POSTER: Bayesian Estimation of the Polychoric Correlation Coefficient with Skewed and Sparse Data
Bibliographic record
Abstract
In applied research and validation practice, it is common to find items, scales and measures exhibiting a strong degree of skewness in the participants’ responses, creating ceiling or floor effects (Ho & Yu, 2015). Although this tends to be attributed to the inability of the items to discriminate among participants, it could also naturally arise in checklists or scales designed to detect severe but infrequent anomalies in a typical sample (Catts et.al., 2009). If polychoric correlations are calculated from data exhibiting these characteristics, the sparseness of the contingency tables that occurs can yield biased estimates of the correlations and incorrect inferences (Savalei, 2011). A Bayesian solution is proposed to this problem through the use of a log-normal latent model that can naturally capture the inherent skewness and sparseness of this kind of data (Albert,1992). In order to document the extent of the problem and offer a potential solution, two computer simulations were conducted in the R programming language to explore this issue. The first one sets a value of 0 in the population for the correlation coefficient and varies the thresholds at 2, 2.3 and 3 standard deviations above the mean with sample sizes from 200 to 1000. The second one compares three effect sizes (0.1, 0.3 and 0.5) with two and three response option thresholds set at real-life estimated parameters from empirical research and compares the bias and variability of the correlation estimates. Preliminary results indicate that the maximum likelihood (ML) approach yields biased correlation estimates whereas the Bayesian alternative shows less bias and outperforms the normal theory ML method in cases with extreme skeweness of item responses and sparse contingency tables.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.018 | 0.116 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.018 | 0.005 |
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 source (direct Gemma or distilled Codex), 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".