## 4 Results
To answer the second research question of this study, we compared the results of random search and genetic algorithm with those from the NT10, NT15, NT20, and NT25 methods. The top part of Figure 4 shows the RT thresholds (in seconds) identified by the six threshold-setting methods for each item. For all items in the assessment, the identified RT thresholds were less than 2 s. However, the thresholds identified by random search and genetic algorithm were consistently higher than those identified by the NT methods across all items. In other words, these two optimization algorithms (i.e., random search and genetic algorithm) identified more liberal RT thresholds for detecting rapid guessing. Moreover, the RT thresholds produced by random search and genetic algorithm were very similar to each other. As recent research also suggested, the NT10 method seemed to be very conservative in finding RT thresholds, leading to the under-identification of rapid guesses (e.g., [9; 53]). Figure 3: Item characteristic curves for item 38 based on the item parameters obtained from the baseline and adjusted IRT models. The bottom part of Figure 4 shows the percentage of students who were flagged for rapidly guessing their responses in the low-stakes math assessment. Since the random search and genetic algorithm methods appeared to produce more liberal RT thresholds, it was not surprising that these two methods also flagged a higher percentage of students for exhibiting rapid guessing behavior across all items. The random search and genetic algorithms flagged 5% to 15% of the students across the items, whereas the NT methods (except for NT25) generally flagged less than 10% of the students. Given the high similarity between the RT thresholds identified by random search and genetic algorithm, the percentages of students flagged for rapid guessing were nearly identical across all items. We also compared the threshold-setting methods at the model level. Table 3 shows a summary of model fit indices for the baseline IRT model, the adjusted IRT models (based on random search, genetic algorithm, and NT methods), and the simulation study based on the random deletion of responses. Lower values of AIC, BIC, SABIC, and HQ and higher values of log-likelihood and reliability indicate better model-data fit. The results presented in Table 3 indicate that the random search and genetic algorithms outperformed all variants of the NT method across all model evaluation metrics. Between the two optimization algorithms, the genetic algorithm was superior to random search, although the differences in their model fit indices were mostly negligible. In addition, we found a consistent and  
Figure 4: RT thresholds (**top**) and percentage of rapid guessing cases (**bottom**) identified by each threshold-setting method. steady pattern for the NT methods. The higher RT thresholds yielded better model fit performance. Although this pattern suggests that selecting a higher RT threshold (e.g., NT30) might result in an even better model fit, using the same RT threshold across all items still remains a major limitation of the NT method. Unlike the NT method, our proposed threshold-setting method determined the optimal RT threshold for each item independently, allowing for greater flexibility for excluding noise in the response dataset (i.e., rapidly guessed responses). Table 3 also shows the average model fit indices (across 500 replications) for the IRT model, in which a number of responses for each item were removed randomly, regardless of their rapid guessing status. The model fit results suggest that removing item responses randomly, instead of using RT thresholds, produced lower relative fit indices at the expense of empirical reliability. Although the random deletion of responses yielded better values for AIC, BIC, SABIC, and HQ, it decreased empirical reliability significantly, even below the reliability of the baseline model based on the original dataset. This finding has two important implications.