least square is a complicated model consisting of a large number of variables. Therefore it can be formulated even in cases where not much theoretical information is present and with a small sample size (Yi fan, 2016). In the above figure, there are three different confirmatory factor analysis models or measurement models with the square boxes while one structural model is shown in the rectangle box.

Latent growth modelling

Latent growth modelling is a successful longitudinal data analysis methodology when the focus of the study is on individual change. It enables the examination of data that changes over time (Serva, 2011). Thus, it enables the comparison of variables’ effects for different periods.

For example; a vocational training program has been organized by higher educational institutions for improving the skill set of students. A model needs to be built for comparing the effect pre and post-training periods. Thus, herein latent growth modeling could be used.

Figure 6: Latent growth modelling (Escobar, 2019)

Thus, the latent growth curve model is particularly useful in assessing time-varying effects because longitudinal data is frequent in ecological research. (Yi fan, 2016)

Presenting structural equation modelling analysis with the measurement model

The measurement model depicts the relationships between the measured, where there is a value and the latent variables, where the value needs to be computed based on other variables. It simply refers to the model formulation by including observed variable, latent variable, and measurement error in the model.

The measurement model symbolizes the confirmatory factor analysis model. It specifies the pattern through which each measure loads on a specific factor, i.e. the weightage of the relationship between two variables (DeVault, 2018).

Presenting structural equation modelling analysis with the measurement model
Figure 7: Measurement model

Where,

  • LV = Latent variable
  • OV = Observed variable
  • ME = Measurement error

Here, the model consists of measurement error terms, latent variables, and observed variables. Therefore, there is a complete description of each element linkage. Hence, the measurement model is the one wherein a detailed presentation of the model is provided.

Presenting structural equation modelling analysis with structural model

The structural model is the technical linkage building of the model wherein the focus is just on the constructs or the latent variable, describing the relationship. It is just a specification of linkage between main variables without stating the statements on which these variables are dependent. The structural model is like the overview of the relationship that exists between the main variables of the study.

For example; the impact of employee commitment on organizational performance without considering the statements measuring these variables.

Herein, the model is formulated by including only latent variables so that just the impact relationship could be stated (DeVault, 2018). Since it identifies only the relationship and not the actual variables, it provides only a brief overview of the model. The below figure represents a sample structural model.

Structural model
Figure 8: Structural model

Here, LV1 represents the first latent variable while LV2 depicts the second latent variable. Though the analysis is still computed by including measurement error and observed variables, the structural model is just a representation of the main component i.e. latent variables.

Applying different types of structural equation modelling analysis

Structural equation modelling (SEM) is a powerful modelling tool that generalizes many statistical techniques, but it must be utilized with caution. SEM works best for models with explicit and causal motivations, such as those with temporal or physical relationships. The examination of different types of SEM helps in constructing and inspecting models as per the need of the problem. However, a clear formulation is possible only when the applicability or suitability of different models discussed in this article is understood.

References

  • Ashley Crossman. (2019). Understanding Path Analysis.
  • DeVault, G. (2018). Structural Equation Modeling (SEM). Market Research.
  • Escobar, M. R. (2019). The four models you meet in Structural Equation Modeling. The Analysis Factor.
  • Fan, Y. (2016). Applications of structural equation modeling (SEM) in ecological studies: an updated reviewtle.
  • Henseler, J., Hubona, G., & Ray, P. A. (2016). Using PLS path modeling in new technology research: Updated guidelines. Industrial Management and Data Systems, 116(1), 2–20. https://doi.org/10.1108/IMDS-09-2015-0382
  • Henseler, J., Ringle, C. M., & Sinkovics, R. R. (2009). The use of partial least squares path modeling in international marketing. Advances in International Marketing, 20(January), 277–319. https://doi.org/10.1108/S1474-7979(2009)0000020014
  • Holtzman, S. (2011). Confirmatory Factor Analysis and Structural Equation Modeling of Noncognitive Assessments using PROC CALIS.
  • Schuberth, F., Henseler, J., & Dijkstra, T. K. (2018). Confirmatory composite analysis. Frontiers in Psychology, 9(DEC). https://doi.org/10.3389/fpsyg.2018.02541
  • Serva, M. A. (2011). Using Latent Growth Modeling to Understand Longitudinal Effects in MIS Theory: A Primer. CAIS.
  • Yi fan. (2016). Applications of structural equation modeling (SEM) in ecological studies: an updated review.
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