Confirming Testlet Effects

Testlet design has been widely adopted in educational and psychological assessment. A testlet is a cluster of items that share a common stimulus(e.g., a reading comprehension passage or a figure), and the possible local dependence among items within a testlet is called testlet-effect. Various models have been developed to take into account such testlet effect. Examples included the Rasch testlet model, two-parameter logistic Bayesian testlet model, and higher-order testlet model. However, these existing models all assume that an item is affected by only one single testlet effect. Therefore, they are essentially unidimensional testlet-effect models. In practice, multiple testlet effects may simultaneously affect item responses in a testlet. For example, in addition to common stimulus, items can be grouped according to their domains, knowledge units, or item format, such that multiple testlet effects are involved. In essence, an item measures multiple latent traits, in addition to the target latent trait(s) that the test was designed to measure. Existing unidimensional testlet-effect models become inapplicable when multiple testlet effects are involved. To account for multiple testlet effect, in this study we develop the so-called(within-item) multidimensional testlet-effect Rasch model. The parameters can be estimated with marginal maximum likelihood estimation methods or Bayesian methods with Markov chain Monte Carlo(MCMC) algorithms. In this study, a popular computer program for Rasch models, ConQuest, was used. A series of simulations were conducted to evaluate parameter recovery of the new model, consequences of model misspecification, and the effectiveness of model-data fit statistics. Results show that the parameters of the new model can be recovered fairly well; and ignoring the multiple testlet effects resulted in a biased estimation of item parameters, and an overestimation of test reliability. Additionally, it did little harm on parameter estimation to fit a more complicated model(i.e., the multidimensional testlet-effect Rasch model) to data with a simple structure. In conclusion, the new model is feasible and flexible.

Reliability and differential item functioning (DIF) analyses were conducted on testlets displaying local item dependence in this study. The data set employed in the research was obtained from the answers given by 1500 students to the 20 items included in six testlets given in English Proficiency Exam by the School of Foreign Languages of a state University in Turkey. One of the purposes of this study was to determine the influences of the tests composed of testlets on reliability, so the reliability coefficients obtained for cases where the influences of testlets were considered and those for cases where the testlet influences were not considered were compared. In consequence of the G theory analyses conducted in this context, it was found that the G and Phi coefficients estimated by not considering the testlet effects were higher than those estimated by considering the testlet effects. It was concluded that the reliability was estimated to be relatively higher when the influences of the testlet were not considered. Two methods were used in this study so as to determine the effects of testlets on differential item functioning and the results were compared. In the DIF-determining method considering the testlet effect, both the number of items displaying DIF at the significant and estimated levels of DIF were found to be higher than in the method not considering the testlet effect.

The development of tools for automated analysis of data collected for mine countermeasures (MCM) search, classify and map (SCM) has predominantly focused on automated target recognition for individual mines. As MCM target detection becomes more automated, detecting spatial patterns in the positioning of mines should follow. Natural restrictions on mine deployment such as depth and bottom contour as well as mine deployment methodology and protocol effectively create mine line patterns that are typical to coastal areas. We have developed a mine line detection algorithm that uses nonparametric spatial analysis to identify mine-like contacts (MLCs) that fit into mine line patterns dictated by standard mine laying protocol in coastal regions. In general, a set of MLCs reported from a mine detection sensor will consist of both actual mines and false alarms; the algorithm classifies every MLC in this set into one of three classes: fixed — the MLCψfits into a mine line pattern with fixed mine spacing; random -the MLCψfits into a mine line pattern with random mine spacing; or false alarm-ψ-the MLCψdoes not fit into a mine line pattern and is subsequently not considered a mine. The latest version of the algorithm utilizes nonparametric techniques and requires no knowledge of either the detection sensor's probability of detection (P d ) or probability of false alarm (P fa ). A nonparametric anomaly detector first identifies regions with unusually high MLC density for more detailed analysis. Suspected regions are subsequently analyzed for unusually regular patterns of MLCs. The probabilities that the observed target densities and target patterns could occur simply by chance are estimated by comparison with results from nearby areas using basic information about mine deployment. To ensure that a mine line's full extent is captured, the algorithm attempts to grow a line after it is detected. And a more detailed probability analysis distinguishes random mine lines from fixed-spaced mine lines. Extensive Matlab simulations characterize the algorithm's performance across a wide range of operating environments and simulated minefield configurations. In total, ten replications each of 1,367 different configurations have been evaluated. These configurations include three different water depths (10 ft., 6 ft. and 200 ft.), six false notional alarm rates (1, 2,5,10,15 and 20 false alarms per sq. NM), three false alarm distributions (uniform, sloped, and striped), three sensor probabilities of detections (0.4, 0.6 and 0.9), three target confidence scores (0.6,0.8 and 1.0) and four false alarm confidence scores (0.5, 0.6, 0.8 and 1.0). The range of simulation parameters was selected in part as an attempt to push the algorithm past its acceptable performance limits. However, the algorithm performed remarkably well even under the worst conditions. For MLC sets with false alarm rates as high as 20 per square nautical mile, the algorithm correctly classifies over 98% of the MLCs as mines and detects 97% of the mine lines. Furthermore, it reduces the false alarm rate from 20 to 0.2 per square nautical mile with a false mine line rate of 0.14 false lines per square nautical mile. The algorithm achieves even lower false alarm rates when the initial false alarm rate is less than 20. The automated mine line detection discovers many obscure lines that are virtually undetectable to the naked eye.

Purpose: This study examines the test equating performance under various item response theory models and sample size conditions in testlet based tests. Design/Methodology/Approach: Utilizing data from the eTIMSS 2019 science test, the study compares scale transformation methods and test equating results under Unidimensional Item Response Theory (UIRT), Testlet Response Theory (TRT) and bifactor models with varying sample sizes. Scale transformation methods, including the mean-sigma and Stocking-Lord methods, as well as observed and true score equating methods, were employed within the framework of a common-item nonequivalent groups design. To evaluate the equating performance, RMSE and BIAS values were calculated. Findings: The findings indicate that in a science test with low testlet effects, scale transformation results based on the UIRT model and test equating results based on the bifactor model demonstrated lower error rates. Moreover, as sample size increased, the error in parameter estimations generally decreased, with the TRT model specifically requiring a sample size of at least 500 for robust estimations. Highlights: The bifactor model, taking testlet effects into account, yielded more precise and consistent results, facilitating fair and reliable score equating. This study, utilizing real data, concretely illustrates the practical implications of testlet effects in tests containing testlets.

Development of an algorithm to discriminate between valid and false alarms in a loose-parts monitoring system

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates. Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation. Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation. Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.

A convergence analysis of the angular position and velocity tracking errors and parametric estimation errors for a 2-link robot dynamics in the absence of noise exist in the literature (Slotine and Li in Applied nonlinear control. Prentice- Hall Inc, Englewood Cliffs, NJ, 1991). In this paper, we consider the effect of noise on the robot dynamics as well as on the parameter update equation. Noise in the robot dynamics arises due to errors in reading \(q,\dot{q}\), i.e., the angular positions and velocities of the robot link that are used for calculating the errors e, \(\dot{e}\) used to generate the feedback torque via the PD controller. Noise is chosen as Gaussian because it is produced as the cumulative effect of several small independent random effects like electrons moving in the motor wire and dust friction, and we know from the central limit theorem that the sum of a large number of small independent effects has a Gaussian distribution. Noise in the parametric update equation arises due to finite register effects in the digital computer. Both of these noises are modeled as white Gaussian, and the robot and parametric update dynamics have thus been modeled as nonlinear coupled stochastic differential equations. Using linearization of this coupled SDE system around the non-random components of the trajectory estimation error and parametric estimation errors, we first derive stochastic integral expressions for the random components in these errors. We then evaluate the average rate of change of the Lyapunov energy function using Ito calculus and obtain conditions on the noise amplitude so that the limiting value of this average rate of change is negative, guaranteeing asymptotic average stability of the system and parametric estimation algorithm. One of the novelties of this work is the new algorithm for parameter estimation which enables us to improve on the algorithm convergence rate as compared to previous work (Slotine and Li 1991). Finally, our stochastic algorithm is verified by performing hardware experiments with the actual PHANToM Omni robot.

This study demonstrated the equivalence between the Rasch testlet model and the three‐level one‐parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE) with the expectation‐maximization algorithm in ConQuest and the sixth‐order Laplace approximation estimation in HLM6. The results indicated that the estimation methods had significant effects on the bias of the testlet variance and ability variance estimation, the random error in the ability parameter estimation, and the bias in the item difficulty parameter estimation. The Laplace method best recovered the testlet variance while the MMLE best recovered the ability variance. The Laplace method resulted in the smallest random error in the ability parameter estimation while the MCMC method produced the smallest bias in item parameter estimates. Analyses of three real tests generally supported the findings from the simulation and indicated that the estimates for item difficulty and ability parameters were highly correlated across estimation methods.

The prediction of human motion is essential for safe human-robot collaboration (HRC). For existing prediction methods based on adaptive neural network (NN) models, estimation errors (EEs) of model parameters are directly coupled with prior EEs of trajectories. This results in poor assessment of the mean square estimation error (MSEE) of model parameters, which is a potential danger to the safety HRC. In this paper, a novel “look-backward-and-forward” method is proposed to assess the EEs of model parameters. This method firstly computes EEs of model parameters in the past few time instants based on the actual error of trajectory predicted in the past. Subsequently, the EEs of model parameters are recursively updated till the current time instant. In this way, the trajectory of a single particle and its MSEE are accurately accessed. The direct coupling between the MSEE of the trajectory and that of model parameters is cut off and the mean estimation errors (MEEs) of parameters are only affected by the EEs of the past trajectory at the recent several time instants, rather than accumulating as the time propagates. This method is further extended to estimate the pose trajectory of a rigid body based on fitting of an ellipsoid’s parameters. The experimental results of predicting 3-D trajectories of human motions show the effectiveness of the proposed method.

Eigenvector spatial filtering (ESF) is becoming a popular way to address spatial dependence. Recently, a random effects specification of ESF (RE-ESF) is receiving considerable attention because of its usefulness for spatial dependence analysis considering spatial confounding. The objective of this study was to analyze theoretical properties of RE-ESF and extend it to overcome some of its disadvantages. We first compare the properties of RE-ESF and ESF with geostatistical and spatial econometric models. There, we suggest two major disadvantages of RE-ESF: it is specific to its selected spatial connectivity structure, and while the current form of RE-ESF eliminates the spatial dependence component confounding with explanatory variables to stabilize the parameter estimation, the elimination can yield biased estimates. RE-ESF is extended to cope with these two problems. A computationally efficient residual maximum likelihood estimation is developed for the extended model. Effectiveness of the extended RE-ESF is examined by a comparative Monte Carlo simulation. The main findings of this simulation are as follows: Our extension successfully reduces errors in parameter estimates; in many cases, parameter estimates of our RE-ESF are more accurate than other ESF models; the elimination of the spatial component confounding with explanatory variables results in biased parameter estimates; efficiency of an accuracy maximization-based conventional ESF is comparable to RE-ESF in many cases.

In this article, an adaptive dynamic surface control approach is proposed for uncertain strict‐feedback systems (SFSs) to guarantee both the prescribed transient tracking performance and the asymptotic tracking while realizing the accurate parameter estimation. It is assumed that SFSs are subject to linearly parametric uncertainties in both the drift terms and the control coefficients. A new inequality on the arctangent function, which can be widely used in the robust or the adaptive control designs, is established. Owing to this inequality, nonlinear robust filters with arctangent functions are designed and embedded into the backstepping control algorithm to avoid the “differential explosion” problem. Moreover, an improved forgetting‐factor‐based parameter estimation error reconstruction mechanism is proposed. And the obtained parameter estimation errors are integrated into the adaptive laws to achieve the accurate parameter estimation. Furthermore, the projection operator is applied to avoid the singularity problem of the control law. Besides, an asymmetric error transformation is introduced to restrict the tracking error within the prescribed performance envelope. It is proved that the tracking error and the parameter estimation errors asymptotically converge to zero and the tracking error satisfies the prescribed transient performance. Finally, the effectiveness of the proposed control approach is validated in terms of the single‐link manipulator actuated by a brush DC motor.

This paper presents a global damage detection and assessment algorithm based on a parameter estimation method using a finite-element model and the measured modal response of a structure. Damage is characterized as a reduction of the member constitutive parameter from a known baseline value. An optimization scheme is proposed to localize damaged parts of the structure. The algorithm accounts for the possibility of multiple solutions to the parameter estimation problem that arises from using spatially sparse measurements. Errors in parameter estimates caused by sensitivity to measurement noise are reduced by selecting a near-optimal measurement set from the data at each stage of the localization algorithm. Damage probability functions are computed upon completion of the localization process for candidate elements. Monte Carlo methods are used to compute the required probabilities based on the statistical distributions of the parameters for the damaged and the associated baseline structure. The algorithm is tested in a numerical simulation environment using a planar bridge truss as a model problem.

Bayesian and non-Bayesian moment-based inference methods are commonly used to estimate the parameters defining stochastic models of gene regulatory networks from noisy single cell or population snapshot data. However, a systematic investigation of the accuracy of the predictions of these methods remains missing. Here, we present the results of such a study using synthetic noisy data of a negative auto-regulatory transcriptional feedback loop, one of the most common building blocks of complex gene regulatory networks. We study the error in parameter estimation as a function of (i) number of cells in each sample; (ii) the number of time points; (iii) the highest-order moment of protein fluctuations used for inference; (iv) the moment-closure method used for likelihood approximation. We find that for sample sizes typical of flow cytometry experiments, parameter estimation by maximizing the likelihood is as accurate as using Bayesian methods but with a much reduced computational time. We also show that the choice of moment-closure method is the crucial factor determining the maximum achievable accuracy of moment-based inference methods. Common likelihood approximation methods based on the linear noise approximation or the zero cumulants closure perform poorly for feedback loops with large protein–DNA binding rates or large protein bursts; this is exacerbated for highly heterogeneous cell populations. By contrast, approximating the likelihood using the linear-mapping approximation or conditional derivative matching leads to highly accurate parameter estimates for a wide range of conditions.

A process-based erosion model is used to study parameterization problems of sediment entrainment equations in overland flow areas. One of the equations for entrainment by flow is developed based on a theory of excess stream power, while the other two relate to excess hydraulic shear. The investigation is conducted in two steps. The first step examines parameter optimization for simulated data sets where the parameter values are known. In the second step, parameter optimization for the most robust equation is examined using experimental data from rainfall simulator plots. Results demonstrate that although the model is capable of estimating total sediment yields with relatively small errors in parameter estimates, the converse is true when the optimization is performed for sediment concentrations. Although sediment yields calculated from simulated sediment concentrations match well with observed data, the parameter estimates generally underestimate sediment concentrations on the rising limb of the sediment graphs, and they overestimate them on the falling limb. This difficulty might be related to structural problems in the model, and unique solutions for parameter estimates cannot be obtained.

Adaptive model predictive control for a class of constrained linear systems based on the comparison model