Abstract. There has been an increase of interest in psychometric models referred to as cognitive diagnosis models (CDMs). A critical concern is in selecting the most appropriate model at the item level. Several tests for model comparison have been employed, which include the likelihood ratio (LR) and the Wald (W) tests. Although the LR test is relatively more robust than the W test, the current implementation of the LR test is very time consuming, given that it requires calibrating many different models and comparing them to the general model. In this article, we introduce the two-step LR test (2LR), an approximation to the LR test based on a two-step estimation procedure under the generalized deterministic inputs, noisy, “and” gate (G-DINA) model framework, the two-step LR test (2LR). The 2LR test is shown to have similar performance as the LR test. This approximation only requires calibration of the more general model, so that this statistic may be easily applied in empirical research.

中文翻译：

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认知诊断模型中项目级模型比较的两步似然比检验

摘要。人们对被称为认知诊断模型（CDM）的心理测量模型越来越感兴趣。关键问题是在项目级别选择最合适的模型。已经采用了几种用于模型比较的测试，其中包括似然比（LR）和Wald（W）测试。尽管LR测试比W测试相对更健壮，但是LR测试的当前实现非常耗时，因为它需要校准许多不同的模型并将它们与通用模型进行比较。在本文中，我们介绍了两步LR测试（2LR），它是在广义确定性输入，噪声和“与”门（G-DINA）模型框架下，基于两步估算程序的LR测试的近似值，两步LR测试（2LR）。2LR测试显示出与LR测试相似的性能。这种近似只需要校准更通用的模型，这样该统计就可以轻松地用于经验研究。