A Tutorial in Longitudinal Measurement Invariance and Cross-lagged Panel Models Using Lavaan
Bibliographic record
Abstract
In longitudinal studies involving multiple latent variables, researchers often seek to predict how iterations of latent variables measured at early time points predict iterations measured at later time points. Cross-lagged panel modeling, a form of structural equation modeling, is a useful way to conceptualize and test these relationships. However, prior to making causal claims, researchers must first ensure that the measured constructs are equivalent between time points. To do this, they test for measurement invariance, constructing and comparing a series of increasingly strict and parsimonious models, each making more constraints across time than the last. This comparison process, though challenging, is an important prerequisite to interpretation of results. Fortunately, testing for measurement invariance in cross-lagged panel models has become easier, thanks to the wide availability of R and its packages. This paper serves as a tutorial in testing for measurement invariance and cross-lagged panel models using the lavaan package. Using real data from an openly available study on perfectionism and drinking problems, we provide a step-by-step guide of how to test for longitudinal measurement invariance, conduct cross-lagged panel models, and interpret the results. Original data source with materials: https://osf.io/gduy4/. Project website with data/syntax for the tutorial: https://osf.io/hwkem/.
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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 | 0.011 | 0.033 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.058 | 0.031 |
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".