Contributing to the success of PLS in SEM: An action research perspective

The article below discusses how I employed an action research approach, by working closely with WarpPLS users, to contribute to the success of PLS in SEM. A big thank you to WarpPLS users!

Kock, N. (2023). Contributing to the success of PLS in SEM: An action research perspective. Communications of the Association for Information Systems, 52(1), 730-734.

Link to full-text file for this article:

Contributing to the success of PLS in SEM: An action research perspective

Abstract:

I share with Evermann and Rönkkö (2022) the belief that classic composite-based partial least squares path modeling (PLS-PM) presents shortcomings when used to conduct structural equation modeling (SEM) analyses. The shortcomings can be traced back to one fundamental problem, which is that latent variables (LVs) are approximated in PLS-PM as exact linear combinations of their corresponding indicators. In SEM, each LV is in fact a factor; i.e., a linear combination of the indicators and a measurement residual. My approach to addressing the shortcomings of PLS-PM is rather unique among researchers concerned with quantitative methods. I have employed an action research approach, helping investigators employ SEM in their empirical studies. This has led to my development of a widely used software tool for SEM analyses. I illustrate my action research orientation by discussing three recent methodological developments with which I have been closely involved.

Best regards to all!

Minimum sample size estimation in SEM: Contrasting results for models using composites and factors

The article below discusses how one can conduct a minimum sample size estimation, contrasting results for models using composites and factors, in the context of structural equation modeling via partial least squares (PLS-SEM).

Ezeugwa, B., Talukder, M. F., Amin, M. R., Hossain, S. I., & Arslan, F. (2022). Minimum sample size estimation in SEM: Contrasting results for models using composites and factors. Data Analysis Perspectives Journal, 3(4), 1-7.

Link to full-text file for this and other DAPJ articles:

https://scriptwarp.com/dapj/#Published_Articles

Abstract:

Estimating the minimum required sample size is an essential issue for studies that use structural equation modeling employing partial least squares (PLS-SEM). Several PLS-SEM-based studies ignore this critical step or use simple techniques, which lead to inaccurate sample size estimations. This paper illustrates two effective heuristic methods to estimate the minimum required sample size using WarpPLS, a leading PLS-SEM software tool.

Best regards to all!

Statistical power and minimum sample size requirements

The WarpPLS menu option “Explore statistical power and minimum sample size requirements”, available starting in version 6.0, allows you to obtain estimates of the minimum required sample sizes for empirical studies based on the following model elements: the minimum absolute significant path coefficient in the model (e.g., 0.21), the significance level used for hypothesis testing (e.g., 0.05), and the power level required (e.g., 0.80). Two methods are used to estimate minimum required sample sizes, the inverse square root and gamma-exponential methods. These methods simulate Monte Carlo experiments, and thus produce estimates that are in line with the estimates that would be produced through the Monte Carlo method.

Related YouTube video:

Explore Statistical Power and Minimum Sample Size in WarpPLS
http://youtu.be/mGT6-NKUe3E

Article in the Information Systems Journal discussing the methods:
http://onlinelibrary.wiley.com/doi/10.1111/isj.12131/full

Minimum sample size in PLS-SEM, regression, and path analyses

Based on Monte Carlo simulations, the minimum sample size in PLS-SEM can be reliably and conservatively estimated based on the inequality below:

N > ( 2.48 / Abs(bm) ) ^ 2

Extensive tests suggest that this also applies to multiple regression, and path analyses. In the latter, only single-indicator variables are included in the model, even though it looks a lot like an SEM model.

The inequality above is discussed in the article titled: "Minimum sample size estimation in PLS‐SEM: The inverse square root and gamma‐exponential methods" (). It refers to the inverse square root method. The gamma‐exponential method, also discussed in the article, is a refinement of the inverse square root method that relies on equations that are much more complex.

In the inequality above, N is the required sample size, and Abs(bm) is the absolute value of the path coefficient with the minimum expected magnitude in the model. This inequality assumes that:

- One-tailed P values are used for hypothesis testing. A previous post discusses this issue in more detail ().

- The threshold for P values is .05. That is, P values should be equal to or lower than .05.

- Effect sizes (ESs), as calculated by WarpPLS, are also used for hypothesis testing ().

- The threshold for ESs is .02. That is, ESs should be equal to or greater than .02.

- Acceptable statistical power is equal to or greater than .8.

- The latent variables in the model are not collinear, when both lateral and vertical collinearity are considered. That is, the full collinearity VIFs calculated by WarpPLS for all latent variables are equal to or lower than 3.3 ().

This inequality highlights the fact that path coefficient strength is a much stronger determinant of statistical power in Monte Carlo simulations than the configuration of the structural model.

The inequality is proposed as an alternative to the widely used (and discredited) "10 times rule". It yields minimum sample sizes that are consistent with Cohen's power tables for multiple regression.

For example, let us say one has a model where the path coefficient with the minimum expected magnitude is .3. Then the required sample size is:

N > ( 2.48 / .3 ) ^ 2 = 68.34

The minimum required sample size is thus:

Nm = 69

The above assumes a pre-analysis minimum sample size estimation, where the path coefficient with the minimum expected magnitude is set prior to the analysis.

A post-analysis minimum sample size estimation, on the other hand, would be based on the results of a full PLS-SEM analysis. Generally pre-analysis estimation is recommended over post-analysis estimation.

The latter, post-analysis estimation, can only confirm that an appropriate sample size was used.