Signal detection theory (SDT; Tanner & Swets in Psychological Review 61:401–409, 1954) is a dominant modeling framework used for evaluating the accuracy of diagnostic systems that seek to distinguish signal from noise in psychology. Although the use of response time data in psychometric models has increased in recent years, the incorporation of response time data into SDT models remains a relatively underexplored approach to distinguishing signal from noise. Functional response time effects are hypothesized in SDT models, based on findings from other related psychometric models with response time data. In this study, an SDT model is extended to incorporate functional response time effects using smooth functions and to include all sources of variability in SDT model parameters across trials, participants, and items in the experimental data. The extended SDT model with smooth functions is formulated as a generalized linear mixed-effects model and implemented in the gamm4 R package. The extended model is illustrated using recognition memory data to understand how conversational language is remembered. Accuracy of parameter estimates and the importance of modeling variability in detecting the experimental condition effects and functional response time effects are shown in conditions similar to the empirical data set via a simulation study. In addition, the type 1 error rate of the test for a smooth function of response time is evaluated.

信号检测理论（SDT；Tanner & Swets in Psychology Review 61:401–409, 1954）是一种主要的建模框架，用于评估旨在区分心理学信号和噪音的诊断系统的准确性。尽管近年来心理测量模型中响应时间数据的使用有所增加，但将响应时间数据纳入 SDT 模型仍然是一种相对未充分探索的区分信号和噪声的方法。基于其他相关心理测量模型和响应时间数据的发现，在 SDT 模型中假设了功能响应时间效应。在本研究中，SDT 模型被扩展为使用平滑函数合并功能响应时间效应，并包括跨试验、参与者和实验数据项目的 SDT 模型参数的所有变异源。具有平滑函数的扩展 SDT 模型被制定为广义线性混合效应模型，并在gamm4 R包中实现。使用识别记忆数据来说明扩展模型，以了解会话语言是如何被记住的。通过模拟研究，在与经验数据集相似的条件下显示了参数估计的准确性以及建模变异性在检测实验条件效应和功能响应时间效应中的重要性。此外，还评估了响应时间平滑函数测试的 1 类错误率。