Cognitive Trait Model · bounded trait scoring

A score that says how far along, not who is ahead

This learner reads 62% of mastery, give or take 9. The band is not decoration: on a short test the same responses can read 67%, 75% or 100% depending on which estimator you use. The number alone is a claim the data does not support.

Everything runs in this page. Your responses are never uploaded.

If you use this tool, cite

Choi, J. (2026). Mastery scoring: A browser implementation of the cognitive trait model (Version 1.0.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.22050655

Method and reference implementation

Choi, J. (2022). Cognitive trait model: Measurement model for mastery level and progression of learning. Mathematics, 10(15), 2651. https://doi.org/10.3390/math10152651

Choi, J. (2026). cogtraitmodel: Bounded-trait psychometrics with the anchored logistic family (Version 0.2.1) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.22031040

1 Bring in the responses

One row per learner, one column per item, values 0 or 1. Commas, tabs or spaces all work. Leave a cell empty for an item that was not administered.

2 Calibrate the items

Item parameters have to be estimated before anyone can be scored. Two parameters is the safer default; add a guessing parameter only if the items are multiple choice and you have enough low scorers to identify it — step 3 will tell you whether you do.

Model

3 Read the warnings

These are the conditions under which an estimate should not be reported as it stands. They are checked automatically because they are easy to miss and expensive to get wrong.

4 Score the learners

Each row shows the estimate as a mark on the mastery rule, with the band covering one standard deviation either side. Read the band before the number.