08. SEMinR Lecture Series. Bootstrapping the PLS Model and generating Summary Results

Bootstrapping in SEMinR is used to test whether PLS-SEM path coefficients are statistically significant by generating standard errors and confidence intervals from resampled data. After estimating a PLS model, the workflow shifts from “what are the path estimates?” to “how reliable are those paths?”—a non-parametric step that matters because it avoids relying on strict distributional assumptions.

The session begins with a quick recap of the SEMinR setup: load the SEMinR library, import the dataset into an R object, inspect it for issues, then define the measurement model using the `constructs` function (composites) and the structural model using `relationships` (the directional paths among constructs). The model is then estimated with a PLS algorithm call that takes the data, measurement model, structural model, and missing-value handling options. Results are stored as an estimated PLS model object, and `summary` is used to produce a report. That summary object can be queried for specific details—such as path coefficients, reliability, and other metrics—via `$` access to sub-objects like `summary_model`.

Bootstrapping comes next. Because bootstrapping is non-parametric, it estimates standard errors and confidence intervals by repeatedly resampling the data and re-estimating the model. SEMinR’s `bootstrap_model` function performs this task on a previously estimated SEMinR PLS model object. Key inputs include the model to bootstrap, the number of bootstrap subsamples, the number of CPU cores for parallel processing, and a seed for reproducibility. In the example, 1,000 bootstrap subsamples are used for the run, while the recommended practice is to use 10,000 for final reporting; parallelization can be controlled through the `cores` argument.

The transcript also highlights a practical debugging point: errors during bootstrapping can stem from invisible formatting issues—like extra spaces introduced when copying code from other software. Removing problematic spaces and rerunning resolves the issue, after which the bootstrap completes successfully.

To interpret results, the workflow again uses `summary`, this time on the bootstrapped model object. The resulting summary object includes bootstrapped means, standard deviations, t statistics, and confidence intervals for paths (plus additional outputs like loadings and HTMT results, which are deferred to later sessions). For significance testing, the confidence interval is central: if the interval does not cross zero, the path is treated as significant. The example notes that under a one-tailed interpretation, significance can be tied to a threshold such as 1.645, and it demonstrates that the confidence intervals for the listed paths exclude zero—so the effects are considered significant.

Finally, the session shows how to narrow output to only the desired section of the summary object (e.g., only bootstrap paths), and it closes with a step-by-step checklist: load library, read and inspect data, define measurement and structural models, estimate the PLS model, bootstrap with `bootstrap_model`, and summarize bootstrapped results with `summary` for targeted inference.