Multilevel modelling for measuring interaction of effects between multiple categorical variables: An illustrative application using risk factors for preeclampsia
Bibliographic record
Abstract
BACKGROUND: Measuring multiple and higher-order interaction effects between multiple categorical variables proves challenging. OBJECTIVES: To illustrate a multilevel modelling approach to studying complex interactions. METHODS: We apply a two-level random-intercept linear regression to a binary outcome for individuals (level-1) nested within strata (level-2) defined by all observed combinations of multiple categorical exposure variables. As a pedagogic application, we analyse 36 strata defined by five risk factors of preeclampsia (parity, previous preeclampsia, chronic hypertension, multiple pregnancies, body mass index category) among 652,603 women in the Swedish Medical Birth Registry between 2002 and 2010. RESULTS: The absolute risk of preeclampsia was 4% but was predicted to vary from 1% to 44% across strata. The stratum discriminatory accuracy was 30% according to the variance partition coefficient (VPC) and 0.73 according to the area under the receiver operating characteristic curve (AUC). While the risk heterogeneity across strata was primarily due to the main effects of the categories defining the strata, 5% of the variation was attributable to their two- and higher-way interaction effects. One stratum presented a positive interaction, and two strata presented negative interaction. CONCLUSIONS: Multilevel modelling is an innovative tool for identifying and analysing higher-order interaction effects. Further work is needed to explore how this approach can best be applied to making causal inferences.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".