27. SEMinR Lecture Series - Reflective-Reflective Higher Order Construct Analysis
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Validate every lower-order construct first by estimating a measurement model and checking loadings, reliability, HTMT, and the Fornell–Larcker criterion.
Briefing
Higher-order constructs in SEMinR can be modeled and tested by first validating the lower-order measurement model, then adding the higher-order reflective construct using a two-stage approach and re-running reliability/validity plus bootstrapping. The key practical takeaway is that reflective–reflective higher-order modeling works cleanly in two steps: validate “subdimensions” first (e.g., Vision development and Rewards), then treat them as indicators of the higher-order construct (e.g., Internal marketing) and assess whether the higher-order construct significantly predicts the outcome (e.g., Organizational performance).
The lecture walks through a concrete reflective–reflective example. Internal marketing is defined as a second-order reflective construct made up of three reflective subdimensions: Vision development, Rewards, and (as described in the model) the remaining internal-marketing dimension. Each subdimension is measured reflectively, and Internal marketing itself is also measured reflectively using those subdimensions. Organizational performance serves as the dependent variable.
Step one focuses only on the lower-order constructs. A separate SEMinR/R file is created to assess reliability and validity for Vision development, Rewards, and Organizational performance—without including the higher-order construct yet. The measurement model is built with these lower-order constructs, then linked in the structural model to the dependent variable (and among lower-order constructs if needed). After estimating, the standard reporting outputs are generated: factor loadings, reliability, HTMT, and the Fornell–Larcker criterion, along with a plot that can be exported. Any reliability/validity issues are handled at this stage before moving on.
Step two adds the higher-order construct. The model changes by introducing a higher composite function—specifically “higher_composite”—where the higher-order construct name (Internal marketing) is defined by its lower-order components (Vision development and Rewards). Because the example is reflective–reflective, the lecture notes that mode or weighting scheme adjustments are not required; the two-stage method is used with default settings. The structural model is then updated so that the higher-order construct Internal marketing links to Organizational performance, rather than linking each subdimension directly to the outcome.
After estimating the updated model, reliability and validity are checked again, now for the higher-order construct itself. The lecture also adds bootstrapping to test significance of the higher-order path. Bootstrapping is run using the summary and boot object, and the results indicate Internal marketing has a significant positive effect on Organizational performance: the t-statistic exceeds the 1.96 threshold (with no zero between bounds), and the effect size is described as reasonably strong. The session concludes by framing this as a template for reflective–reflective higher-order SEMinR modeling, with more complex examples promised later and code to be made available for download.
Cornell Notes
The lecture provides a two-stage workflow for reflective–reflective higher-order construct modeling in SEMinR. First, all lower-order constructs (e.g., Vision development and Rewards) are validated in a measurement model by checking loadings, reliability, HTMT, and the Fornell–Larcker criterion. Next, the higher-order construct (Internal marketing) is introduced using the higher_composite function with the lower-order components and the two-stage method. The structural model is then updated so the higher-order construct predicts Organizational performance. Finally, bootstrapping is used to test whether the higher-order path is statistically significant, using t-statistics (e.g., > 1.96) and confidence intervals that exclude zero.
Why validate lower-order constructs before building the higher-order model?
How does SEMinR represent a reflective–reflective higher-order construct like Internal marketing?
What changes in the structural model when moving from subdimension links to a higher-order link?
Which statistics are used to assess reliability and validity for both lower-order and higher-order constructs?
How is the significance of the higher-order effect tested?
Review Questions
- What are the specific outputs (e.g., HTMT and Fornell–Larcker) used to confirm reliability and validity in the lower-order measurement model?
- In a reflective–reflective higher-order setup, what does the higher_composite function do, and how does the two-stage method fit in?
- When testing the higher-order path to Organizational performance, what bootstrapping evidence indicates statistical significance?
Key Points
- 1
Validate every lower-order construct first by estimating a measurement model and checking loadings, reliability, HTMT, and the Fornell–Larcker criterion.
- 2
Use a separate SEMinR/R file for the initial lower-order validation stage before introducing the higher-order construct.
- 3
Define the reflective–reflective higher-order construct with higher_composite, listing its lower-order subdimensions (e.g., Vision development and Rewards) and using the two-stage approach.
- 4
Update the structural model so the higher-order construct predicts the dependent variable, avoiding direct subdimension-to-outcome links in the second stage.
- 5
Re-run reliability and validity checks after adding the higher-order construct to ensure the second-order measurement is acceptable.
- 6
Use bootstrapping to test whether the higher-order construct has a statistically significant effect on the dependent variable, interpreting t-statistics (e.g., > 1.96) and confidence intervals excluding zero.