Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data
Why this work is in the frame
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Bibliographic record
Abstract
The Mantel test is widely used to test the linear or monotonic independence of the elements in two distance matrices. It is one of the few appropriate tests when the hypothesis under study can only be formulated in terms of distances; this is often the case with genetic data. In particular, the Mantel test has been widely used to test for spatial relationship between genetic data and spatial layout of the sampling locations. We describe the domain of application of the Mantel test and derived forms. Formula development demonstrates that the sum-of-squares (SS) partitioned in Mantel tests and regression on distance matrices differs from the SS partitioned in linear correlation, regression and canonical analysis. Numerical simulations show that in tests of significance of the relationship between simple variables and multivariate data tables, the power of linear correlation, regression and canonical analysis is far greater than that of the Mantel test and derived forms, meaning that the former methods are much more likely than the latter to detect a relationship when one is present in the data. Examples of difference in power are given for the detection of spatial gradients. Furthermore, the Mantel test does not correctly estimate the proportion of the original data variation explained by spatial structures. The Mantel test should not be used as a general method for the investigation of linear relationships or spatial structures in univariate or multivariate data. Its use should be restricted to tests of hypotheses that can only be formulated in terms of distances.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it