Multi-group analyses and measurement invariance assessment

The menu options “Explore multi-group analyses” and “Explore measurement invariance”, available in WarpPLS starting in version 6.0, now allow you to conduct analyses where the data is segmented in various groups, all possible combinations of pairs of groups are generated, and each pair of groups is compared. 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

Lateral collinearity and misleading results in variance-based SEM: An illustration and recommendations

A new article discussing methodological issues based on WarpPLS is available. The article is titled “Lateral collinearity and misleading results in variance-based SEM: An illustration and recommendations”. It has been recently published in the Journal of the Association for Information Systems. A full text version of the article is available here as a PDF file. Below is the abstract of the article.

Variance-based structural equation modeling is extensively used in information systems research, and many related findings may have been distorted by hidden collinearity. This is a problem that may extend to multivariate analyses, in general, in the field of information systems as well as in many other fields. In multivariate analyses, collinearity is usually assessed as a predictor-predictor relationship phenomenon, where two or more predictors are checked for redundancy. This type of assessment addresses vertical, or “classic”, collinearity. However, another type of collinearity may also exist, here called “lateral” collinearity. It refers to predictor-criterion collinearity. Lateral collinearity problems are exemplified based on an illustrative variance-based structural equation modeling analysis. The analysis employs WarpPLS 2.0, with the results double-checked with other statistical analysis software tools. It is shown that standard validity and reliability tests do not properly capture lateral collinearity. A new approach for the assessment of both vertical and lateral collinearity in variance-based structural equation modeling is proposed and demonstrated in the context of the illustrative analysis.

Multi-group analysis with WarpPLS: Comparing path coefficients for two or more group samples

Starting in version 6.0 of WarpPLS, the menu options “Explore multi-group analyses” and “Explore measurement invariance” allow you to conduct analyses where the data is segmented in various groups, all possible combinations of pairs of groups are generated, and each pair of groups is compared. 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

Explore Measurement Invariance in WarpPLS

The text below is for an older version of this post. It discusses other approaches to multi-group analysis that are only partially automated, and that are thus more time-consuming to implement.

***

I previously discussed on this post multi-group analysis with WarpPLS from the perspective of comparing means of two or more groups. This is also explored in an article titled: Using WarpPLS in e-collaboration studies: What if I have only one group and one condition?

A different type of multi-group analysis would be one in which the same model is analyzed for two or more different samples, where each sample refers to a data group.

For example, a researcher could test the same model with data from the USA and Mexico. In this case, two project files would be used, and the goal of the multi-group analysis would be to assess whether the path coefficients differ significantly across groups.

An approach to conduct this type of multi-group analysis, employing the pooled and Satterthwaite standard error methods, is discussed in a recent publication (Kock, 2014). This approach is implemented through an Excel spreadsheet available from the “Resources” area of the WarpPLS.com site, under “Excel files”.

The Excel spreadsheet above takes as inputs coefficients generated by WarpPLS, including path coefficients and their standard errors. The outputs are T and P values for each pair of coefficients being compared. The formulas used in it are discussed in a recent publication (Kock, 2014).

Reference

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.

Multi-group analysis with WarpPLS: Comparing means of two or more groups

Comparing means of two groups is something that behavioral researchers often do. In fact, this is the most widely used quantitative analysis approach. This is also a form of multi-group analysis, where the number of groups is two. Common tests for comparing means are the t and and one-way ANOVA tests.

There is an arguably much better way of doing comparison of means test, with WarpPLS. Follow the steps below. This is a two-group test. Multi-group tests can be done in a similar way, through multiple two-group tests where conditions (i.e., groups) are compared pair by pair.

- Create a dummy variable (G) with numbers associated with each of the two groups - e.g., 0 for one group, and 1 for the other group. This dummy variable should be implemented as a LV with 1 indicator.

- Define your dependent (or criterion) construct (T) as you would normally do; in this case, I think that would be as a reflective LV with 3 indicators.

- Create a link between G and T, with G pointing at T.

- Estimate the model parameters with WarpPLS; this will calculate the beta and P values for the link. The P value is analogous to the P value you would obtain with a t test.

The following article goes into some detail about this procedure, contrasting it with other approaches:

Kock, N. (2013). Using WarpPLS in e-collaboration studies: What if I have only one group and one condition?  International Journal of e-Collaboration, 9(3), 1-12.

This type of WarpPLS test has a number of advantages over a standard t test or a one-way ANOVA test (which are essentially the same thing). For example, it allows for the use of LVs as dependent variables; and it is a robust test, which does not require that the dependent variables be normally distributed.

Multi-group tests, with more than two groups, can also be conducted by assigning different values to each of the groups. The key here is to decide what values to assign to each group. This choice is often somewhat arbitrary in exploratory analyses. The “Save grouped descriptive statistics into a tab-delimited .txt file” option may be helpful in this respect. This is a special option that allows you to save descriptive statistics (means and standard deviations) organized by groups defined based on certain parameters. For more details, see the user manual for WarpPLS, which is available from Warppls.com.

Starting in version 6.0 of WarpPLS, the menu options “Explore multi-group analyses” and “Explore measurement invariance” allow you to conduct analyses where the data is segmented in various groups, all possible combinations of pairs of groups are generated, and each pair of groups is compared. 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 now 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

Explore Measurement Invariance in WarpPLS

What are the inner and outer models in SEM?

In a structural equation modeling (SEM) analysis, the inner model is the part of the model that describes the relationships among the latent variables that make up the model. The outer model is the part of the model that describes the relationships among the latent variables and their indicators.

In this sense, the path coefficients are inner model parameter estimates. The weights and loadings are outer model parameter estimates. The inner and outer models are also frequently referred to as the structural and measurement models, respectively.

More precisely, the mathematical equations that express the relationships among latent variables are referred to as the structural model. The equations that express the relationships among latent variables and indicators are referred to as the measurement model.

The term structural equation model is used to refer to both the structural and measurement model, combined.

How do I control for the effects of one or more demographic variables in an SEM analysis?

As part of an SEM analysis using WarpPLS, a researcher may want to control for the effects of one ore more variables. This is typically the case with what are called “demographic variables”, or variables that measure attributes of a given unit of analysis that are (usually) not expected to influence the results of the SEM analysis.

For example, let us assume that one wants to assess the effect of a technology, whose intensity of use is measured by a latent variable T, on a behavioral variable measured by B. The unit of analysis for B is the individual user; that is, each row in the dataset refers to an individual user of the technology. The researcher hypothesizes that the association between T and B is significant, so a direct link between T and B is included in the model.

If the researcher wants to control for age (A) and gender (G), which have also been collected for each individual, in relation to B, all that is needed is to include the variables A and G in the model, with direct links pointing at B. No hypotheses are made. For that to work, gender (G) has to be included in the dataset as a numeric variable. For example, the gender "male" may be replaced with 1 and "female" with 2, in which case the variable G will essentially measure the "degree of femaleness" of each individual. Sounds odd, but works.

After the analysis is conducted, let us assume that the path coefficient between T and B is found to be statistically significant, with the variables A and G included in the model as described above. In this case, the researcher can say that the association between T and B is significant, “regardless of A and G” or “when the effects of A and G are controlled for”.

In other words, the technology (T) affects behavior (B) in the hypothesized way regardless of age (A) and gender (B). This conclusion would remain the same whether the path coefficients between A and/or G and B were significant, because the focus of the analysis is on B, the main dependent variable of the model.

The discussion above is expanded in the publication below, which also contains a graphical representation of a model including control variables.

Kock, N. (2011). Using WarpPLS in e-collaboration studies: Mediating effects, control and second order variables, and algorithm choices. International Journal of e-Collaboration, 7(3), 1-13.

http://www.scriptwarp.com/warppls/pubs/Kock_2011_IJeC_WarpPLSEcollab3.pdf

Some special considerations and related analysis decisions usually have to be made in more complex models, with multiple endogenous variables, and also regarding the fit indices.

View nonlinear relationships in WarpPLS: YouTube video

A new Youtube video is available for WarpPLS:

http://www.youtube.com/watch?v=lHrTxWmM43A

This video shows how one can view nonlinear and linear relationships estimated through a structural equation modeling (SEM) analysis using the software WarpPLS.

The video also highlights one fact that makes software like WarpPLS particularly useful - most relationships in nature are nonlinear. This includes relationships in biology, business, sociology, physics etc.

As you will see in this video, the software shows a table with the types of relationships, warped or linear, between latent variables that are linked in the model. The term “warped” is used for relationships that are clearly nonlinear, and the term “linear” for linear or quasi-linear relationships. Quasi-linear relationships are slightly nonlinear relationships, which look linear upon visual inspection on plots of the regression curves that best approximate the relationships.

Plots with the points as well as the regression curves that best approximate the relationships can be viewed by clicking on a cell containing a relationship type description. These cells are the same as those that contain path coefficients, in the path coefficients table.

The plots of relationships between pairs of latent variables provide a much more nuanced view of how each pair of latent variables is related. However, caution must be taken in the interpretation of these plots, especially when the distribution of data points is very uneven.

An extreme example would be a warped plot in which all of the data points would be concentrated on the right part of the plot, with only one data point on the far left part of the plot. That single data point, called an outlier, would influence the shape of the nonlinear relationship. In these cases, the researcher must decide whether the outlier is “good” data that should be allowed to shape the relationship, or is simply “bad” data resulting from a data collection error.

Structural equation modeling made easy with WarpPLS: YouTube video

Conducting a basic structural equation modeling (SEM) analysis using WarpPLS is relatively easy. The software takes the user through 5 steps, from project file creation to model building (using a graphical user interface) and viewing the results of the analysis. Take a look at the Youtube video below.




The link below should take you directly to the video on YouTube, in case you have problems viewing the video above.

http://www.youtube.com/watch?v=yUojJaV3jlA

Choose the high quality (HQ) option for viewing the video clip above, if it is available (usually at the bottom of the video screen), and expand it to the full screen mode.

As you'll see at the end of the video, the project file is quite small, and it contains everything that is needed for the analysis. The file can be copied into a separate file, which the user can then open and change, by modifying the model for example, to conduct a different analysis.

Welcome to the WarpPLS blog!

Welcome to the WarpPLS blog! WarpPLS is a powerful structural equation modeling (SEM) software. It is commercialized by ScriptWarp Systems: www.scriptwarp.com.

Among other things, WarpPLS identifies nonlinear (or “warped”, hence the name of the software) relationships among latent variables and corrects the values of path coefficients accordingly. WarpPLS is arguably the first SEM software to do this.

Since most relationships between numeric variables are nonlinear, one could argue that WarpPLS finds the "real" relationships between latent variables in an SEM analysis. Typically path coefficients are increased, in some cases going from non-significant to significant at the P lower than 1 percent level.

The underlying algorithm employed by WarpPLS as its outer model default is partial least squares (PLS) regression, whose main characteristic is its ability to minimize multicollinearity among latent variables (even in the presence of overlapping manifest variables, or indicators). Other PLS-based outer model algorithms are also available, including PLS modes A and B.

Additionally, WarpPLS offers the following features, which are largely absent from most, if not all, PLS-based SEM software packages available today:

• It estimates P values for path coefficients automatically, instead of providing only standard errors or T values, and leaving the user to figure out what the corresponding P values are.
• It estimates several model fit indices, which have been designed to be meaningful in the context of PLS-based SEM analyses.
• It automatically builds the indicators’ product structure underlying moderating relationships, and goes a little further. It shows those moderating relationships, related path coefficients, and related P values in a model graph as they should be shown – that is, as links between latent variables and direct links. The latter connect pairs of latent variables, while the former connect latent variables and direct links between pairs of latent variables.
• It allows users to view scatter plots of each of the relationships among latent variables (when they are connected through arrows in the model), together with the curves that best approximate those relationships, and save those plots as .jpg files for inclusion in research reports.
• It provides a variety of graphs from which users can choose, including zoomed 2D graphs and 3D graphs; the latter for moderating effects. Both multivariate and bivariate relationship graphs are provided, for linear and nonlinear relationships, using standardized and unstandardized scales.
• It allows users to segment curves based on increments in the first derivative of the predictor latent variables on each of their criteria latent variables. This provides an alternative to data segmentation approaches such as FIMIX-PLS, without any reduction in sample.
• It calculates variance inflation factor (VIF) coefficients for latent variable predictors associated with each latent variable criterion. This allows users to check whether some predictors should be removed due to multicolinearity (this feature is particularly useful with latent variables that are measured based on only 1 or a few indicators).
• It calculates effect size coefficients analogous to Cohen’s f-squared coefficients for all paths. These are calculated as the absolute values of the individual contributions of the corresponding predictor latent variables to the R-square coefficients of the criterion latent variable in each latent variable block.
• It calculates indirect effects for paths with 2, 3 etc. segments; as well as total effects. The corresponding P values, standard errors, and effect sizes are also calculated. Indirect and total effects can be critical in the evaluation of downstream effects of latent variables that are mediated by other latent variables, especially in complex models with multiple mediating effects along concurrent paths.
• It calculates a variety of causality assessment coefficients, all of which are reported. These can be used in the assessment of the plausibility and direction of hypothesized cause-effect relationships.

These are only a few of the new features offered by WarpPLS.

Ned Kock

WarpPLS developer