Learning models and the double monotone model

The goal of some assessments is to evaluate a person’s ability levels while others aim to teach through an intervention. In Chapter 1, we propose some IRT growth models for learning and estimate their learning parameters under the restrictions of the Linear Logistic Test Model. We also examine the potential benefit of using an adaptive selection method in conjunction with these models which aims to increase the rate of learning. In 1971, Mokken proposed the Double Monotone Model (DMM), a non-parametric item response model which is widely used to assess peoples’ abilities or attitudes. In Chapter 2, we introduce a procedure for estimating the DMM. We study its performance in simulation and use M-estimation to develop an asymptotic theory for estimation of ICCs using isotonic regression. Previous isotonic regression theory showed that the isotonic regression estimator, ˆ Pj , is consistent for Pj when θ is observable. When θ is unknown and estimated by θˆ, we show that the isotonic regression estimator, P˜j , is also consistent for Pj . We perform a real data analysis and illustrate how to select subsets of items to achieve double monotonicity, and we develop a test for double monotonicity with a null hypothesis of double monotonicity. In Chapter 3, we compare the performance of the 1PL to the DMM under various conditions with the constraints of double monotonicity. We found that fitting a 1PL can perform at least as well as the DMM for short exams and small sample sizes, even when the 1PL does not hold. This is due to the requirement of a plug-in estimate of theta for the nonparametric model. We also study the implication for ability estimation and found that nonparametric estimation is quite good. Recommendations are given for when to use or not use the nonparametric DMM.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Yu, Albert

Contributors dc:contributor

• Douglas, Jeffrey
• Culpepper, Steven
• Kern, Justin
• Zhang, Susu

• Irt
• Double Monotone Model
• Learning Models

Statement dc:rights

• Copyright 2022 Albert Yu

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/117700

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F117700