# Factors and composites in structural equation modeling

By Riya Jain & Priya Chetty on January 27, 2022

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 and composite variables 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.

In figure 1 the arrows depict that all the variables x1, x2, and x3 contribute 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).

A 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 the most popular to examine the role of factors by determining their composition in the computation of a construct.

## 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.

## 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.

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