as if they had received the same test, as is common in tests designed using classical test theory). The psychometric technology that allows equitable Computerized adaptive testing (CAT) is a form of computer-based test that adapts to the examinee's ability level. For this reason, it has also been called tailored testing. In other words, it is a form of computer-administered test in which the next item or set of items selected to be administered depends on the correctness of the test taker's responses to the most recent items administered. The pool of available items is searched for the optimal item, based on the current estimate of the examinee's ability The chosen item is presented to the examinee, who then answers it correctly or incorrectly The ability estimate is updated, based on all prior answers Steps 1–3 are repeated until a termination criterion is met Nothing is known about the examinee prior to the administration of the first item, so the algorithm is generally started by selecting an item of medium, or medium-easy, difficulty as the first item. As a result of adaptive administration, different examinees receive quite different tests. Although examinees are typically administered different tests, their ability scores are comparable to one another (i.e., as if they had received the same test, as is common in tests designed using classical test theory). The psychometric technology that allows equitable scores to be computed across different sets of items is item response theory (IRT). IRT is also the preferred methodology for selecting optimal items which are typically selected on the basis of information rather than difficulty, per se. A related methodology called multistage testing (MST) or CAST is used in the Uniform Certified Public Accountant Examination. MST avoids or reduces some of the disadvantages of CAT as described below.

are topics of research in psychometrics. The SAT is a norm-referenced test intended to yield scores that follow a bell curve distribution among test-takers The SAT ( , ess-ay-TEE) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times. For much of its history, it was called the Scholastic Aptitude Test and had two components, Verbal and Mathematical, each of which was scored on a range from 200 to 800. Later it was called the Scholastic Assessment Test, The mathematics portion of the SAT is divided into two modules, each 35 minutes long with 22 questions. The topics covered are algebra (13 to 15 questions), advanced high school math (13 to 15 questions), problem solving and data analysis (5 to 7 questions), and geometry and trigonometry (5 to 7 questions). Roughly 75% of the math questions are 4-option multiple-choice; the remaining 25% are student-produced response (SPR) questions and require the student to type in a numerical response. The SPR questions may have more than one correct answer. Calculators are permitted on all questions in the math portion of the SAT. A Desmos-based calculator is available and built into the testing software; in addition, students may use an approved type of physical calculator. A study of calculator use on SAT I: Reasoning Test math scores found that performance on the… Afte…

ruction purposes is discussed. Keywords: Item Response Theory, Mplus, latent variable modeling, CES-D, Health and Retirement Study 概述 项目反应理论（Item response theory, IRT）是用来评估精神病学领域那些尚未被充分使用的测量量表效度一种重要方法。 IRT描述了潜在心理特征（例如，该量表拟评估心理问题的架构）、量表中各项目的属性、以及被测试者对各项目应答之间的关系。本文介绍了IRT的基本前提，假设和方法。为了帮助解释这些概念，我们依据流行病学调查中心抑郁量表修订版中三个答案为是/否二分类选项的问题制定了一个假设的量表。流行病学调查中心抑郁量表已经用于19,399被测试者。我们首先用因子分析确认这三个项目的单维性，然后用Mplus软件建立2-Parameter Logic (2-PL) IRT模型，这是一种用来评估量表中各项目两两差异和项目难度的方法。本文将就这些分析结果的临床意义和在量表结构中的用途展开讨论。 1. Introduction to item response theory Item response theory (IRT) first gained attention in the 1970s when it was used in the development of standardized tests, such as the Scholastic Aptitude Tests (SATs). [1] IRT subsequently became the most important psychometric method of validating scales because it provides a method for resolving many of the measurement challenges that need to be addressed when constructing a test or scale. [2] IRT is a model-based method of estimating parameters for each item included in a scale that separates the person’s responses to the items from the person’s underlying level (or ability) of the latent construct that is being measured by the scale. [3] In contrast, Classical Test Theory (CTT) has had a longer tradition in the education field and is test- and sample-dependent. [3] In CTT, the raw score, which is the summation of responses of a person to a test or scale, represents the person’s average score if they had taken the test an infinite number of times (which is impossible and, therefore, a hypothetical measure of ability) and the random error of the summated score from the test items. Tests developed under CTT need to be interpreted in the context of the person’s characteristics and test characteristics. Therefore, CTT-developed tests are usually used to test persons with the same sample characteristics as those of the persons who were used during the development of the test. Under CTT, the person’s ability will appear low if the test questions are d