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Log-linear model of problem solving times analogical to the IRT three-parameter model

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Description

A generative student model for interactive problem solving that specifies the distribution of problem solving times rather than correctness probability. It assumes, in the article's words, "a linear relationship between a problem solving skill and a logarithm of time to solve a problem": tsp = bp + apθs + N(0, cp²), where b is basic difficulty, a a discrimination factor, and c a randomness factor. The notation is deliberately chosen to mirror the IRT three-parameter logistic model, and the model is also related to k=1 collaborative filtering. It supports prediction of solving times and estimation of problem and student parameters.

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  • Log-linear model of problem solving times analogical to the IRT three-parameter model: A generative student model for interactive problem solving that specifies the distribution of problem solving times rather than correctness probability. It assumes, in the article's words, "a linear relationship between a problem solving skill and a logarithm of time to solve a problem": tsp = bp + apθs + N(0, cp²), where b is basic difficulty, a a discrimination factor, and c a randomness factor. The notation is deliberately chosen to mirror the IRT three-parameter logistic model, and the model is also related to k=1 collaborative filtering. It supports prediction of solving times and estimation of problem and student parameters. (Pelánek et al. (2015))

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Key Sources

  • Pelánek, R., & Jarušek, P. (2015). Student Modeling Based on Problem Solving Times. International Journal of Artificial Intelligence in Education. https://doi.org/10.1007/s40593-015-0048-x
Page metadata
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type research-method
id log-linear-model-of-problem-solving-times-analogical-to-the-irt-three-parameter-model
title Log-linear model of problem solving times analogical to the IRT three-parameter model
description A generative student model for interactive problem solving that specifies the distribution of problem solving times rather than correctness probability.
status review
generated by process:settle-candidates on 2026-10-27
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