# PLS-SEM Compared with CB-SEM

We do not use the term “PLS-SEM vs. CB-SEM”. Both methods are complementary rather than competitive. Even though this issue is well-know (see for example Jöreskog and Wold, 1982), many researchers still focus on comparing the differences of model estimations when using covariance-based structural equation modeling (CB-SEM) and partial least squares structural equation modeling (PLS-SEM). Instead of distinguishing between common factor models and composite models (Henseler et al., 2014), these discussions focus on PLS-SEM’s capabilities to mimic CB-SEM. But PLS-SEM in its original form (Wold, 1982; Lohmöller, 1989) has not been created to mimic CB-SEM! PLS-SEM researchers should follow Rigdon’s (2012) call and begin emancipating the method from its CB-SEM sibling (also see Sarstedt et al., 2014; Rigdon 2014). For example, Fornell and Bookstein (1982), Chin and Newsted (1999), Hair et al. (2011), Hair et al. (2012), Hair et al. (2014), Jöreskog and Wold (1982), and Reinartz et al. (2009) provide recommendations when to use CB-SEM or PLS-SEM. The most important reason to select CB-SEM or PLS-SEM is the research goal (structure or prediction): “The primary purpose of the ML approach is to study the structure of the observables […].The primary purpose of the PLS approach is to predict the indicators by means of the components expansion (1).” Jöreskog and Wold, 1982; p. 266). In line with this notion, Hair et al. (2011; p. 144) recommend:

- “If the goal is predicting key target constructs or identifying key 'driver' constructs, select PLS-SEM.
- If the goal is theory testing, theory confirmation, or comparison of alternative theories, select CB-SEM.
- If the research is exploratory or an extension of an existing structural theory, select PLS-SEM.”

However, recently Bentler and Huang (2014), Dijkstra (2014), and Dijkstra and Henseler (2015) introduced methods that provide consistent PLS-SEM estimations. These consistent PLS (PLSc) estimations of common factor models have been designed to mimic CB-SEM. Thereby, researchers can also use PLS-SEM to study structure. As a result, we see two developments of PLS-SEM: One direction use PLS-SEM for prediction-oriented studies and another direction uses PLS-SEM (via PLSc) to mimic CB-SEM for studies that focus on analyzing and testing the model structure.

In face of these recent developments, we use an application of the well-known technology acceptance model (TAM, Davis, 1989). The model estimation uses a dataset with 1,190 responses and the SmartPLS (Ringle et al., 2015) and AMOS (Arbuckle, 2006) software (alternative structural equation modeling software solutions are, for example, EQS, LISREL, and MPLUS). You can download the TAM example, which can be imported as a project into the SmartPLS software, from the resources of this webpage.

In fact, the results show strong similarities between the CB-SEM (ML) and PLSc results. In contrast, it is interesting to note the huge differences of results when using alternative CB-SEM estimation techniques (e.g., GLS, ULS, and ADF).

### Partial least squares (PLS) results (SmartPLS)

### Consistent PLS (PLSc) results (SmartPLS)

### Maximum likelihood (ML) results (AMOS; standardized coefficients)

### Generalized least squares (GLS) results (AMOS; standardized coefficients)

### Unweighted least squares (ULS) results (AMOS; standardized coefficients)

### Asymptotically distribution-free (ADF) results (AMOS; standardized coefficients)

## References

Arbuckle, J. L. 2006. "Amos (Version 7.0)." Chicago: SPSS.

Chin, W. W., and Newsted, P. R. 1999. "Structural Equation Modeling Analysis with Small Samples Using Partial Least Squares." In Statistical Strategies for Small Sample Research. Ed. R. H. Hoyle. Thousand Oaks: Sage, 307-341.

Jöreskog, K. G., and Wold, H. O. A. 1982. "The ML and PLS Techniques For Modeling with Latent Variables: Historical and Comparative Aspects." In Systems Under Indirect Observation, Part I. Eds. H. O. A. Wold and K. G. Jöreskog. Amsterdam: North-Holland, 263-270.

Lohmöller, J.-B. 1989. Latent Variable Path Modeling with Partial Least Squares. Heidelberg: Physica.

Ringle, C. M., Wende, S., and Becker, J.-M. 2015. "SmartPLS 3." Bönningstedt: SmartPLS GmbH.

Wold, H. O. A. 1982. "Soft Modeling: The Basic Design and Some Extensions." In Systems Under Indirect Observations: Part II. Eds. K. G. Jöreskog and H. O. A. Wold. Amsterdam: North-Holland, 1-54.