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Statistical Methods for Small Sample...

Arthur, David B.,

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Statistical Methods for Small Sample Cognitive Diagnosis /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Statistical Methods for Small Sample Cognitive Diagnosis // David B Arthur.
作者:	Arthur, David B.,
面頁冊數:	1 electronic resource (127 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
Contained By:	Dissertations Abstracts International86-04B.
標題:	Sample size. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31345199
ISBN:	9798342102926

Statistical Methods for Small Sample Cognitive Diagnosis /
Arthur, David B.,

Statistical Methods for Small Sample Cognitive Diagnosis /David B Arthur. - 1 electronic resource (127 pages)

Source: Dissertations Abstracts International, Volume: 86-04, Section: B.

It has been shown that formative assessments can lead to improvements in the learning process. Cognitive Diagnostic Models (CDMs) are a powerful formative assessment tool that can be used to provide individuals with valuable information regarding skill mastery in educational settings. These models provide each student with a ``skill mastery profile'' that shows the level of mastery they have obtained with regard to a specific set of skills. These profiles can be used to help both students and educators make more informed decisions regarding the educational process, which can in turn accelerate learning for students. However, despite their utility, these models are rarely used with small sample sizes. One reason for this is that these models are often complex, containing many parameters that can be difficult to estimate accurately when working with a small number of observations. This work aims to contribute to and expand upon previous work to make CDMs more accessible for a wider range of educators and students.There are three main small sample statistical problems that we address in this work: 1) accurate estimation of the population distribution of skill mastery profiles, 2) accurate estimation of additional model parameters for CDMs as well as improved classification of individual skill mastery profiles, and 3) improved selection of an appropriate CDM for each item on the assessment. Each of these problems deals with a different aspect of educational measurement and the solutions provided to these problems can ultimately lead to improvements in the educational process for both students and teachers. By finding solutions to these problems that work well when using small sample sizes, we make it possible to improve learning in everyday classroom settings and not just in large scale assessment settings.In the first part of this work, we propose novel algorithms for estimating the population distribution of skill mastery profiles for a popular CDM, the Deterministic Inputs Noisy ``and'' Gate (DINA) model. These algorithms borrow inspiration from the concepts behind popular machine learning algorithms. However, in contrast to these methods, which are often used solely for prediction, we illustrate how the ideas behind these methods can be adapted to obtain estimates of specific model parameters. Through studies involving simulated and real-life data, we illustrate how the proposed algorithms can be used to gain a better picture of the distribution of skill mastery profiles for an entire population students, but can do so by only using a small sample of students from that population.In the second part of this work, we introduce a new method for regularizing high-dimensional CDMs using a class of Bayesian shrinkage priors known as catalytic priors. We show how a simpler model can first be fit to the observed data and then be used to generate additional pseudo-observations that, when combined with the original observations, make it easier to more accurately estimate the parameters in a complex model of interest. We propose an alternative, simpler model that can be used instead of the DINA model and show how the information from this model can be used to formulate an intuitive shrinkage prior that effectively regularizes model parameters.

English

ISBN: 9798342102926Subjects--Topical Terms:

3642155
Sample size.

Statistical Methods for Small Sample Cognitive Diagnosis /
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