Measurement invariance testing using confirmatory factor analysis and alignment optimization: A tutorial for transparent analysis planning and reporting.
Bibliographic record
Abstract
Measurement invariance-the notion that the measurement properties of a scale are equal across groups, contexts, or time-is an important assumption underlying much of psychology research. The traditional approach for evaluating measurement invariance is to fit a series of nested measurement models using multiple-group confirmatory factor analyses. However, traditional approaches are strict, vary across the field in implementation, and present multiplicity challenges, even in the simplest case of two groups under study. The alignment method was recently proposed as an alternative approach. This method is more automated, requires fewer decisions from researchers, and accommodates two or more groups. However, it has different assumptions, estimation techniques, and limitations from traditional approaches. To address the lack of accessible resources that explain the methodological differences and complexities between the two approaches, we introduce and illustrate both, comparing them side by side. First, we overview the concepts, assumptions, advantages, and limitations of each approach. Based on this overview, we propose a list of four key considerations to help researchers decide which approach to choose and how to document their analytical decisions in a preregistration or analysis plan. We then demonstrate our key considerations on an illustrative research question using an open dataset and provide an example of a completed preregistration. Our illustrative example is accompanied by an annotated analysis report that shows readers, step-by-step, how to conduct measurement invariance tests using R and Mplus. Finally, we provide recommendations for how to decide between and use each approach and next steps for methodological research. (PsycInfo Database Record (c) 2023 APA, all rights reserved).
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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 | 0.069 | 0.197 |
| Meta-epidemiology (narrow) | 0.008 | 0.005 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.014 | 0.013 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.090 | 0.059 |
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".