In norm-referenced psychological testing, an individual's performance is expressed in relation to a reference population using a standardized score, like an intelligence quotient score. The reference population can depend on a continuous variable, like age. Current continuous norming methods transform the raw score into an age-dependent standardized score. Such methods have the shortcoming to solely rely on the raw test scores, ignoring valuable information from individual item responses. Instead of modeling the raw test scores, we propose modeling the item scores with a Bayesian two-parameter logistic (2PL) item response theory model with age-dependent mean and variance of the latent trait distribution, 2PL-norm for short. Norms are then derived using the estimated latent trait score and the age-dependent distribution parameters. Simulations show that 2PL-norms are overall more accurate than those from the most popular raw score-based norming methods cNORM and generalized additive models for location, scale, and shape (GAMLSS). Furthermore, the credible intervals of 2PL-norm exhibit clearly superior coverage over the confidence intervals of the raw score-based methods. The only issue of 2PL-norm is its slightly lower performance at the tails of the norms. Among the raw score-based norming methods, GAMLSS outperforms cNORM. For empirical practice this suggests the use of 2PL-norm, if the model assumptions hold. If not, or the interest is solely in the point estimates of the extreme trait positions, GAMLSS-based norming is a better alternative. The use of the 2PL-norm is illustrated and compared with GAMLSS and cNORM using empirical data, and code is provided, so that users can readily apply 2PL-norm to their normative data. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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基于项目反应理论的连续测试规范。


在常模参考心理测试中，个人的表现使用标准化分数（如智商分数）与参考人群的关系来表示。参考总体可以取决于连续变量，如年龄。当前的连续规范方法将原始分数转换为与年龄相关的标准化分数。这种方法的缺点是完全依赖于原始测试分数，而忽略了来自单个项目响应的有价值的信息。我们建议使用贝叶斯双参数逻辑 （2PL） 项目反应理论模型对项目分数进行建模，而不是对原始测试分数进行建模，该模型具有年龄依赖性平均值和潜在特征分布的方差，简称 2PL-norm。然后使用估计的潜在特征分数和年龄依赖性分布参数得出规范。模拟表明，2PL 规范总体上比最流行的基于原始分数的规范方法 cNORM 和位置、比例和形状的广义加法模型 （GAMLSS） 的规范更准确。此外，2PL-norm 的可信区间明显优于基于原始分数的方法的置信区间。2PL-norm 的唯一问题是它在 norm 尾部的性能略低。在基于原始分数的规范方法中，GAMLSS 的性能优于 cNORM。对于实证实践，如果模型假设成立，则建议使用 2PL 规范。如果不是，或者兴趣仅在于极端特征位置的点估计，则基于 GAMLSS 的规范是更好的选择。使用经验数据说明了 2PL-norm 的使用并与 GAMLSS 和 cNORM 进行了比较，并提供了代码，以便用户可以轻松地将 2PL-norm 应用于他们的规范数据。 （PsycInfo 数据库记录 （c） 2024 APA，保留所有权利）。