Recent developments of parameter estimation methods in item response theory models

This research reviewed the recent development of parameter estimation methods in item response theory models. Various new methods to manage the computational burden problem with respect to the item factor analysis and multidimensional item response models, which have high dimensional factors, were introduced. Monte Carlo integral methods, approximation methods for marginal likelihood, new optimization methods, and techniques used in the machine learning field were employed for the estimation methods. Theoretically, a new type of asymptotical setting, that assumes infinite number of sample sizes and items, was considered. Several methods were classified apart from the maximum likelihood method or Bayesian method. Theoretical development of interval estimation methods for individual latent traits were also proposed and they provided highly accurate intervals

A Comprehensive Simulation Study of Estimation Methods for the Rasch Model

The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alternatives of marginal maximum likelihood (MML) estimation, conditional maximum likelihood (CML) estimation, and several limited information methods (LIM). The type of ability distribution (i.e., nonnormality), the number of items, sample size, and the distribution of item difficulties were systematically varied. Across different simulation conditions, MML methods with flexible distributional specifications can be at least as efficient as CML. Moreover, in many situations (i.e., for long tests), penalized JML and JML with ε adjustment resulted in very efficient estimates and might be considered alternatives to JML implementations currently used in statistical software. Moreover, minimum chi-square (MINCHI) estimation was the best-performing LIM method. These findings demonstrate that JML estimation and LIM can still prove helpful in applied research.

Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors

In data-driven modeling besides the point estimate of the model parameters, an estimation of the parameter uncertainty is of great interest. For this, bounded error parameter estimation methods can be used. These are particularly interesting for problems where the stochastical properties of the random effects are unknown and cannot be determined. In this paper, different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models. Case studies with simulated data and with measured data from a manufacturing process are presented.

Inferring pulmonary exposure based on clinical PK data: accuracy and precision of model-based deconvolution methods

Determining and understanding the target-site exposure in clinical studies remains challenging. This is especially true for oral drug inhalation for local treatment, where the target-site is identical to the site of drug absorption, i.e., the lungs. Modeling and simulation based on clinical pharmacokinetic (PK) data may be a valid approach to infer the pulmonary fate of orally inhaled drugs, even without local measurements. In this work, a simulation-estimation study was systematically applied to investigate five published model structures for pulmonary drug absorption. First, these models were compared for structural identifiability and how choosing an inadequate model impacts the inference on pulmonary exposure. Second, in the context of the population approach both sequential and simultaneous parameter estimation methods after intravenous administration and oral inhalation were evaluated with typically applied models. With an adequate model structure and a well-characterized systemic PK after intravenous dosing, the error in inferring pulmonary exposure and retention times was less than twofold in the majority of evaluations. Whether a sequential or simultaneous parameter estimation was applied did not affect the inferred pulmonary PK to a relevant degree. One scenario in the population PK analysis demonstrated biased pulmonary exposure metrics caused by inadequate estimation of systemic PK parameters. Overall, it was demonstrated that empirical modeling of intravenous and inhalation PK datasets provided robust estimates regarding accuracy and bias for the pulmonary exposure and pulmonary retention, even in presence of the high variability after drug inhalation.

Performance Comparison of New Generation Parameter Estimation Methods for Weibull Distribution to Compute Wind Energy Density

To install a wind energy conversion system to a region, the wind speed characteristics of that region must be identified. The two-parameter Weibull distribution is highly efficient in modeling wind speed characteristics. In this study, the wind speed data of 32 cities in three different regions of Turkey have been comparatively analysed to estimate Weibull distribution function parameters by the use of three well-known methods (Graphical Method (GM), Maximum Likelihood Method (MLM), Justus Moment Method (JMM)) and three new parameter estimation methods (Energy Pattern Factor Method (EPFM), Wind Energy Intensification Method (WEIM), Power Density Method (PD)) which have been proposed in recent years. Three years of hourly wind speed data of the specified regions have been used. The performance metrics of these analyses have been compared using Wind Energy Error (WEE), Root Mean Square Error (RMSE), and Coefficient of Determination (R2). The results have shown that while the PD method has high model performance, the JMM is closely competitive with the MLM. Besides, the wind energy densities that were estimated by using actual data have been compared with the resulting Weibull distribution. It has been clear that the method that has the closest estimation to the actual values is the PD method.

Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns

The paper aims at presentation of a methodology where the classical linear regression model is modified to guarantee more realistic estimations and lower parameter oscillations for a specific urban system. That can be achieved by means of the weighted regression model which is based on weights ascribed to individual cities. The major shortcoming of the methods used so far – especially the classical simple linear regression – is the treatment of individual cities as points carrying the same weight, in consequence of which the linear regression poorly matches the empirical distribution of cities. The aim is reached in a several-stage process: demonstration of the drawbacks of the linear parameter estimation methods traditionally used for the purposes of urban system analyses; introduction of the weighted regression which to a large extent diminishes specific drawbacks; and empirical verification of the method with the use of the input data for the USA and Poland

An application of the ensemble Kalman filter in epidemiological modelling

Since the novel coronavirus (COVID-19) outbreak in China, and due to the open accessibility of COVID-19 data, several researchers and modellers revisited the classical epidemiological models to evaluate their practical applicability. While mathematical compartmental models can predict various contagious viruses’ dynamics, their efficiency depends on the model parameters. Recently, several parameter estimation methods have been proposed for different models. In this study, we evaluated the Ensemble Kalman filter’s performance (EnKF) in the estimation of time-varying model parameters with synthetic data and the real COVID-19 data of Hubei province, China. Contrary to the previous works, in the current study, the effect of damping factors on an augmented EnKF is studied. An augmented EnKF algorithm is provided, and we present how the filter performs in estimating models using uncertain observational (reported) data. Results obtained confirm that the augumented-EnKF approach can provide reliable model parameter estimates. Additionally, there was a good fit of profiles between model simulation and the reported COVID-19 data confirming the possibility of using the augmented-EnKF approach for reliable model parameter estimation.