## 2 Background
### Limitations of the NT and CUMP Methods  
The NT and CUMP methods share several commonalities in the identification of rapid guessing. First, both methods rely on RT as a means for detecting rapidly guessed responses. Second, both methods can be easily implemented with large-scale assessments where the RT information is available for the items. Third, unlike the other methods (e.g., visual inspection) that lack a definitive range for the RT threshold, both the NT and CUMP methods enable researchers to set the maximum RT threshold when identifying rapid guessing. The maximum RT threshold is the user-defined percentage value for the NT method and the percentage that differentiates the chance and non-chance response for the CUMP method [4; 5; 9]. Instead of diverging from each other, these two methods are complementary in their work, because CUMP does not work well with extremely easy or difficult items [9]. For such items, the NT method, rather than the CUMP method, can be used to identify the RT thresholds [4]. The NT and CUMP methods also have some limitations that could hamper their effectiveness in detecting rapid guessing. In the NT method, the RT threshold is often determined without empirical evidence (e.g., other quantitative metrics such as response accuracy or item-total correlation) or validation, as this method relies on the researcher's subjective judgment to determine the optimal threshold [4; 10; 11]. The NT method also applies the same percentage (e.g., 15% of the average RT value) to all items in the test. However, since the items often differ in their content and psychometric characteristics (e.g., difficulty and discrimination), they may require different RT thresholds to detect rapid guessing [30; 31; 32]. For example, using more time with high-difficulty items may raise the chance for students to find the correct answer (i.e., taking time to think), while using more time with low-difficulty items may lower the chance to answer the items correctly (e.g., overthinking the answer or being inattentive) [33]. As explained earlier, the CUMP method is not suitable for items that are too easy or too hard, because it assumes a large discrepancy between the response accuracy values of students with solution behavior and those who rapidly guess the answer. However, this discrepancy might be small in the items with extremely high or low difficulty levels [7]. That is, if the item is very easy (or very hard), the cumulative proportion-correct, regardless of the selected RT threshold, may never get closer to the anticipated chance rate for students who exhibit rapid guessing behavior [7]. Moreover, the same assumption underlying the CUMP method may not hold in other cases where the cumulative proportion-correct for rapid guesses is below the chance rate due to various cognitive biases. For example, students who exhibit rapid guessing behavior may choose a particular response option (e.g., option C) consistently [7] or select a response option based on the quality and positions of distractors(i.e., incorrect response options) [34; 35; 36]. In this case, the accuracy of rapidly guessed responses may be above the chance level, especially if the rapid guessing mechanism is aligned with the answer key (e.g., the middle response options of B or C are the key for most items) [37]. To address the limitations of the NT and CUMP methods, we propose to employ a data-driven method to identify the optimal RT thresholds for detecting rapid guessing. Specifically, we use two optimization algorithms (random search and genetic algorithm) to search for the optimal RT threshold iteratively within a range of possible RT thresholds. Instead of following a one-size-fits-all approach (e.g., applying the same percentage to all items in the NT method), this method aims to detect the optimal RT threshold for each item by taking the peculiarities of an assessment into account.