2009年DINA模型详解：参数估计教程

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DINA模型及其参数估计是心理学与教育测量领域的一项关键理论，由作者Jimmy de la Torre在2009年的一篇名为《DINAModel and Parameter Estimation: A Didactic》的文章中详细介绍。该模型属于认知诊断理论（Cognitive Diagnostic Modeling）的一个分支，主要用于分析个体在多选题测验中的反应行为，区分出他们真正掌握的知识点与随机猜测的能力。DINA模型有两个主要类型：HO-DINA（Hierarchical Ordered DINA）和EM-MCMC（Expectation-Maximization Markov Chain Monte Carlo）。 HO-DINA模型假设个体的知识水平分为多个层次，每个层次对应一个能力节点，只有当所有较低层次的知识点被正确回答后，个体才可能回答更高层次的问题。这种模型强调了知识的递进性，并通过参数估计来确定每个知识点的难度和个体掌握这些知识点的概率。 EM-MCMC方法是一种统计学中的迭代算法，用于估计DINA模型中的参数。它结合了最大似然估计（Maximum Likelihood Estimation）和马尔科夫链蒙特卡洛（Markov Chain Monte Carlo）技术，能够有效地处理复杂的模型结构和数据不确定性，从而得到更精确的参数估计。文章发表在《行为科学与教育统计学杂志》(Journal of Educational and Behavioral Statistics)上，该刊于2008年6月11日在线首发，并在同年3月25日发表了最终版本。作者Jimmy de la Torre是来自罗格斯大学的新泽西州立大学的认知与技能诊断模型专家，他在这篇文章中提供了一个教学性质的指南，帮助读者理解并应用DINA模型进行实际研究。这篇文章的重要性在于它不仅介绍了DINA模型的基本原理，还提供了如何通过EM-MCMC方法对模型参数进行有效估计的步骤，这对于教育测量、心理评估以及教育干预策略的制定具有重要意义。由于其较高的引用次数（385次），表明其理论价值和实践应用得到了广泛认可。此外，文章还包含了相关链接，如电子期刊订阅、提醒服务、再版权限等，方便读者获取最新研究成果和获取学术支持。

of the required skills. The ‘‘and’’ gate component of the model refers to the con-

junctive process in determining Z

in that a correct response to an item requires

the presence all the prescribed skills for the item. In the example above, students

who lack any one of the three required skills are not expected to answer the item

correctly. Thus, the DINA model exhibits the same property as standard non-

compensatory multidimensional IRMs. If the process is completely determinis-

tic (i.e., error-free or nonstochastic), the latent response vector is identical to the

manifest or observed response vector. However, because the underlying process

is inherently stochastic, the latent response vector represents only an ideal

response pattern. The noise introduced in the process is due to slip and guessing

parameters—that is, examinees who possess all the required skills for an item

can slip and miss the item, and examinees who lack at least one of the required

skills can guess and still answer the item correctly with typically nonzero prob-

abilities. In the DINA model, the slip and guessing parameters of item j are

deﬁned as s

= PðX

= 0|Z

= 1) and g

= PðX

= 1|Z

= 0), respectively. There-

fore, the probability of examinee i with the skills vector α

answering item j cor-

rectly is given by

ðα

Þ = PðX

= 1|α

Þ = g

1 − Z

ð1 − s

: ð2Þ

From this equation, answering an item correctly requires an examinee who

has all the necessary skills to not slip and an examinee who lacks at least one of

the required skills to guess correctly. Note that if there is no guessing and no

slippage, the model probability of correct response to an item is either 0 or 1;

that is, the response is solely determined by the interaction of α and the Q-vector

for the item. However, as noted by de la Torre and Douglas (2004), guessing

in this context assumes a general interpretation; it is not conﬁned to a correct

response arrived through a random response but rather includes the use of alter-

native strategies not articulated in the Q-matrix. For example, if an item can be

solved using a different set of skills, examinees who possess these skills but not

those prescribed in the Q-matrix may appear to be guessing but in fact are sys-

tematically solving the problem using a different strategy.

A graphical representation of the DINA model is given in Figure 1. As the

graph shows, the latent response Z

is a function of the examinee’s skills fa

and the requisites of the item fq

g. Once Z

has been determined, the probabil-

ity that examinee i will give a correct response to item j is g

if Z

= 0 and 1 − s

if Z

= 1:

The DINA model is a parsimonious and interpretable model that requires

only two parameters for each item (i.e., g

and s

) regardless of the number of

attributes being considered, and despite its simplicity, it has been shown to pro-

vide good model ﬁt (e.g., de la Torre & Douglas, 2004, 2005). De la Torre and

Douglas (2004) and Junker and Sijtsma (2001) provide some applications of

the DINA model. Although labeled differently, other discussions of the DINA

DINA Model and Parameter Estimation

117

at CARNEGIE MELLON UNIV LIBRARY on April 27, 2012http://jebs.aera.netDownloaded from

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