The Effect of Test Length on the Accuracy of Estimating Ability Parameter in the Two- and Three-Parameter Logistic Models: Comparison by Using the Bayesian Method of Expected Prior Mode and Maximum Likelihood Estimation

This study aims to compare the effect of test length on the degree of ability parameter estimation in the two-parameter and three-parameter logistic models, using the Bayesian method of expected prior mode and maximum likelihood. The experimental approach is followed, using the Monte Carlo method of simulation. The study population consists of all subjects with the specified ability level. The study includes random samples of subjects and of items. Results reveal that estimation accuracy of the ability parameter in the two-parameter logistic model according to the maximum likelihood method and the Bayesian method increases with the increase in the number of test items. Results also show that with long and average length tests, the effectiveness is related to the maximum likelihood method and to all conditions of the sample size, whereas in short tests, the Bayesian method of prior mode outperformed in all conditions. Results indicate that the increase of the ability parameter in the three-parameter logistic model increases with the increase of test items number. The Bayesian method outperforms with respect to the accuracy of estimation at all conditions of the sample size, whereas in long tests the maximum likelihood method outperforms at all different conditions. Received: 17 September 2021 / Accepted: 24 November 2021 / Published: 3 January 2022

Assessing the Accuracy of Parameter Estimates in the Presence of Rapid Guessing Misclassifications

The presence of rapid guessing (RG) presents a challenge to practitioners in obtaining accurate estimates of measurement properties and examinee ability. In response to this concern, researchers have utilized response times as a proxy of RG, and have attempted to improve parameter estimation accuracy by filtering RG responses using popular scoring approaches, such as the Effort-moderated IRT (EM-IRT) model. However, such an approach assumes that RG can be correctly identified based on an indirect proxy of examinee behavior. A failure to meet this assumption leads to the inclusion of distortive and psychometrically uninformative information in parameter estimates. To address this issue, a simulation study was conducted to examine how violations to the assumption of correct RG classification influences EM-IRT item and ability parameter estimation accuracy and compares these results to parameter estimates from the three-parameter logistic (3PL) model, which includes RG responses in scoring. Two RG misclassification factors were manipulated: type (underclassification vs. overclassification) and rate (10%, 30%, and 50%). Results indicated that the EMIRT model provided improved item parameter estimation over the 3PL model regardless of misclassification type and rate. Furthermore, under most conditions, increased rates of RG underclassification were associated with the greatest bias in ability parameter estimates from the EM-IRT model. In spite of this, the EM-IRT model with RG misclassifications demonstrated more accurate ability parameter estimation than the 3PL model when the mean ability of RG subgroups did not differ. This suggests that in certain situations it may be better for practitioners to: (a) imperfectly identify RG than to ignore the presence of such invalid responses, and (b) select liberal over conservative response time thresholds to mitigate bias from underclassified RG.

Assessing the Accuracy of Parameter Estimates in the Presence of Rapid Guessing Misclassifications

The presence of rapid guessing (RG) presents a challenge to practitioners in obtaining accurate estimates of measurement properties and examinee ability. In response to this concern, researchers have utilized response times as a proxy of RG and have attempted to improve parameter estimation accuracy by filtering RG responses using popular scoring approaches, such as the effort-moderated item response theory (EM-IRT) model. However, such an approach assumes that RG can be correctly identified based on an indirect proxy of examinee behavior. A failure to meet this assumption leads to the inclusion of distortive and psychometrically uninformative information in parameter estimates. To address this issue, a simulation study was conducted to examine how violations to the assumption of correct RG classification influences EM-IRT item and ability parameter estimation accuracy and compares these results with parameter estimates from the three-parameter logistic (3PL) model, which includes RG responses in scoring. Two RG misclassification factors were manipulated: type (underclassification vs. overclassification) and rate (10%, 30%, and 50%). Results indicated that the EM-IRT model provided improved item parameter estimation over the 3PL model regardless of misclassification type and rate. Furthermore, under most conditions, increased rates of RG underclassification were associated with the greatest bias in ability parameter estimates from the EM-IRT model. In spite of this, the EM-IRT model with RG misclassifications demonstrated more accurate ability parameter estimation than the 3PL model when the mean ability of RG subgroups did not differ. This suggests that in certain situations it may be better for practitioners to (a) imperfectly identify RG than to ignore the presence of such invalid responses and (b) select liberal over conservative response time thresholds to mitigate bias from underclassified RG.

The Influence of 3d and 4d Transition Metals on the Glass Forming Ability of Ternary FeCo-Based Alloys

Thermodynamic modeling was used to determine enthalpies of formation and other thermodynamic parameters describing glass forming ability of Fe-Co-TM (TM = V, Nb, Cr, Mo) alloys. FeCo-based alloys are considered as candidates for applications as high magnetic flux density materials due to their high magnetic saturation and low magnetic anisotropy. Nevertheless, mechanical properties, especially the lack of ductility, are their main weakness. Therefore, further optimization by vitrification, further heat treatment and alloying should be considered. As the most crucial step is the synthesis of amorphous precursors, discussion is concentrated on the effect of transition metal substitution on the glass forming ability. The highest glass forming ability was reported for Fe-Co-Nb alloys. It can be also noted that the driving force for vitrification can be improved by substitution of Fe by other transition elements, as glass forming ability parameter ∆PHS reaches the lowest values for Fe-less compositions.

Parameter Estimation Accuracy of the Effort-Moderated Item Response Theory Model Under Multiple Assumption Violations

As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the effort-moderated item response theory (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., two-parameter logistic [2PL]) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (Assumption 1) and is unrelated to the underlying ability of examinees (Assumption 2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of Assumption 1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating Assumption 2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating Assumption 2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared with the 2PL model.

Parameter Estimation Accuracy of the Effort-Moderated IRT Model Under Multiple Assumption Violations

As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the Effort-Moderated IRT (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., 2PL) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (assumption #1) and is unrelated to the underlying ability of examinees (assumption #2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of assumption #1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating assumption #2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating assumption #2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared to the 2PL model.

Parameter Estimation Accuracy of the Effort-Moderated IRT Model Under Multiple Assumption Violations

As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the Effort-Moderated IRT (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., 2PL) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (assumption #1) and is unrelated to the underlying ability of examinees (assumption #2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of assumption #1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating assumption #2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating assumption #2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared to the 2PL model.

Quantifying Individuals’ Theory-Based Knowledge Using Probabilistic Causal Graphs: A Bayesian Hierarchical Approach

Extracting an individual’s knowledge structure is a challenging task as it requires formalization of many concepts and their interrelationships. While there has been significant research on how to represent knowledge to support computational design tasks, there is limited understanding of the knowledge structures of human designers. This understanding is necessary for comprehension of cognitive tasks such as decision making and reasoning, and for improving educational programs. In this paper, we focus on quantifying theory-based causal knowledge, which is a specific type of knowledge held by human designers. We develop a probabilistic graph-based model for representing individuals’ concept-specific causal knowledge for a given theory. We propose a methodology based on probabilistic directed acyclic graphs (DAGs) that uses logistic likelihood function for calculating the probability of a correct response. The approach involves a set of questions for gathering responses from 205 engineering students, and a hierarchical Bayesian approach for inferring individuals’ DAGs from the observed responses. We compare the proposed model to a baseline three-parameter logistic (3PL) model from the item response theory. The results suggest that the graph-based logistic model can estimate individual students’ knowledge graphs. Comparisons with the 3PL model indicate that knowledge assessment is more accurate when quantifying knowledge at the level of causal relations than quantifying it using a scalar ability parameter. The proposed model allows identification of parts of the curriculum that a student struggles with and parts they have already mastered which is essential for remediation.