Bibliographic record
Abstract
The linear regression model, with its numerous extensions including multivariate ordination, is fundamental to quantitative research in many disciplines. However, spatial or temporal structure in the data may invalidate the regression assumption of independent residuals. Spatial structure at any spatial scale can be modeled flexibly based on a set of uncorrelated component patterns (e.g., Moran's eigenvector maps, MEM) that is derived from the spatial relationships between sampling locations as defined in a spatial weight matrix. Spatial filtering thus addresses spatial autocorrelation in the residuals by adding such component patterns (spatial eigenvectors) as predictors to the regression model. However, space is not an ecologically meaningful predictor, and commonly used tests for selecting significant component patterns do not take into account the specific nature of these variables. This paper proposes "spatial component regression" (SCR) as a new way of integrating the linear regression model with Moran's eigenvector maps. In its unconditioned form, SCR decomposes the relationship between response and predictors by component patterns, whereas conditioned SCR provides an alternative method of spatial filtering, taking into account the statistical properties of component patterns in the design of statistical hypothesis tests. Application to the well-known multivariate mite data set illustrates how SCR may be used to condition for significant residual spatial structure and to identify additional predictors associated with residual spatial structure. Finally, I argue that all variance is spatially structured, hence spatial independence is best characterized by a lack of excess variance at any spatial scale, i.e., spatial white noise.
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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 | 0.000 | 0.000 |
| 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 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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; both teacher heads agree on what is shown here.
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".