Using WarpPLS in e-Collaboration Studies: Mediating Effects, Control and Second Order Variables, and Algorithm Choices

This is a follow-up on two previous articles on WarpPLS and e-collaboration. The first discussed the five main steps through which a variance-based nonlinear structural equation modeling analysis could be conducted with the software WarpPLS (Kock, 2010b). The second covered specific features related to grouped descriptive statistics, viewing and changing analysis algorithm and resampling settings, and viewing and saving various results (Kock, 2011). This and the previous articles use data from the same e-collaboration study as a basis for the discussion of important WarpPLS features. Unlike the previous articles, the focus here is on a brief discussion of more advanced issues, such as: testing the significance of mediating effects, including control variables in an analysis, using second order latent variables, choosing the right warping algorithm, and using bootstrapping and jackknifing in combination. settings, and viewing and saving various results (Kock, 2011). This and the previous articles focus on version 1.0 of the software, and use data from the same e-collaboration study as a basis for the discussion of important WarpPLS features. While the articles use an e-collaboration study as a basis, the discussions are very generic and apply to areas unrelated to e-collaboration. In fact, the discussions are pertinent to research in many different fields. At the time of this writing, published examples of the use of WarpPLS existed in marketing, management, finance, accounting, anthropology, psychology, and nursing. DOI: 10.4018/jec.2011070101 2 International Journal of e-Collaboration, 7(3), 1-13, July-September 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Unlike the two previous articles in the three-article set, the focus here is on a brief discussion of more advanced issues, such as: testing the significance of mediating effects, including control variables in an analysis, using second order latent variables, choosing the right warping algorithm, and using bootstrapping and jackknifing in combination. THE E-COLLABORATION STUDY Several screen snapshots and composites are used here to illustrate important WarpPLS features. These snapshots and composites were generated based on a study of e-collaboration in virtual teams. Overall, 209 teams were studied. The teams carried out product innovation and development tasks in a variety of economic industries and sectors. The study focused on five main latent variables, referred to here as “ECU”, “ECUVar”, “Proc”, “Effi”, and “Effe”. “ECU” and “ECUVar” are technologyrelated variables. “ECU” refers to the extent to which electronic communication media, in addition to face-to-face communication, were used by each team. “ECUVar” refers to the variety of different electronic communication media used by each team, or the number of electronic communication media with different features (e.g., e-mail, teleconferencing, telephone) used by each team. “Proc”, “Effi”, and “Effe” are non-technology-related variables. “Proc” refers to the degree to which each team employed established project management techniques, referred to in the study as “procedural structuring” techniques, hence the name of the variable. “Effi” refers to the efficiency of each team, in terms of task completion cost and time, assessed against previously planned task completion cost and time. “Effe” refers to the effectiveness of each team (a team can be effective but not efficient, and vice-versa), in terms of the actual commercial success of the new goods or services that each team developed. TESTING THE SIGNIFICANCE OF MEDIATING EFFECTS Using WarpPLS, one can test the significance of a mediating effect of a variable M, which is hypothesized to mediate the relationship between two other variables X and Y, by using Baron and Kenny’s (1986) criteria. The procedure is outlined below. It can be easily adapted to test multiple mediating effects, and more complex mediating effects (e.g., with multiple mediators). Please note that we are not referring to moderating effects here; these can be tested directly with WarpPLS, by adding moderating links to a model. First two models must be built. The first model should have X pointing at Y, without M being included in the model. (You can have the variable in the WarpPLS model, but there should be no links from or to it.) The second model should have X pointing at Y, X pointing at M, and M pointing at Y. This is a “triangle”-looking model. A WarpPLS analysis must be conducted with both models, which may be saved in two different project files; this analysis may use linear or nonlinear analysis algorithms. The mediating effect will be significant if the three following criteria are met: • In the first model, the path between X and Y is significant (e.g., P < 0.05, if this is the significance level used). • In the second model, the path between X and M is significant. • In the second model, the path between M and Y is significant. Note that, in the second model, the path between M and Y controls for the effect of X. That is the way it should be. Also note that the effect of X on Y in the second model is irrelevant for this mediation significance test. Nevertheless, if the effect of X on Y in the second model is insignificant (i.e., indistinguishable from zero, statistically speaking), one can say that the case is one of “perfect” mediation. On the other hand, if the effect of X on Y in the second model is significant, one can say that International Journal of e-Collaboration, 7(3), 1-13, July-September 2011 3 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. the case is one of “partial” mediation. This of course assumes that the three criteria are met. Generally, the lower the effect of X on Y in the second model, the more “perfect” the mediation is, if the three criteria for mediating effect significance are met. Figures 1(a) and 1(b) show two models created for a mediating effect significance test. The mediating variable is “Proc”; the degree to which each team in our sample e-collaboration study employed established project management techniques. These techniques are referred to in the study as procedural structuring techniques. The effect that is hypothesized to be mediated by “Proc” is that between “ECU” and “Effi”. “ECU” refers to the extent to which electronic communication media were used by each team. “Effi” refers to the efficiency of each team, in terms of task completion cost and time. In this case, the mediating effect of “Proc” is not significant, because the first of the three criteria is not met. That is, in the first model, the path between “ECU” and “Effi” is not significant (beta = -.01, P = 0.44). The conclusion above is reached even though the two other criteria are met. In the second model, the path between “ECU” and “Proc” is significant (beta = .16, P < .01), and the path between “Proc” and “Effi” is also significant (beta = .47, P < .01). INCLUDING CONTROL 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. Figure 1(a). First WarpPLS model in a mediating effect significance test Figure 1(b). Second WarpPLS model in a mediating effect significance test 4 International Journal of e-Collaboration, 7(3), 1-13, July-September 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 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. 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. Some special considerations and related analysis decisions usually have to be made in more complex models, with multiple endogenous latent variables (i.e., variables to which arrows point), and also regarding the fit indices. For example, with multiple endogenous latent variables, you may want to add controls to all of them. Normally this will artificially reduce your APC (the average path coefficient, a model fit index); even thought your ARS (the average R-squared, another model fit index) will most certainly go up. Figure 2 shows a model created in WarpPLS where the effect of “Proc” on “Effi” is analyzed, controlling for the effects of “ECU” and “ECUVar”. Control variables can be latent variables, as is the case here. “ECU” is a latent variable measured formatively through 16 indicators, as indicated by the “(F)16i” notation under the name of the variable. Based on the results of the analysis we can say that “Proc” is significantly associated with “Effi”, regardless of “ECU” and “ECUVar”. Again, in this case it does not matter whether the effects associated with control variables are significant or not; in this case they are not. In models like the one above, with one main dependent variable, it is advisable to place the control variables on the right side of the model. This improves the readability of the model. Figure 2. Including control variables in an SEM analysis International Journal of e-Collaboration, 7(3), 1-13, July-September 2011 5 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. USING SECOND ORDER LATENT VARIABLES Second order latent variables can be implemented in WarpPLS through two steps. These steps are referred to as Step 1 and Step 2 in the paragraphs below. Higher order latent variables can also be implemented, following a similar procedure, but with additional steps. With second order latent variables, a set of latent variables scores are used as indicators of another latent variable. Often second order latent variables are decompositions of a formative latent variable into a few reflective latent variables, but this is not always the case. If this is the case, the scores of the component reflective latent variables are used as indicators of the original formative latent variables. In Step 1, you will create a model that relates latent variables to their indicators, as in Figure 3(a). Only the latent variables and their indicators should be included. No links between latent variables should be created. This will allow you to calculate the latent variables scores for the latent variables, based on the indicators. You will then save the latent variables scores using the option “Save factor scores into a tabdelimited .txt file”, available from the “Save” option of the “View and save results” window menu, as shown in Figure 3(b). In Step 2, you will create a new model where the saved latent variables scores are indicators of a new latent variable. This latent variable is usually called the second order latent variable, although sometimes the indicators (component latent variables) are referred to as second order latent variables. The rest of the data will be the same. Note that you will have to create and read the raw data used in the SEM analysis again, for this second step. CHOOSING THE RIGHT WARPING ALGORITHM: THE ROLE OF THEORY WarpPLS offers the following analysis algorithms: Warp3 PLS Regression, Warp2 PLS Regression, PLS Regression, and Robust Path