Generating spatially constrained null models for irregularly spaced data using <scp>M</scp>oran spectral randomization methods
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Bibliographic record
Abstract
Summary Spatial autocorrelation jeopardizes the validity of statistical inference, for example correlation and regression analysis. Restricted randomization methods can account for the effect of spatial autocorrelation in the observed data by building it into an empirical null model for hypothesis testing. This can be achieved, for example, based on conditional simulation, which fits a highly parameterized geostatistical model to the observed spatial structure, or, for data observed on a regular transect or grid, with Fourier spectral randomization methods that can flexibly model spatial structure at any scale. This study uses M oran eigenvector maps to extend spectral randomization to irregularly spaced samples. We present different algorithms to perform restricted randomization to suit different types of research questions: individual randomization of each variable, joint randomization of a group of variables while keeping within‐group correlations fixed, and randomization with a fixed correlation between original data and randomized replicates (e.g. as input for simulation studies). The performance of the proposed M oran spectral randomization methods for regularly and irregularly spaced samples is assessed with correlation analysis of simulated data. Moran spectral randomization closely matched the spatial structure of original simulated data sets, with identical or nearly identical M oran's I values and power spectra, depending on the algorithm. In correlation analysis of two spatially autocorrelated variables, M oran spectral randomization produced correct type I error rates for stationary spatial data, even for very small and highly irregular samples, but was sensitive to linear trend. When one or both variables lacked spatial structure, M oran spectral randomization tests were more conservative than correlation t ‐tests. The proposed M oran spectral randomization method requires a minimum of parameterization and is able to address multivariate data with spatial structure at multiple scales, with the option of controlling levels of correlation with the original data. It can provide technically unlimited numbers of randomizations even for small samples while closely maintaining the spatial characteristics of uni‐ or multivariate data at all spatial scales. The method is applicable for correlation analysis of stationary, autocorrelated spatial or temporal series. Further research should assess whether the method can be extended to multiple regression analysis.
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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 | 0.006 | 0.003 |
| 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 | 0.000 | 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 it