Joe F. Hair, Jr.Founder & Senior Scholar

Using the SmartPLS SoftwareAssessment of Measurement Models

Indicators for SEM Model Exogenous Constructs Assessing Content Validity

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*All rights reserved . Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.Assessing Formative Constructs and Indicators

Evaluating formative constructs and indicators involves the following:First examine convergent validity using redundancy analysis. That is achieved by correlating each formative construct with a global measure for that construct. The construct is modeled as the independent variable and the global measure is the dependent variable. A path coefficient above the threshold of 0.80 provides support for convergent validity of the formative construct. The next step is to examine the collinearity of the indicators. SmartPLS software does not do this. SPSS or some other software must be used.The third step is to examine the statistical significance of the outer weights (not the loadings). This is done with the bootstrapping option of SmartPLS. Results for our Corporate Reputation example indicate that all formative indicators are significant except csor_2, csor_4, qual_2, and qual_4.If any indicator weights are not statistically significant, then we examine the size and significance of the indicator loadings. The SmartPLS default report provides the outer loadings and t values. The lowest loading for the four non-significant indicator weight is 0.57, and all t values are above 2.57, which indicates all four outer loadings are significant (

*All rights reserved . Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.Testing Convergent Validity Formative Constructs

The next two slides show the findings of the redundancy analysis for the four formative constructs in our SEM model. The first model shows the results for the redundancy analysis for the ATTR construct. The original formative construct is labeled with ATTR_F, whereas the global assessment of the companys attractiveness using a single-item construct is labeled with ATTR_G. As can be seen, this analysis yields a path coefficient of 0.87, which is above the threshold of 0.80, thus providing support for the formative constructs convergent validity. The redundancy analyses of the remaining formative constructs (CSOR, PERF & QUAL) yield estimates of 0.86, 0.81, and 0.81, respectively.

Thus, all formatively measured constructs have sufficient degrees of convergent validity.

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Testing Collinearity of IndicatorsThe SmartPLS software does not provide users with the tolerance and the VIF values. Statistical software packages such as R, IBM SPSS Statistics, or Statistica, however, have collinearity statistics in their linear regression modules. We will use the Full Data file that has been converted to SPSS format. To convert, open the Full Data.csv file with SPSS and use the Import Wizard (be sure to specify that the top Row contains the variable names).After converting the data file into SPSS format run a multiple regression with the formative indicators of a specific formative construct as independent variables and any other indicator, which is not included in that specific measurement model, as the dependent variable (otherwise, it does not matter which indicator serves as the dependent variable). With the exception of the collinearity analysis, the results of the regression analysis do not matter and are not further analyzed. The only result that is important for assessing collinearity issues is the VIF (or tolerance) value.

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*All rights reserved . Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.This is the SPSS linear regression output. The dependent variable is csor_1 and the three independent variables are attr_, attr_2, and attr_3. Note that all of the VIF numbers are slightly above 1, and all well below the threshold value of 5.

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*All rights reserved . Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.Collinearity results for other formative construct indicators are shown in Exhibit 5.22

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*All rights reserved . Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.Check to make sure correct options are selected.No Sign ChangesCorrect number of cases = sample size5,000 samples

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*All rights reserved . Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.Based on the t statistics, all formative indicators are significant except csor_2, csor_4, qual_2, and qual_4. Statistical Significance of Outer WeightsFormative Constructs

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*All rights reserved . Cannot be reproduced or distributed without express written permission from Sage, Prentice-Hall, McGraw-Hill, SmartPLS, and session presenters.The lowest outer loadings of these four indicators are 0.5715 = csor_2 and 0.5667 = qual_2 (note: these values will change slightly with bootstrapping), and all t values are clearly above 2.57, which indicates the significance of their outer loadings (p < .01).

These results provide support for retaining these items. Checking Outer Loadings of non-significant Formative Construct Indicators

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