One-parameter Model Research Articles

Identifiability analysis of the fixed-effects one-parameter logistic positive exponent model.

In addition to the usual slope and location parameters included in a regular two-parameter logistic model (2PL), the logistic positive exponent (LPE) model incorporates an item parameter that leads to asymmetric item characteristic curves, which have recently been shown to be useful in some contexts. Although this model has been used in some empirical studies, an identifiability analysis (i.e., checking the (un)identified status of a model and searching for identifiablity restrictions to make an unidentified model identified) has not yet been established. In this paper, we formalize the unidentified status of a large class of fixed-effects item response theory models that includes the LPE model and related versions of it. In addition, we conduct an identifiability analysis of a particular version of the LPE model that is based on the fixed-effects one-parameter logistic model (1PL), which we call the 1PL-LPE model. The main result indicates that the 1PL-LPE model is not identifiable. Ways to make the 1PL-LPE useful in practice and how different strategies for identifiability analyses may affect other versions of the model are also discussed.

Transitive inference as probabilistic preference learning.

Transitive inference (TI) is a cognitive task that assesses an organism's ability to infer novel relations between items based on previously acquired knowledge. TI is known for exhibiting various behavioral and neural signatures, such as the serial position effect (SPE), symbolic distance effect (SDE), and the brain's capacity to maintain and merge separate ranking models. We propose a novel framework that casts TI as a probabilistic preference learning task, using one-parameter Mallows models. We present a series of simulations that highlight the effectiveness of our novel approach. We show that the Mallows ranking model natively reproduces SDE and SPE. Furthermore, extending the model using Bayesian selection showcases its capacity to generate and merge ranking hypotheses as pairs with connecting symbols. Finally, we employ neural networks to replicate Mallows models, demonstrating how this framework aligns with observed prefrontal neural activity during TI. Our innovative approach sheds new light on the nature of TI, emphasizing the potential of probabilistic preference learning for unraveling its underlying neural mechanisms.

Nonparametric Bayesian optimal designs for Unit Exponential regression model with respect to prior processes(with the truncated normal as the base measure)

Nonlinear regression models are extensively applied across various scientific disciplines. It is vital to accurately fit the optimal nonlinear model while considering the biases of the Bayesian optimal design. We present a Bayesian optimal design by utilising the Dirichlet process as a prior. The Dirichlet process serves as a fundamental tool in the exploration of Nonparametric Bayesian inference, offering multiple representations that are well-suited for application. This research paper introduces a novel one-parameter model, referred to as the ’Unit-Exponential distribution’, specifically designed for the unit interval. Additionally, we employ a stick-breaking representation to approximate the D-optimality criterion considering the Dirichlet process as a functional tool. Through this approach, we aim to identify a Nonparametric Bayesian optimal design.

Characterizing nonlinear constitutive behaviors of fiber metal laminates

Abstract This study characterized the nonlinear tensile behavior of fiber metal laminates (FMLs). FMLs comprise layers of thin metallic sheets and fiber-reinforced composite layers, and a constitutive FML model includes the constitutive relationships of the FML’s constituent materials; however, nonlinear behavior is typically only considered for the metal components of an FML. In this study, a nonlinear constitutive relationship for the unidirectional fiber composites was modeled using a one-parameter plastic model. The nonlinear constitutive law for the metal was formulated using the J2 flow rule. These relationships were summed for each layer in accordance with laminated plate theory to obtain a constitutive FML model, which was then used for numerical predictions of nonlinear stress–strain curves. The model was validated by comparing its predictions with experimental results from the literature. Moreover, the effect of the inclusion of nonlinear fiber composite behavior on the model predictions was investigated. Results revealed that the difference between the model predictions and the experimental results was less than 4%. These predictions with nonlinear fiber composite behavior were substantially more accurate than those of the model without this behavior for FMLs with angle-ply fiber composites.

New one-parameter models of dynamical particles in spatially flat FLRW space-times

New one-parameter models of non-rotating dynamical particles are derived as isotropic solutions of Einstein’s equations with perfect fluid in space-times with FLRW asymptotic behaviour, thus generalizing the models recently proposed by Cotăescu (Eur. Phys. J. C 82:86, 2022). These particles are produced by central singularities of the fluid density but without changing the pressure of the asymptotic FLRW space-times. The principal features of these models are investigated using a brief graphical analysis to elucidate the role of the new free parameter. The conclusion is that this gives rise to families of models which behave as non-rotating black holes in the physical space domain bordered by the black hole and cosmological horizons.

Emergence in string theory and Fermi gases

The Emergence Proposal suggests that some Swampland criteria, in particular on large field distances, are a consequence of the emergent nature of dynamics for fields in the infrared. In the context of type II string theory compactified on Calabi-Yau manifolds, it proposes that the cubic tree-level piece of the genus-zero prepotential is emergent from integrating out massive non-perturbative states. For a certain special non-compact Calabi-Yau, the blown-up conifold, it is known that the full all-genus prepotential can be matched onto the Grand Canonical potential of a two-dimensional Fermi gas. We propose here that this should be understood in the context of emergence: the prepotential is induced by integrating out the Fermi gas degrees of freedom. To make contact with the Swampland we need dynamical gravity, so compact Calabi-Yau manifolds. We show that for specifically the cubic term, an integrating out calculation also works for compact cases. In particular, the exact cubic term coefficient can be recovered from integrating out a Fermi gas for any compact Calabi-Yau that is an elliptic fibration over a reflexive toric base. We also propose a general map, for any one-parameter Calabi-Yau, between the Grand Canonical potential of the ultraviolet non-perturbative system and the period. In particular, this map leads to an emergent cubic term in the genus-zero prepotential for any such one-parameter model.

Multimethods study to develop tools for competency-based assessments of implementation research training programmes in low and middle-income countries

IntroductionMethods and validated tools for evaluating the performance of competency-based implementation research (IR) training programmes in low–middle-income countries (LMICs) are lacking. In this study, we developed tools for assessing the...

Wave height distribution for plunging breakers induced by air bubbles

This study highlights the wave height distributions based on plunging breaking waves and air bubble effects in the surf zone. Wave height distributions predicted previously by different models have been reformulated in terms of air bubble effects. Some of the most commonly applied wave height distributions are judged using laboratory observations in a custom-built wave flume. Results have revealed a notable deviation from the Rayleigh distribution, with the proposed model demonstrating a closer match to experimental data, particularly for larger wave heights. Probability densities of larger wave heights are reduced significantly by entrained air bubbles, leading to measured wave heights below Rayleigh distribution predictions. In addition, the different wave height parameters derived from the proposed model exhibited good agreement with laboratory data compared to the Rayleigh distribution. Furthermore, theoretical analysis shows the scale parameter's dependence on the decay coefficient, aligning well with measurements and simplifying the proposed distribution to a one-parameter model. Again, based on the error analysis, the proposed model's results show good performance compared to others.

HARMONIC ANALYSISIN INVENTORY MANAGEMENT IN LOGISTICSAND SUPPLY CHAINS

The article examines the possibilities of using harmonic analysis apparatus while planning the need in stocks of various categories. The issues of improving material planning (forecasting) are currently quite relevant applied tasks in business, and are also of interest in terms of developing the theory of logistics and supply chain management. Among the approaches to planning the need for inventory, a wide range of statistical theory methods are used in practice, among which two large groups can be distinguished, such as one-parameter time series analysis models for goods of stable and relatively stable demand, as well as correlation and regression models for chaotic consumption stocks. Most of the goods sold to end consumers have a seasonal component, which may not always be explicitly expressed in statistics. However, due to change of seasons, regular fluctuations in the values of consumption from the warehouse, around the average chronological or trend, may necessitate regular recalculation of the main parameters of inventory management models, such as maximum, insurance, threshold inventory levels, etc. In addition, sales statistics may contain fluctuations of a higher order if the stocks sold have life cycles of interest in goods on the market, which can also be attributed to periodic or quasi-periodic processes. One of the methods to formalize such cyclic processes can be trigonometric approximation or harmonic analysis, when the values of a time series are represented as terms of a Fourier series (harmonics) having corresponding amplitudes and phases. The article compares the effectiveness (accuracy) of forecasts of inventory requirements made using harmonic analysis and traditional time series extrapolation methods.

Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data

This article presents Bayesian estimation methods applied to the gamma zero-truncated Poisson (GZTP) and the complementary gamma zero-truncated Poisson (CGZTP) distributions, encompassing both one-parameter and two-parameter models. These distributions are notably flexible and useful for modeling lifetime data. In the one-parameter model case, the Jeffreys prior is mathematically derived. The use of informative and noninformative priors, combined with the random walk Metropolis algorithm within a Bayesian framework, generates samples from the posterior distributions. Bayesian estimators’ effectiveness is examined through extensive simulation studies, in comparison with the maximum likelihood method. Results indicate that Bayesian estimators provide more precise parameter estimates, even with smaller sample sizes. Furthermore, the study and comparison of the coverage probabilities (CPs) and average lengths (ALs) of the credible intervals with those from Wald intervals suggest that Bayesian credible intervals typically yield shorter ALs and higher CPs, thereby demonstrating the effectiveness of Bayesian inference in the context of GZTP and CGZTP distributions. Lastly, Bayesian inference is applied to real data.

Synthetic MRI and amide proton transfer-weighted MRI for differentiating between benign and malignant sinonasal lesions.

To explore the value of the synthetic MRI (SyMRI), combined with amide proton transfer-weighted (APTw) MRI for quantitative and morphologic assessment of sinonasal lesions, which could provide relative scale for the quantitative assessment of tissue properties. A total of 80 patients (31 malignant and 49 benign) with sinonasal lesions, who underwent the SyMRI and APTw examination, were retrospectively analyzed. Quantitative parameters (T1, T2, proton density (PD)) and APT % were obtained through outlining the region of interest (ROI) and comparing the two groups utilizing independent Student t test or a Wilcoxon test. Receiver operating characteristic curve (ROC), Delong test, and logistic regression analysis were performed to assess the diagnostic efficiency of one-parameter and multiparametric models. SyMRI-derived mean T1, T2, and PD were significantly higher and APT % was relatively lower in benign compared to malignant sinonasal lesions (p < 0.05). The ROC analysis showed that the AUCs of the SyMRI-derived quantitative (T1, T2, PD) values and APT % ranged from 0.677 to 0.781 for differential diagnosis between benign and malignant sinonasal lesions. The T2 values showed the best diagnostic performance among all single parameters for differentiating these two masses. The AUCs of combined SyMRI-derived multiple parameters with APT % (AUC = 0.866) were the highest than that of any single parameter, which was significantly improved (p < 0.05). The combination of SyMRI and APTw imaging has the potential to reflect intrinsic tissue characteristics useful for differentiating benign from malignant sinonasal lesions. Combining synthetic MRI with amide proton transfer-weighted imaging could function as a quantitative and contrast-free approach, significantly enhancing the differentiation of benign and malignant sinonasal lesions and overcoming the limitations associated with the superficial nature of endoscopic nasal sampling. • Synthetic MRI and amide proton transfer-weighted MRI could differentiate benign from malignant sinonasal lesions based on quantitative parameters. • The diagnostic efficiency could be significantly improved through synthetic MRI + amide proton transfer-weighted imaging. • The combination of synthetic MRI and amide proton transfer-weighted MRI is a noninvasive method to evaluate sinonasal lesions.

Laser-assisted two-proton radioactivity

In this work, we systematically investigate the two-proton (2p) radioactivity assisted by an ultra-intense laser field within a deformed one-parameter model (OPM). The results show that the ultra-intense laser hardly affects the preformation probability of the emitted 2p-pair, but it can change the 2p radioactive half-lives to a finite extent by affecting the penetrability probability. Moreover, we compare the responses of different 2p radioactivity nuclei to the laser field, and it is found that the 2p radioactivity of nuclei with a low decay width are more easily influenced by the intense laser field. Furthermore, the effects of different physical parameters of a laser pulse on the 2p radioactivity were also discussed. The calculations indicate that the lasers characterized by shorter wavelengths and higher intensities exert a more significant influence on the rate of the average change in pulse duration. Finally, we extended the deformed OPM to predict the half-lives of 2p radioactivity candidates and identified the possible experimental objects of the laser-assisted 2p radioactivity. This study may promote the possibility of future experimental investigations on extensive facilities like GSI and ELI-NP, etc.

An Anisotropic Damage-Plasticity Constitutive Model of Continuous Fiber-Reinforced Polymers.

Accurate structural analyses of continuous fiber-reinforced polymers (FRPs) are imperative for diverse engineering applications, demanding efficient material constitutive models. Nonetheless, the constitutive modeling of FRPs is complicated by the nonlinear behavior resulting from internal damages and the inherent plasticity. Consequently, this study presents an innovative anisotropic constitutive model for FRPs, designed to adeptly capture both the damage evolution and plasticity. All requisite parameters can be easily obtained through fundamental mechanical tests, rendering the model practical and user-friendly. The model utilizes the three-dimensional Puck criteria to determine damages, initiating the evolution process through a combination of continuum damage mechanics and linear stiffness attenuation methods. This evolution is coupled with a one-parameter plastic model. Subsequently, the numerical implementation method, integrated into ANSYS, is detailed. This emphasizes the Cauchy stress and consistent tangent stiffness solution strategy. Finally, the effectiveness of the developed model is demonstrated through comprehensive verification, encompassing existing biaxial tension and open-hole-tension tests conducted on carbon and glass FRP laminates. The simulation results exhibit a remarkable correspondence with the experimental data, validating the reliability and accuracy of the proposed model.

Properties and performance of the one-parameter log-linear cognitive diagnosis model

Diagnostic classification models (DCMs) are psychometric models that yield probabilistic classifications of respondents according to a set of discrete latent variables. The current study examines the recently introduced one-parameter log-linear cognitive diagnosis model (1-PLCDM), which has increased interpretability compared with general DCMs due to useful measurement properties like sum score sufficiency and invariance properties. We demonstrate its equivalence with the Latent Class/Rasch Model and discuss interpretational consequences. The model is further examined in a DCM framework. We demonstrate the sum score sufficiency property and we derive an expression for the cut score for mastery classification. It is shown by means of a simulation study that the 1-PLCDM is fairly robust to model constraint violations in terms of classification accuracy and reliability. This robustness in combination with useful measurement properties and ease of interpretation can make the model attractive for stakeholders to apply in various assessment settings.

Performance evaluation of three bio-optical models in aerosol and ocean color joint retrievals

Abstract. Multi-angle polarimeters (MAPs) are powerful instruments to perform remote sensing of the environment. Joint retrieval algorithms of aerosols and ocean color have been developed to extract the rich information content of MAPs. These are optimization algorithms that fit the sensor measurements with forward models, which include radiative transfer simulations of the coupled atmosphere and ocean systems (CAOSs). The forward model consists of sub-models to represent the optics of the atmosphere, ocean water surface and ocean body. The representativeness of these models for observed scenes and the number of retrieval parameters are important for retrieval success. In this study, we have evaluated the impact of three different ocean bio-optical models with one, three and seven optimization parameters on the accuracy of joint retrieval algorithms of MAPs. The Multi-Angular Polarimetric Ocean coLor (MAPOL) joint retrieval algorithm was used to process data from the airborne Research Scanning Polarimeter (RSP) instrument acquired in different field campaigns. We performed ensemble retrievals along three RSP legs to evaluate the applicability of bio-optical models in geographically varying water of clear to turbid conditions. The average differences between the MAPOL aerosol optical depth (AOD) and spectral remote sensing reflectance (Rrs(λ)) retrievals and the MODerate resolution Imaging Spectroradiometer (MODIS) products were also reported. We studied the distribution of retrieval cost function values obtained for the three bio-optical models. For the one-parameter model, the spread of retrieval cost function values is narrow regardless of the type of water even if it fails to converge over coastal water. For the three- and seven-parameter models, the retrieval cost function distribution is water type dependent, showing the widest distribution over clear, open water. This suggests that caution should be used when using the spread of the cost function distribution to represent the retrieval uncertainty. We observed that the three- and seven-parameter models have similar MAP retrieval performances in all cases, though they are prone to converge at local minima over open-ocean water. It is necessary to develop a screening algorithm to divide open and coastal water before performing MAP retrievals. Given the computational efficiency and the algorithm stability requirements, we recommend the three-parameter bio-optical model as the coastal-water bio-optical model for future MAPOL studies. This study provides important practical guides on the joint retrieval algorithm development for current and future satellite missions such as NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission and ESA's Meteorological Operational-Second Generation (MetOp-SG) mission.

30 Item response theory and differential item functioning of the AD8: The High School &amp; Beyond Study

Objective:The AD8 is a validated screening instrument for functional changes that may be caused by cognitive decline and dementia. It is frequently used in clinics and research studies because it is short and easy to administer, with a cut off score of 2 out of 8 items recommended to maximize sensitivity and specificity. This cutoff assumes that all 8 items provide equivalent “information” about everyday functioning. In this study, we used item response theory (IRT) to test this assumption. To determine the relevance of this measure of everyday functioning in men and women, and across race, ethnicity, and education, we conducted differential item functioning (DIF) analysis to test for item bias.Participants and Methods:Data came from the 2021 follow up of the High School &amp; Beyond cohort (N=8,690; mean age 57.5 ± 1.2; 55% women), a nationally representative, longitudinal study of Americans who were first surveyed in 1980 when they were in the 10th or 12th grade. Participants were asked AD8 questions about their own functioning via phone or internet survey. First, we estimated a one-parameter (i.e., differing difficulty, equal discrimination across items) and two-parameter IRT model (i.e., differing difficulty and differing discrimination across items). We compared model fit using a likelihood-ratio test. Second, we tested for uniform and non-uniform DIF on AD8 items by sex, race and ethnicity (non-Hispanic White, non-Hispanic Black, Hispanic), education level (high school or less, some college, BA degree or more), and survey mode (phone or internet). We examined DIF salience by comparing the difference between original and DIF-adjusted AD8 scores to the standard error of measurement of the original score.Results:The two-parameter IRT model fit the data significantly better than the one-parameter model, indicating that some items were more strongly related to underlying everyday functional ability than others. For example, the “problems with judgment” item had higher discrimination (more information) than the “less interest in hobbies/activities” item. There were significant differences in item endorsement by race/ethnicity, education, and survey mode. We found significant uniform and non-uniform DIF on several items across each of these groups. For example, for a given level of functional decline (theta) White participants were more likely to endorse “Daily problems with thinking/memory” than Black and Hispanic participants. The DIF was salient (i.e., caused AD8 scores to change by greater than the standard error of measurement for a large portion of respondents) for those with a college degree and phone respondents.Conclusions:In a population representative sample of Americans ∼age 57, the items on the AD8 contributed differing levels of discrimination along the range of everyday functioning that is impacted by later life cognitive impairment. This suggests that a simple cut-off or summed score may not be appropriate since some items yield more information about the underlying construct than others. Furthermore, we observed significant and salient DIF on several items by education and survey mode, AD8 scores should not be compared across education groups and assessment modes without adjustment for this measurement bias.

Relating the One-Parameter Logistic Diagnostic Classification Model to the Rasch Model and One-Parameter Logistic Mixed, Partial, and Probabilistic Membership Diagnostic Classification Models

Diagnostic classification models (DCMs) are statistical models with discrete latent variables (so-called skills) to analyze multiple binary variables (i.e., items). The one-parameter logistic diagnostic classification model (1PLDCM) is a DCM with one skill and shares desirable measurement properties with the Rasch model. This article shows that the 1PLDCM is indeed a latent class Rasch model. Furthermore, the relationship of the 1PLDCM to extensions of the DCM to mixed, partial, and probabilistic memberships is treated. It is argued that the partial and probabilistic membership models are also equivalent to the Rasch model. The fit of the different models was empirically investigated using six datasets. It turned out for these datasets that the 1PLDCM always had a worse fit than the Rasch model and mixed and partial membership extensions of the DCM.

Staff-rated ability to provide post-diagnosis support for patients with mild cognitive impairment and related factors.

Proactive interventions for patients with mild cognitive impairment (MCI) are required. We aimed to determine the staff-rated ability to provide post-diagnosis support for patients with MCI at a medical centre for dementia and the related factors. We conducted a web-based survey on post-diagnosis support for patients with MCI among healthcare personnel, such as mental health social workers and public health nurses (hereafter referred to as 'staff'), in consultation and support roles at medical centres for dementia nationwide. The latent characteristic value for 'staff's self-rated ability to provide post-diagnosis support to patients with MCI', which was estimated using the one-parameter logistic model of item response theory, was used as the dependent variable. Multivariate linear regression analysis was used to examine the factors associated with the dependent variable. We conducted the study at 482 medical centres for dementia. We received responses from 162 participants, 158 of which were valid. We applied item response theory to 45 staff-rated items regarding post-diagnosis support for patients with MCI and found that item difficulty ranged from -2.56 to 1.02; 40 items had negative values and were deemed relatively easy. The staff-rated ability to provide post-diagnosis support was significantly higher for 'The role in assisting patients with MCI is clear' (P < 0.005), 'A reasonable number of personnel is available to assist immediately after MCI diagnosis' (P = 0.001), and 'Collaboration with family physician available immediately after MCI diagnosis' (P < 0.001). The results of this study showed that staff rated their ability to provide post-diagnosis support for patients with MCI as relatively easy. The staff-rated ability to provide post-diagnosis support to patients with MCI may be enhanced by increased availability of staff immediately after MCI diagnosis, clarification of staff roles, and collaboration with family doctors.

Exploration and analysis of a generalized one-parameter item response model with flexible link functions.

This paper primarily analyzes the one-parameter generalized logistic (1PGlogit) model, which is a generalized model containing other one-parameter item response theory (IRT) models. The essence of the 1PGlogit model is the introduction of a generalized link function that includes the probit, logit, and complementary log-log functions. By transforming different parameters, the 1PGlogit model can flexibly adjust the speed at which the item characteristic curve (ICC) approaches the upper and lower asymptote, breaking the previous constraints in one-parameter IRT models where the ICC curves were either all symmetric or all asymmetric. This allows for a more flexible way to fit data and achieve better fitting performance. We present three simulation studies, specifically designed to validate the accuracy of parameter estimation for a variety of one-parameter IRT models using the Stan program, illustrate the advantages of the 1PGlogit model over other one-parameter IRT models from a model fitting perspective, and demonstrate the effective fit of the 1PGlogit model with the three-parameter logistic (3PL) and four-parameter logistic (4PL) models. Finally, we demonstrate the good fitting performance of the 1PGlogit model through an analysis of real data.

IRT Models for Learning With Item-Specific Learning Parameters

We propose a new item response theory growth model with item-specific learning parameters, or ISLP, and two variations of this model. In the ISLP model, either items or blocks of items have their own learning parameters. This model may be used to improve the efficiency of learning in a formative assessment. We show ways that the ISLP model’s learning parameters can be estimated in simulation using Markov chain Monte Carlo (MCMC), demonstrate a way that the model could be used in the context of adaptive item selection to increase the rate of learning, and estimate the learning parameters in an empirical data analysis using the ISLP. In the simulation studies, the one-parameter logistic model was used as the measurement model to generate random response data with various test lengths and sample sizes. Ability growth was modeled with a few variations of the ISLP model, and it was verified that the parameters were accurately recovered. Secondly, we generated data using the linear logistic test model with known Q-matrix structure for the item difficulties. Using a two-step procedure gave very comparable results for the estimation of the learning parameters even when item difficulties were unknown. The potential benefit of using an adaptive selection method in conjunction with the ISLP model was shown by comparing total improvement in the examinees’ ability parameter to two other methods of item selection that do not utilize this growth model. If the ISLP holds, adaptive item selection consistently led to larger improvements over the other methods. A real data application of the ISLP was given to illustrate its use in a spatial reasoning study designed to promote learning. In this study, interventions were given after each block of ten items to increase ability. Learning parameters were estimated using MCMC.