---
title: "Learning Factors Analysis – A General Method for Cognitive"
description: "The authors propose Learning Factors Analysis (LFA), a semi-automated way to assess and refine… 17 references, cited by 13 papers here."
authors: ["Hao Cen", "Kenneth Koedinger", "Brian Junker"]
year: 2006
venue: "Lecture Notes in Computer Science"
source: "https://doi.org/10.1007/11774303_17"
doi: "10.1007/11774303_17"
licence: "All rights reserved — free to read at the source"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/cen-2006-learning-factors-analysis-general-method/"
---
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# Learning Factors Analysis – A General Method for Cognitive Model Evaluation and Improvement

**Authors:** Hao Cen, [Kenneth Koedinger](https://md.research.elamur.ai/free/en/authors/kenneth-r-koedinger/) and Brian Junker · **Year:** 2006 · **Venue:** [Lecture Notes in Computer Science](https://md.research.elamur.ai/free/en/venues/lecture-notes-in-computer-science/) ([Lecture notes in computer science 2006](https://md.research.elamur.ai/free/en/venues/lecture-notes-in-computer-science/2006/)) · **Publisher:** [Springer Science+Business Media](https://md.research.elamur.ai/free/en/publishers/springer-science-business-media/) · **Licence:** All rights reserved — free to read at the source

**Links:** [Publisher's page](https://doi.org/10.1007/11774303_17) · [PDF](http://pact.cs.cmu.edu/koedinger/pubs/Cen,%20Koedinger%20&%20Junker06.pdf) · [DOI 10.1007/11774303\_17](https://doi.org/10.1007/11774303_17) · [OpenAlex](https://openalex.org/W1562092080)

**Citations:** 556 citations (OpenAlex, 2026-10-14) · [13](https://md.research.elamur.ai/free/en/papers/cen-2006-learning-factors-analysis-general-method/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Intelligent tutors rely on cognitive models, which are sets of production rules or skills describing how learners solve problems. These models are usually designed by hand by domain experts, cognitive scientists and programmers, and such first versions often miss important distinctions. The authors propose Learning Factors Analysis (LFA), a semi-automated way to assess and refine these models using student-tutor logs. LFA turns the power-law learning curve into a logistic regression. The regression gives each student an intercept and gives each skill both an intercept and a learning slope. Experts then define difficulty factors that can split skills, and an A* search guided by AIC or BIC explores the resulting candidate models. The authors tested LFA on log data collected from the Geometry Cognitive Tutor's unit covering area. It produced models that scored better than the original 15-skill model and were still interpretable. Some of the original skill distinctions were confirmed, while others, such as keeping circumference and diameter as separate skills, looked unnecessary. The fitted parameters also show which skills students practise too much or too little, giving concrete guidance for adjusting the curriculum.

## Key points
- **Dataset:** 4,102 first-attempt actions from 24 students across 115 problem steps. The original cognitive model has 15 skills.
- **Search method:** Four expert-defined factors (Embed, Backward, Repeat, FigurePart) feed a Binary Split operator. An A* search, capped at 50 node expansions, is run once with AIC and once with BIC as the heuristic.
- **Over-practice:** Parallelogram-side starts at about .94 success probability yet gets roughly 14.9 practice opportunities per student.
- **Under-practice:** Trapezoid-height rises only from .29 to .69 after about 4.2 opportunities, so it needs more practice.
- **Hidden weak sub-skill and runtime:** Compose-by-multiplication appears mastered overall (final .92). After splitting, however, its segment variant reaches only .60 with fewer than 2 practices on average. The Java implementation scores one model in seconds and searches hundreds of models in 4–5 hours.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Carnegie Mellon University](https://md.research.elamur.ai/free/en/universities/carnegie-mellon-university/) — University, Pittsburgh, United States · 633 works · 195,218 citations

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🧭 Topics (1): [📏 Evaluation & benchmarks](https://md.research.elamur.ai/free/en/topics/evaluation-benchmarks/) · 1,394 works

## Cite

Cite as: Hao Cen, Kenneth Koedinger and Brian Junker. 2006. Learning Factors Analysis – A General Method for Cognitive Model Evaluation and Improvement. Lecture Notes in Computer Science.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{cen2006learning,
  title = {{Learning Factors Analysis – A General Method for Cognitive Model Evaluation and Improvement}},
  author = {Hao Cen, Kenneth Koedinger and Brian Junker},
  booktitle = {Lecture Notes in Computer Science},
  year = {2006},
  doi = {10.1007/11774303\_17},
  url = {https://doi.org/10.1007/11774303_17}
}
```

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## References

17 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

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*Updated 3 November 2026*