The consequences of checking for zero‐inflation and overdispersion in the analysis of count data
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Count data are ubiquitous in ecology and the Poisson generalized linear model (GLM) is commonly used to model the association between counts and explanatory variables of interest. When fitting this model to the data, one typically proceeds by first confirming that the model assumptions are satisfied. If the residuals appear to be overdispersed or if there is zero‐inflation, key assumptions of the Poison GLM may be violated and researchers will then typically consider alternatives to the Poison GLM. An important question is whether the potential model selection bias introduced by this data‐driven multi‐stage procedure merits concern. Here we conduct a large‐scale simulation study to investigate the potential consequences of model selection bias that can arise in the simple scenario of analysing a sample of potentially overdispersed, potentially zero‐inflated, count data. Specifically, we investigate model selection procedures recently recommended by Blasco‐Moreno et al. (2019) using either a series of score tests or information theoretic criteria to select the best model. We find that, when sample sizes are small, model selection based on preliminary score tests (or information theoretic criteria, e.g. AIC, BIC) can lead to potentially substantial inflation of false positive rates (i.e. type 1 error inflation). When sample sizes are sufficiently large, model selection based on preliminary score tests, is not problematic. Ignoring the possibility of overdispersion and zero‐inflation during data analyses can lead to invalid inference. However, if one does not have sufficient power to test for overdispersion and zero‐inflation, post hoc model selection may also lead to substantial bias. This ‘catch‐22’ suggests that, if sample sizes are small, a healthy skepticism is warranted whenever one rejects the null hypothesis of no association between a given outcome and covariate.
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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 | 0.009 | 0.008 |
| 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