# Enhancing Ability Estimation with Time-Sensitive IRT Models in Computerized Adaptive Testing
## 1 Introduction  
In modern educational assessment, the implementation of adaptive testing based on Item Response Theory (IRT) has significantly enhanced the evaluation of student abilities. Unlike traditional fixed-form examinations, adaptive tests dynamically adjust item difficulty based on a test-taker's performance, improving measurement precision and optimizing test length [1, 2]. This adaptability ensures that each examinee is presented with questions that match their proficiency level, leading to a more accurate skill assessment [3, 4]. As the foundation of this methodology, IRT theory models the probability of a correct response as a function of student ability (\(\theta\)) and item difficulty (b) [5, 6]. Among IRT models, the One-Parameter Logistic (1 PL) Rasch model is widely adopted due to itscomputational efficiency and reliability in ability estimation [6; 7]. However, conventional IRT models focus solely on the accuracy of responses (correct/incorrect) and overlook additional cognitive dimensions, such as response time, which can provide deeper insights into test-taking behaviors and cognitive load [8]. Recent research suggests that response time reflects not only the examinee's familiarity with the content but also their cognitive effort and decision-making process [9; 10]. Consequently, integrating response time into IRT-based models has the potential to refine ability estimation and enhance the interpretability of assessments [10; 11]. In response to this, researchers have explored response-time-adjusted IRT models, categorized broadly into subtractive and multiplicative approaches. Subtractive models, such as Time-Penalized-IRT (TP-IRT) and Dynamic Time-Adjusted-IRT (DTA-IRT), penalize extended response times to prevent undue disadvantages for slower respondents [12]. On the other hand, multiplicative models, including Time-Weighted Difficulty-IRT (TWD-IRT) and Adaptive Response Time-IRT (ART-IRT), dynamically adjust item difficulty based on response speed [13]. These methods aim to incorporate response-time efficiency into ability estimation, refining the overall adaptive testing experience [14]. One key motivation for this study arises from a recurring problem in computer-based testing environments: the mismatch between response accuracy and response time when estimating student ability. Traditional IRT-based models evaluate correctness but overlook the timing dimension, which can lead to over- or underestimation of student performance. For example, a high-ability student might quickly and confidently solve an item, while a lower-ability student could take significantly longer to reach the same correct answer, potentially through guessing or trial-and-error. Failing to account for this timing discrepancy can lead to biased ability estimates. The TestYourself platform--used in this study--was designed to address this by collecting both correctness and response time data. This dual data stream allows for the implementation of time-aware IRT models that aim to improve fairness and diagnostic insight. Therefore, the primary aim of this study is to compare various time-sensitive IRT models under real-world conditions to determine which models most effectively integrate response time into ability estimation. In recent years, the integration of response time into Item Response Theory (IRT) models has gained significant attention, particularly in the context of computer-based and adaptive testing. Researchers have increasingly recognized that response accuracy alone may not fully capture a test-taker's ability, as response behavior and timing can provide valuable information about cognitive effort, problem-solving strategy, and test engagement. For instance, [PERSON], [PERSON], and [PERSON] [15] proposed a response-time-based mixture IRT model capable of distinguishing dynamic item-solving strategies, showing that time-sensitive modeling can improve the precision of ability estimation.