# Enhancing Ability Estimation with Time-Sensitive IRT Models in Computerized Adaptive Testing
## 4 Model Performance and Results Analysis
### Findings of the Highest Performing Approach  
The third approach stands out as the most stable and highest-performing method based on the data in the table. This approach enhances generalization and minimizes overfitting risks through five-fold cross-validation and regularization techniques. The 1 PL-IRT and DTA-IRT models achieve the highest classification performance, with AUC values of 0.803 and 0.804, respectively. Additionally, the AIC and BIC values in this approach are the lowest compared to others, indicating better model fit and reduced complexity. In conclusion, the third approach is the most effective method in terms of both stability and predictive power. In Figure 4, the bar chart compares the Area Under the Curve (AUC) scores for different IRT-based models, including the baseline 1 PL-IRT model and six response-time-adjusted  
Figure 3: Comparison of AUC values across models. variants. The AUC represents the classification performance of each model, where higher values indicate better discrimination between correct and incorrect responses. The DTA-IRT and TP-IRT models achieve the highest AUC scores, suggesting that subtractive time-based adjustments lead to better ability estimation. The 1 PL-IRT model also performs well, indicating its robustness despite the lack of response-time integration. In contrast, multiplicative models such as TWD-IRT and ART-IRT display significantly lower AUC values, highlighting their instability in adjusting difficulty based on response time. These findings confirm that subtracting response time as a penalty is a more reliable approach than multiplicative scaling. The Figure 5 line chart presents AIC and BIC values for each model. Lower AIC and BIC values indicate better model fit while avoiding unnecessary complexity. The DTA-IRT and TP-IRT models exhibit the lowest AIC and BIC scores, reinforcing their efficiency in modeling response-time effects without adding unnecessary complexity. The 1 PL-IRT model has slightly higher AIC/BIC values, likely due to its lack of response-time adjustments. On the other hand, multiplicative models (TWD-IRT, ART-IRT) show significantly higher AIC/BIC values, indicating greater complexity without corresponding improvements in performance. These results align with existing research, which cautions that multiplicative transformations in IRT models can lead to parameter instability. Figure 6 presents the relationship between AUC (Area Under Curve) scores and correlation values for different models. AUC represents the classification performance of a model, while correlation measures the consistency between predicted and actual ability estimates. DTA-IRT, 1 PL-IRT, and TP-IRT models exhibit the highest correlation values (~1.0) while maintaining high AUC scores (~0.80), indicating strong predictive accuracy and stability. STP-IRT achieves a moderate correlation (~0.85) but a slightly lower AUC score, suggesting it may introduce some instability in prediction performance. TWD-IRT and NRT-IRT models show significantly lower AUC scores (~0.70  
Figure 4: AUC comparison chart—model AUC performance. Figure 5: AIC/BIC comparison—model complexity analysis. correlation values, implying weaker classification power compared to higher-performing models. ART-IRT has the lowest AUC score and correlation, indicating poor classification accuracy and unreliable predictions. Overall, models with higher AUC and correlation values (DTA-IRT, 1 PL-IRT, TP-IRT) are more reliable for estimating student abilities, while models with lower values (ART-IRT, NRT-IRT) demonstrate limited predictive effectiveness. The DTA-IRT and TP-IRT models show high AUC values with minimal variance, confirming their robust performance across different data splits. The 1 PL-IRT model also demonstrates consistency, though it lacks response-time sensitivity. In contrast, multiplicative models (TWD-IRT, NRT-IRT, ART-IRT) exhibit high variance, suggesting instability and sensitivity to dataset variations.