This study investigates the impact of response time on ability estimation within an Item Response Theory (IRT) framework, introducing time-sensitive formulations to enhance student assessment accuracy. Seven models were evaluated, including standard 1PL-IRT and six response-time-adjusted variants: TP-IRT, STP-IRT, TWD-IRT, NRT-IRT, DTA-IRT, and ART-IRT. Three optimization techniques—Maximum Likelihood Estimation (MLE), full parameter optimization, and K-fold Cross-Validation (CV)—were employed to assess model performance. Empirical validation was conducted using data from 150 students solving 30 mathematics items on the “TestYourself” platform, integrating response accuracy and timing metrics. Student abilities (θ), item difficulties (b), and time–effect parameters (λ) were estimated using the L-BFGS-B algorithm to ensure numerical stability. The results indicate that subtractive models, particularly DTA-IRT, achieved the lowest AIC/BIC values, highest AUC, and improved parameter stability, confirming their effectiveness in penalizing excessive response times without disproportionately affecting moderate-speed students. In contrast, multiplicative models (TWD-IRT, ART-IRT) exhibited higher variability, weaker generalizability, and increased instability, raising concerns about their applicability in adaptive testing. K-fold CV further validated the robustness of subtractive models, emphasizing their suitability for real-world assessments. These findings highlight the importance of incorporating response time as an additive factor to improve ability estimation while maintaining fairness and interpretability. Future research should explore multidimensional IRT extensions, behavioral response–time analysis, and adaptive testing environments that dynamically adjust item difficulty based on response behavior.

Background/Objectives: Pes planus and pes cavus are common foot deformities, which may lead to pain, functional limitations, and impairment of foot biomechanics. While calcaneal pitch, talar declination, and Meary angles, commonly used in diagnosis, provide objective information, their lack of a gold standard and the observer’s dependence on manual measurements limit their reliability. Therefore, in this study, these angles obtained from weight-bearing lateral foot radiographs were evaluated according to literature references, and the aim was to determine the model that provides the most accurate prediction in the diagnosis of pes planus using machine learning algorithms. It should be emphasized that, because the diagnostic labels were derived from literature-based thresholds of these same angles, the machine-learning task addressed here is the automated reproduction and standardization of expert, angle-threshold-based classification, rather than an independent clinical diagnosis from raw images. Methods: This retrospective study was conducted using weight-bearing lateral foot radiographs of 697 male patients obtained from the archives of public hospitals in Gaziantep. Calcaneal pitch, Meary angle, and talar declination angles were evaluated in both feet, and the data were labeled as normal, pes planus, and pes cavus. The dataset, consisting of a total of 1394 feet, was divided into training and test groups and analyzed using Random Forest, XGBoost, Logistic Regression, Support Vector Machine (SVM), and K-Nearest Neighbors (KNN) algorithms; the diagnostic performance of the models was compared using measures such as accuracy, F1 score, sensitivity, and specificity. Results: A total of 1394 feet from 697 male patients (mean age 24.8 ± 5.57 years) were analyzed using five machine learning algorithms with calcaneal pitch angle (CPA), Meary angle (MA), and talar declination angle (TDA) as reference labels. Ensemble-based methods showed superior performance, with XGBoost achieving perfect classification (Accuracy = 1.000) under all three labels for the left foot and 0.996–1.000 for the right foot, while Random Forest reached 0.986–1.000 across all experiments. Logistic Regression and SVM yielded moderate accuracies (0.905–0.973), whereas KNN consistently performed the weakest (0.905–0.964), particularly in the pes cavus subgroup. The near-perfect accuracy obtained when the labeling angle was itself included among the predictors reflects, at least in part, the algebraic reconstruction of the threshold rule from a same-source variable rather than genuine diagnostic generalization; results should therefore be interpreted with this in mind. Conclusions: This study demonstrates that machine learning, particularly ensemble methods such as XGBoost and Random Forest, provides high accuracy and consistency in diagnosing foot arch deformities based on radiographic angle measurements. Traditional models, such as Logistic Regression, still hold value in terms of clinical interpretability despite their lower performance. The findings suggest that machine learning-based approaches can offer objective, rapid, and reliable decision support tools for diagnosing pes planus and pes cavus, but external validation studies are necessary for clinical generalizability.