## 4 Results
For the majority of the items, their proportion-correct values of the rapid guesses were either 0 or very close to 0. Only 4 items out of 40 items (i.e., items 1, 6, 21, and 35) had proportion-correct values greater than 1 (i.e., 1%). For example, based on the genetic algorithm, approximately 18% of the students who, on average, spent 0.419 s on item 1 were able to answer this item correctly, whereas none of the students could answer the following three questions (i.e., items 2, 3, 4) correctly. As explained earlier, the assessment used in this study consisted of constructed-response items that required short answers (rather than selecting a response option in a multiple-choice item), and thus  
Figure 2: RT thresholds for each threshold-setting method as percentages of the average RT values of the items. rapid guesses were very unlikely to be correct. In line with this information, the results presented in Table 2 indicate that random search and genetic algorithm produced viable RT thresholds to identify rapid guesses. To illustrate the adjustment in item characteristics after removing rapid guesses based on random search and genetic algorithm, we identified a particular item (item 38) from the assessment and created an item characteristic curve (ICC) plot for the baseline IRT model based on the original response dataset and the adjusted IRT models based on the response datasets where rapid guesses were eliminated by the two optimization methods. In Figure 3, the \(x\)-axis demonstrates the ability (\(\theta\)), and the \(y\)-axis shows the probability of answering item 38 correctly. Compared with the baseline model (i.e., solid line), the adjusted models seem to produce lower item difficulty, increasing the probability of success. For example, a student with the ability level of \(\theta=0\) had a 75% chance of answering the item correctly in the baseline model, whereas the same student had roughly an 80% chance \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**Average Response Time (s)**} & \multicolumn{2}{c}{**Proportion-Correct**} \\ \cline{2-5}  & **Random Search** & **Genetic Algorithm** & **Random Search** & **Genetic Algorithm** \\ \hline  
& 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average RT and proportion-correct values for rapid guessers. of answering the item correctly in the adjusted models. This finding was not surprising because many incorrect answers associated with rapid guessing were removed before estimating the adjusted IRT models. Despite the visible change in item difficulty, the slopes of the ICCs from the baseline and adjusted IRT models showed that item discrimination remained unchanged, suggesting that removing rapid guesses did not affect how accurately the item could distinguish low-achieving and high-achieving students. Finally, we also compared the performances of random search and genetic algorithm with regard to computational time (in minutes) in a computer with a 3.6 GHz, i7 processor and 16 GB RAM. Our results show that random search was a less computationally demanding and remarkably faster algorithm (computation time per item: \(M=11.45\) min, \(SD=0.7\) min) than the genetic algorithm (computation time per item: \(M=86.58\) min, \(SD=4.04\) min). The minimum and maximum computation times were 10.86 min and 15.01 min (range = 4.15) for random search and 82.71 min and 109.43 min (range = 26.72) for the genetic algorithm. These results are in line with our expectations because, despite using the same search space, the genetic algorithm involves multiple rounds of drawing random values until it finds the most optimal value, whereas random search takes a single random sample of values within the search space and then looks for the best solution. Research Question 2: How Consistent Are the Responses Identified as Rapid Guessing across the Different Threshold-Setting Methods?