## 1 Introduction  
The primary goal of educational assessments is to produce valid scores that indicate what students know and can do. When participating in an educational assessment, each student (or test taker) is expected to show effortful test-taking behavior by reading each item carefully and making a genuine attempt to find the correct answer. In practice, however, some students (referred to as \"disengaged test-takers\") may not be motivated enough to provide maximal effort, especially on low-stakes assessments with minimal consequences for students, such as international large-scale assessments, national or statewide assessments, and progress monitoring and screening measures used in K-12 classrooms [1, 2, 3]. For students exhibiting non-effortful test-taking behavior, the resulting assessment scores become less valid, as they are likely to underestimate the students' true proficiency levels. To alleviate the negative impact of non-effortful test-taking on assessment results (e.g., scores estimated from the assessment), responses associated with non-effortful test-taking behaviors can be removed from response data using a post hoc approach (i.e., after the test administration rather than real-time surveillance). To date, researchers have proposed various methods to detect item responses where disengaged students fail to show effortful test-taking behavior (e.g., [4, 5]). These methods often rely on the use of response times (RTs)--the total duration elapsed between when the student views a particular item (or task) and when she or he either moves to the next item after answering the current item or reaches the end of the assessment. Researchers use RTs extracted from digital or computer-basedassessments to identify students who demonstrate rapid guessing behavior by spending a very short amount of time on the items. The presence of rapid guessing leads to a variety of psychometric issues, such as contaminating item response data prior to estimating item parameters and test scores, negatively impacting the validity of test scores and hampering the test development process [6]. To date, several methods have been proposed to find an RT threshold that distinguishes students who rapidly guess their answers from those who put sufficient effort into answering the items. Some of these methods include the normative threshold (NT) method [5], the cumulative proportion (CUMP) method [4], the information-based RT flagging method [7], and the mixture log-normal (MLN) method [8]. As [PERSON] et al. [9] discussed in their recent study, each of these threshold-setting methods has some limitations that impact their accuracy in detecting rapid guessing behavior. For example, the MLN method relies on a highly restrictive assumption that the RT distribution of an item must be bimodal, where the lower mode represents rapid guessing and the upper mode indicates effortful responding. The CUMP method also depends on another restrictive assumption that the proportion-correct value for students flagged for rapid guessing must be equal to the chance rate for each item (e.g., for an item with four response options, the chance rate is \(1/4=25\%\)). Unlike the MLN and CUMP methods, the NT method provides a simplified solution by identifying a user-defined RT threshold (e.g., 10% of the average RT value), which may not be empirically supported in practice [10]. In the recent literature, [PERSON] et al. [9] and [PERSON] et al. [11] provided a comparison of various threshold-setting methods using real data from adaptive and non-adaptive large-scale assessments. Both studies reported that the current methods tend to yield RT thresholds that identify very different rates of rapid guessing behavior in the response data. In this study, we propose a data-driven approach based on the NT and CUMP methods that iteratively searches for the optimal RT threshold in identifying rapidly guessed responses.