In knowledge space theory, the (latent) knowledge state of a student consists of the subset of test items that he masters in principle. Even at a given stage of apprenticeship, the student’s knowledge state may vary in a given collection of subsets. The collection of all possible states of all potential students forms a knowledge structure. In the modeling of student answer production, the probabilities governing the knowledge state are parameters. Moreover, for each item, two additional parameters capture the probabilities of careless errors and lucky guesses in the answers to the item. From all the latter parameters, the Correct Response Model (CRM) predicts the probability of a correct answer to any isolated item. From the same parameters, the Basic Local Independence Model (BLIM) predicts the probability of any possible pattern of correct responses. Here, a particular pattern records at a given time all the items to which a given student would provide correct answers. While general properties of the BLIM (such as identifiability of parameters) have been investigated, the simpler Correct Response Model still requires scrutiny. The present paper investigates the CRM as regards testability, identifiability and characterizability. It either provides explicit answers or points out serious difficulties garnered from various mathematical disciplines.

在知识空间理论中，学生的（潜在）知识状态由他原则上掌握的测试项目的子集组成。即使在给定的学徒阶段，在给定的子集集合中，学生的知识状态也可能有所不同。所有潜在学生的所有可能状态的集合形成了一个知识结构。在学生答案产生的模型中，支配知识状态的概率是参数。而且，对于每个项目，两个附加参数捕获了项目答案中粗心的错误和幸运猜测的概率。根据所有后面的参数，正确响应模型（CRM）可以预测对任何孤立项目的正确答案的可能性。根据相同的参数，基本本地独立模型（BLIM）可以预测任何可能的正确响应模式的可能性。在这里，一个特定的模式在给定的时间记录了给定学生将提供正确答案的所有项目。虽然已经研究了BLIM的一般属性（例如参数的可识别性），但更简单的正确响应模型仍需要仔细检查。本文从可测试性，可识别性和可表征性方面对CRM进行了研究。它提供了明确的答案，或者指出了各种数学学科都遇到的严重困难。更简单的正确响应模型仍然需要仔细检查。本文从可测试性，可识别性和可表征性方面对CRM进行了研究。它提供了明确的答案，或者指出了各种数学学科都遇到的严重困难。更简单的正确响应模型仍然需要仔细检查。本文从可测试性，可识别性和可表征性方面对CRM进行了研究。它提供了明确的答案，或者指出了各种数学学科都遇到的严重困难。