#SmartPLS4 Series 21 - Simple Structural Model Analysis/Hypothesis Testing

Structural equation modeling in two stages hinges on a simple idea: first prove the constructs are measured well, then test whether the hypothesized relationships among those constructs hold. After reliability, validity, and construct quality checks are completed in the measurement (outer) model—covering indicator reliability, composite reliability (including alpha), and construct validity via convergent and discriminant validity—the next task shifts to the structural (inner) model. That structural step asks whether internal marketing relates to mediators, whether mediators relate to an outcome (organizational performance), and whether mediation or moderation patterns exist.

Before interpreting any path coefficients, the structural model must be checked for multicollinearity. Path coefficients in structural models are estimated using ordinary least squares (OLS)-style regressions for each endogenous construct on its predictor constructs. If predictor constructs are highly collinear, the resulting path estimates can become biased, making hypothesis tests unreliable. In SmartPLS, multicollinearity is diagnosed using variance inflation factor (VIF) values computed from construct scores in each regression. As a rule of thumb, VIF values above 5 signal probable multicollinearity problems; values below 3 are generally preferred, while values under 5 are often acceptable.

If multicollinearity is detected, one common remedy is to create higher-order constructs, reducing redundancy among predictors. Once collinearity is under control, attention turns to hypothesis testing: whether each proposed structural path is statistically significant and practically meaningful. In SmartPLS, this significance testing is typically done through bootstrapping, which resamples the data to generate standard errors for the estimated path coefficients.

In the worked example, two relationships are tested: CC → OP and OC → OP (with OP treated as the endogenous outcome). The output provides beta (original sample) path coefficients, p-values, and bootstrap-derived statistics. A path is treated as supported when its p-value is below the 0.05 threshold, indicating a statistically significant effect between the latent variables. The same decision can be framed using a t-statistic: dividing the bootstrapped standard deviation by the original sample coefficient yields a t value, and a t-statistic greater than 1.96 corresponds to significance at the 5% level.

The report view in SmartPLS organizes these results by path coefficients, including the original sample estimate, the sample mean from bootstrapping, and the standard deviation. The p-values and the t-statistics together determine whether each hypothesis is accepted or whether the null hypothesis is rejected. The practical workflow is therefore: confirm measurement quality, check multicollinearity with VIF, run bootstrapping, then interpret path significance using p-values (<0.05) and/or t-statistics (>1.96). The next planned step is to extend this baseline approach into mediation and moderation analyses, then scale up to more complex models.