A Didactic Presentation of Snijders’s <i> l <sub>z</sub> * </i> Index of Person Fit With Emphasis on Response Model Selection and Ability Estimation
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Bibliographic record
Abstract
This paper focuses on two likelihood-based indices of person fit, the index l z and the Snijders’s modified index l z *. The first one is commonly used in practical assessment of person fit, although its asymptotic standard normal distribution is not valid when true abilities are replaced by sample ability estimates. The l z * index is a generalization of l z , which corrects for this sampling variability. Surprisingly, it is not yet popular in the psychometric and educational assessment community. Moreover, there is some ambiguity about which type of item response model and ability estimation method can be used to compute the l z * index. The purpose of this article is to present the index l z * in a simple and didactic approach. Starting from the relationship between l z and l z *, we develop the framework according to the type of logistic item response theory (IRT) model and the likelihood-based estimators of ability. The practical calculation of l z * is illustrated by analyzing a real data set about language skill assessment.
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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 | 0.002 | 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