## 3 Methods
### Setting RT Thresholds with Genetic Algorithm  
In addition to the random search method, we also used a genetic algorithm to look for the optimal RT threshold for detecting rapid guessing. The genetic algorithm [47] is a metaheuristic optimization approach inspired by the theory of natural selection. According to natural selection, species and individuals who can adapt better to their environment have a greater chance of survival and reproduction potential, and thus, are more likely to pass their genes to future offspring. Similarly, the genetic algorithm iteratively selects the fittest solutions from a set of potential candidates to reproduce the next generation, resulting in solutions that \"evolve\" to become better. Given the adaptability, scalability, and simplicity of the genetic algorithm's implementation, it has been used to solve various optimization problems in the disciplines of the physical and social sciences [48; 49].  
In a traditional genetic algorithm [50], each candidate solution is represented by a vector with a finite length analogous to the concept of a chromosome. All the candidate solutions (i.e., all chromosomes) collectively constitute the population. Just like a chromosome consists of a set of genes, the vector of each candidate solution is composed of a set of parameters (variables) that are encoded as a string of characters, integers, floats, or bits. Additionally, a fitness score is assigned to each chromosome (candidate solution) to assess their ability to compete. In order to find the optimal solution, the genetic algorithm employs an iterative reproduction process comprised of three key elements: selection, crossover, and mutation [51]. The term \"selection\" refers to the process of prioritizing candidate solutions with high fitness scores and allowing them to pass on their genes to future generations of solutions. Thus, future generations tend to have better performance than their predecessors. Crossover is the random selection of parameters from paired \"parents\" solutions to generate \"child\" solutions. Lastly, mutation aims to keep the diversity of genes and prevent early convergence by inserting random genes into offspring genes. Since the overall goal of the genetic algorithm is to maximize the fitness score of the population, the reproduction process repeats until when the fitness score converges or when the algorithm reaches the maximum number of iterations.  
In this study, we use the genetic algorithm in the same way as we utilize the random search method. The algorithm starts with the estimation of the baseline model based on all item responses. Next, we define a search space that includes a population of candidate RT thresholds (i.e., 10% and 30% of the average RT value for each). We set the size of the population as 100 values randomly drawn within the range of 10% and 30% of the average RT value for each item. Using the candidate RT thresholds, we employ the genetic algorithm through an iterative reproduction process. We used the default options in the GA package [38] to determine the selection, crossover, and mutation settings. For each selected RT threshold, we compute the fitness score (i.e., adjusted deviance difference) and compare it with the fitness score of successive generations. Using this information, the algorithm runs a series of iterative reproduction phases, during which it selects the best RT thresholds, mates them, reproduces offspring RT thresholds, and inserts random genes into the offspring genes. The iteration is terminated when the maximum number of iterations is reached, which we set to 10 in this study. In the end, the algorithm reports the RT threshold at which the fitness score converges. Figure 1 illustrates how the random search and genetic algorithms can be used for finding the optimal RT threshold.