# Factors and composites in structural equation modeling

**Structural equation modeling (SEM)** is a statistical test that helps to build a relationship between variables. It requires the inclusion of latent (unobserved) and measured (observed) variables. However, choosing the right variable is a challenge in **SEM**. The previous article explained different **SEM **methods like CFA and CCA. In order to decide which **SEM **method to apply in a study, it is important to first determine whether to treat a variable as a factor or a composite. Composite variables when clustered help to come up with a new model. Factor variables are measured variables that help determine the impact of one element on another. This article explains in detail the difference between interconnected components in **SEM**, factors and composites. It helps to determine the optimal **SEM** method for a study.

## Understanding composite variables in **SEM**

A composite variable is similar to a latent variable. It is used for presenting concepts involving multiple variables. However, the major distinction between the latent variable and composite variable is that the former can be formulated using unobserved variables or other latent variables. But, a composite variable is only computed using measured or observed variables (Lefcheck, 2021). The figure below shows a composite variable.

Here, in figure 1 the arrows depict that all the variables x1, x2, and x3 are contributing to η computation. The composite variable is defined as the interconnected components represented as a linear combination of observed variables. In other words, a composite variable is the weighted sum of different indicators of components (Lefcheck, 2021; Rademaker, 2021).

For example; the soil condition is defined by a combination of its moisture, pH level, nutrient content, and grain size. Thus, all the items providing an idea about soil condition are components while the soil condition is the composite variable which is defined by combining all components.

Composite variable thus is not a cause-effect relationship but a statement of how variables should be arranged to formulate a new entity (Henseler, 2017).

## What is a factor in **SEM**?

Factors in the **SEM **model are regarded as the observed variables representing components that influence another variable. Since they cause an impact on another variable, factors are measurable variables.

In figure 2, the variables visperc, cubes, and lozenges contribute to the ‘spatial’ component while paragraph, sentence, and wordmean contribute to the ‘verbal’ component. Thus, visperc, cubes, lozenges, paragraph, sentence, and wordmean are the factors (Hox & Bechger, 2015). In different available **SEM **models, CFA is most popular to examine the role of factors by determining their composition in the computation of a construct.

For example; in the case stated for the composite model, the soil condition is a composite model but all components contributing to it i.e. pH, moisture, or nutrients could be regarded as factors.

Lefcheck, 2021; Willmer et al., 2019

## Difference between factors and composites in **SEM**

Factors and composites in **SEM **are often accepted as similar terminologies. However as both variables define completely different parts of the model, they are not the same. The table below summarises the differences between them.

Base | Composite | Factor |
---|---|---|

Meaning | It is the linear combination of an observed variable having interlinkage or the contribution in formulating a new variable | It is the observed variable contributing towards the formulation of other variables or impacting another variable |

Formulation | The composite model is used for computing the value of a new latent variable using already measured/observed variables | The value of factors is generally already measured as they are observed variables, thus, only measurement error is included for stating possible bias in computation |

Usage | It is used to build a structural model and compute the impact of something whose value could not be directly derived. | It is used to state the measurement form of the model and have the computation of each component weightage in the model like in CFA analysis |

Example | The composite variable project management practices for an organization could be measured by considering time management, scope management, or cost management | The factors like customer satisfaction and project success help in the computation of project performance for the organization. |

## Applicability of factors and composites in **SEM**

Composite variables are a type of latent variable that is suitable for path analysis, partial least square modeling, and confirmatory composite analysis models (Lefcheck, 2021). As composites create an interconnected component, they provide a better understanding of variables that cannot be measured directly. Hence they help establish a relationship (Henseler, 2017).

On the other hand, factors are components supporting other latent and composite variables. Thus, they are applicable for CFA analysis, measurement model of path analysis, partial least square modeling, and confirmatory composite analysis (Willmer et al., 2019). Thus, in SEM, the usage of interconnected components of composite and factors is different and based on the requirement of establishing a relationship or computing a new variable, the respective variable is chosen.

#### References

- Henseler, J. (2017). Bridging Design and Behavioral Research With Variance-Based Structural Equation Modeling.
*Journal of Advertising*,*46*(1), 178–192. https://doi.org/10.1080/00913367.2017.1281780 - Hox, J. J., & Bechger, T. M. (2015). An introduction to structural equation models.
*Family Science Review*,*11*, 354–373. https://doi.org/10.1007/978-3-319-16507-3_1 - Lefcheck, J. (2021). Composite Variables. In
*Github*. https://jslefche.github.io/sem_book/index.html - Rademaker, M. (2021).
*Terminology*. https://cran.r-project.org/web/packages/cSEM/vignettes/Terminology.html#fbmethods - Willmer, M., Westerberg Jacobson, J., & Lindberg, M. (2019). Exploratory and Confirmatory Factor Analysis of the 9-Item Utrecht Work Engagement Scale in a Multi-Occupational Female Sample: A Cross-Sectional Study.
*Frontiers in Psychology*,*10*(December), 1–7. https://doi.org/10.3389/fpsyg.2019.02771

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