Multiplicity Control in Structural Equation Modeling: Incorporating Parameter Dependencies
Bibliographic record
Abstract
When structural equation modeling (SEM) analyses are conducted, significance tests for all important model relationships (parameters including factor loadings, covariances, etc.) are typically conducted at a specified nominal Type I error rate (α). Despite the fact that many significance tests are often conducted in SEM, rarely is multiplicity control applied. Cribbie (2000, 2007) demonstrated that without some form of adjustment, the familywise Type I error rate can become severely inflated. Cribbie also confirmed that the popular Bonferroni method was overly conservative due to the correlations among the parameters in the model. The purpose of this study was to compare the Type I error rates and per-parameter power of traditional multiplicity strategies with those of adjusted Bonferroni procedures that incorporate not only the number of tests in a family, but also the degree of correlation between parameters. The adjusted Bonferroni procedures were found to produce per-parameter power rates higher than the original Bonferroni procedure without inflating the familywise error rate.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.205 | 0.623 |
| Meta-epidemiology (narrow) | 0.004 | 0.003 |
| Meta-epidemiology (broad) | 0.004 | 0.005 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.003 | 0.007 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.006 | 0.008 |
| Research integrity | 0.004 | 0.010 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".