Measurement invariance assessment in PLS-SEM

WarpPLS users can assess measurement invariance in PLS-SEM analyses in a way analogous to a multi-group analysis. That is, WarpPLS users can compare pairs of measurement models to ascertain equivalence, using one of the multi-group comparison techniques building on the pooled and Satterthwaite standard error methods discussed in the article below. By doing so, they will ensure that any observed between-group differences in structural model coefficients, particularly in path coefficients, are not due to measurement model differences.

Kock, N. (2014). Advanced mediating effects tests, multi-group analyses, and measurement model assessments in PLS-based SEM. International Journal of e-Collaboration, 10(3), 1-13.

For measurement invariance assessment, the techniques discussed in the article should be employed with weights and/or loadings. While with path coefficients researchers may be interested in finding statistically significant differences, with weights/loadings the opposite is typically the case – they will want to ensure that differences are not statistically significant. The reason is that significant differences between path coefficients can be artificially induced by significant differences between weights/loadings in different models.

A spreadsheet with formulas for conducting a multi-group analysis building on the pooled and Satterthwaite standard error methods is available from WarpPLS.com, under “Resources”. As indicated in the article linked above, this same spreadsheet can be used in the assessment of measurement invariance in PLS-SEM analyses.

The menu options “Explore multi-group analyses” and “Explore measurement invariance”, available in WarpPLS starting in version 6.0, allow you to automatically conduct analyses like the ones above. Through these the data is segmented in various groups, all possible combinations of pairs of groups are generated, and each pair of groups is compared. As noted above, in multi-group analyses normally path coefficients are compared, whereas in measurement invariance assessment the foci of comparison are loadings and/or weights. The grouping variables can be unstandardized indicators, standardized indicators, and labels. These types of analyzes can also be conducted via the new menu option “Explore full latent growth”, which presents several advantages (as discussed in the WarpPLS User Manual).

Related YouTube videos:

Explore Multi-Group Analyses in WarpPLS

http://youtu.be/m2VKQGET-K8

Explore Measurement Invariance in WarpPLS

http://youtu.be/29VqsAjhzqQ

Advantages of nonlinear over segmentation analyses in path models

Nonlinear analyses employing the software WarpPLS allow for the identification of linear segments emerging from a nonlinear analysis, but without the need to generate subsamples. A new article is available demonstrating the advantages of nonlinear over data segmentation analyses. These include a larger overall sample size for calculation of P values, and the ability to uncover very high segment-specific path coefficients. Its reference, abstract, and link to full text are available below.

Kock, N. (2016). Advantages of nonlinear over segmentation analyses in path models. International Journal of e-Collaboration, 12(4), 1-6.

The recent availability of software tools for nonlinear path analyses, such as WarpPLS, enables e-collaboration researchers to take nonlinearity into consideration when estimating coefficients of association among linked variables. Nonlinear path analyses can be applied to models with or without latent variables, and provide advantages over data segmentation analyses, including those employing finite mixture segmentation techniques (a.k.a. FIMIX). The latter assume that data can be successfully segmented into subsamples, which are then analyzed with linear algorithms. Nonlinear analyses employing WarpPLS also allow for the identification of linear segments mirroring underlying nonlinear relationships, but without the need to generate subsamples. We demonstrate the advantages of nonlinear over data segmentation analyses.

Among other things this article shows that identification of linear segments emerging from a nonlinear analysis with WarpPLS allows for: (a) a larger overall sample size for calculation of P values, which enables researchers to uncover actual segment-specific effects that could otherwise be rendered non-significant due to a combination of underestimated path coefficients and small subsample sizes; and (b) the ability to uncover very high segment-specific path coefficients, which could otherwise be grossly underestimated.

Enjoy!

Hypothesis testing with confidence intervals and P values

While P values are widely used in PLS-based SEM, as well as in SEM in general, the statistical significances of path coefficients, weights and loadings can also be assessed employing T ratios and/or confidence intervals. These can be obtained in WarpPLS through the menu option “Explore T ratios and confidence intervals”, which also allows you to set the confidence level to be used. This menu option becomes available after Step 5 is completed.

Related YouTube video: Explore T Ratios and Confidence Intervals in WarpPLS

https://youtu.be/Xao0T2MxJZM

An article is also available explaining how WarpPLS users can test hypotheses based on confidence intervals, contrasting that approach with the one employing P values. A variation of the latter approach, employing T ratios, is also briefly discussed. Below are the reference, link to PDF file, and abstract for the article.

Kock, N. (2016). Hypothesis testing with confidence intervals and P values in PLS-SEM. International Journal of e-Collaboration, 12(3), 1-6.

PDF file

Abstract:
E-collaboration researchers usually employ P values for hypothesis testing, a common practice in a variety of other fields. This is also customary in many methodological contexts, such as analyses of path models with or without latent variables, as well as simpler tests that can be seen as special cases of these (e.g., comparisons of means). We discuss here how a researcher can use another major approach for hypothesis testing, the one building on confidence intervals. We contrast this approach with the one employing P values through the analysis of a simulated dataset, created based on a model grounded on past theory and empirical research. The model refers to social networking site use at work and its impact on job performance. The results of our analyses suggest that tests employing confidence intervals and P values are likely to lead to very similar outcomes in terms of acceptance or rejection of hypotheses.

Note 1:
On Table 1 in the article, each T ratio and confidence interval limits (lower and upper) are calculated through the formulas included below. Normally a hypothesis will not be supported if the confidence interval includes the number 0 (zero).

T ratio = (path coefficient) / (standard error).

Lower confidence interval = (path coefficient) - 1.96 * (standard error).

Upper confidence interval = (path coefficient) + 1.96 * (standard error).

Note 2:
Here is a quick note to technical readers. The P values reported in Table 1 in the article are calculated based on the T ratios using the incomplete beta function, which does not assume that the T distribution is exactly normal. In reality, T distributions have heavier tails than normal distributions, with the difference becoming less noticeable as sample sizes increase.