scholarly journals A Novel and Highly Effective Bayesian Sampling Algorithm Based on the Auxiliary Variables to Estimate the Testlet Effect Models

2021 ◽  
Vol 12 ◽  
Author(s):  
Jing Lu ◽  
Jiwei Zhang ◽  
Zhaoyuan Zhang ◽  
Bao Xu ◽  
Jian Tao
Keyword(s):  
Goodness Of Fit ◽  
Theory Model ◽  
Estimation Methods ◽  
Model Assessment ◽  
Auxiliary Variables ◽  
Acceptance Probability ◽  
Sampling Algorithm ◽  
Testlet Response Theory ◽  
Bayesian Sampling ◽  
Highly Effective

In this paper, a new two-parameter logistic testlet response theory model for dichotomous items is proposed by introducing testlet discrimination parameters to model the local dependence among items within a common testlet. In addition, a highly effective Bayesian sampling algorithm based on auxiliary variables is proposed to estimate the testlet effect models. The new algorithm not only avoids the Metropolis-Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability, but also overcomes the dependence of the Gibbs sampling algorithm on the conjugate prior distribution. Compared with the traditional Bayesian estimation methods, the advantages of the new algorithm are analyzed from the various types of prior distributions. Based on the Markov chain Monte Carlo (MCMC) output, two Bayesian model assessment methods are investigated concerning the goodness of fit between models. Finally, three simulation studies and an empirical example analysis are given to further illustrate the advantages of the new testlet effect model and Bayesian sampling algorithm.

The Changing Size Distribution of California's North Coast Wineries

2014 ◽  
Vol 9 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Don Cyr ◽  
Joseph Kushner ◽  
Tomson Ogwang
Keyword(s):  
Size Distribution ◽  
Small Firms ◽  
Goodness Of Fit ◽  
Nonparametric Density Estimation ◽  
Wine Industry ◽  
Estimation Methods ◽  
North Coast ◽  
Size Distribution Of Firms ◽  
Goodness Of Fit Tests ◽  
Kernel Density Estimates

AbstractIn this paper, we use three different goodness-of-fit tests for log-normality in conjunction with kernel nonparametric density estimation methods to examine both the size distribution of California North Coast wineries over time and by age. Our kernel density estimates indicate that the size distribution of wineries has changed from positively skewed to bimodal. These results are inconsistent with those in other industries, but are consistent with recent empirical research in the wine industry, which finds that smaller firms are comprising a larger component of market share. In terms of the distribution of firm size by age, our results indicate that as wineries age, the size distribution of firms becomes less skewed and more bimodal, which is also inconsistent with the research on other industries which finds that as firms age, the size distribution becomes more normal. Our results indicate that unlike other industries, where entry is very difficult, small firms can enter the wine industry and survive. (JEL Classifications: L11, L22, L25)

scholarly journals Improving generalizability coefficient estimate accuracy: A way to incorporate auxiliary information

2018 ◽  
Vol 11 (2) ◽  
pp. 205979911879139 ◽  
Author(s):  
Zhehan Jiang ◽  
Kevin Walker ◽  
Dexin Shi ◽  
Jian Cao
Keyword(s):  
Structural Equation Modeling ◽  
Structural Equation ◽  
Generalizability Theory ◽  
Theory Model ◽  
Bias Reduction ◽  
Equation Modeling ◽  
Coefficient Estimate ◽  
Auxiliary Variables ◽  
Modeling Approach ◽  
Generalizability Coefficient

Initially proposed by Marcoulides and further expanded by Raykov and Marcoulides, a structural equation modeling approach can be used in generalizability theory estimation. This article examines the utility of incorporating auxiliary variables into the structural equation modeling approach when missing data is present. In particular, the authors assert that by adapting a saturated correlates model strategy to structural equation modeling generalizability theory models, one can reduce any biased effects caused by missingness. Traditional approaches such as an analysis of variance do not possess such a feature. This article provides detailed instructions for adding auxiliary variables into a structural equation modeling generalizability theory model, demonstrates the corresponding benefits of bias reduction in generalizability coefficient estimate via simulations, and discusses issues relevant to the proposed approach.

Qualities and Methods of Highly Effective Surgical Educators: A Grounded Theory Model

2019 ◽  
Vol 76 (5) ◽  
pp. 1293-1302 ◽  
Author(s):  
Robert A. Swendiman ◽  
Daniel I. Hoffman ◽  
Adrienne N. Bruce ◽  
Thane A. Blinman ◽  
Michael L. Nance ◽  
...  
Keyword(s):  
Grounded Theory ◽  
Theory Model ◽  
Highly Effective

scholarly journals Fitting Hidden Markov Models to Psychological Data

2002 ◽  
Vol 10 (3) ◽  
pp. 185-199 ◽  
Author(s):  
Ingmar Visser ◽  
Maartje E.J. Raijmakers ◽  
Peter C.M. Molenaar
Keyword(s):  
Model Selection ◽  
Hidden Markov Models ◽  
Implicit Learning ◽  
Goodness Of Fit ◽  
Markov Models ◽  
Hidden Markov ◽  
Learning Task ◽  
Model Assessment ◽  
Psychology Of Learning ◽  
Theoretical Issues

Markov models have been used extensively in psychology of learning. Applications of hidden Markov models are rare however. This is partially due to the fact that comprehensive statistics for model selection and model assessment are lacking in the psychological literature. We present model selection and model assessment statistics that are particularly useful in applying hidden Markov models in psychology. These statistics are presented and evaluated by simulation studies for a toy example. We compare AIC, BIC and related criteria and introduce a prediction error measure for assessing goodness-of-fit. In a simulation study, two methods of fitting equality constraints are compared. In two illustrative examples with experimental data we apply selection criteria, fit models with constraints and assess goodness-of-fit. First, data from a concept identification task is analyzed. Hidden Markov models provide a flexible approach to analyzing such data when compared to other modeling methods. Second, a novel application of hidden Markov models in implicit learning is presented. Hidden Markov models are used in this context to quantify knowledge that subjects express in an implicit learning task. This method of analyzing implicit learning data provides a comprehensive approach for addressing important theoretical issues in the field.

scholarly journals A comparison of three parameter estimation methods of the gamma distribution of annual maximum low flow duration and deficit in the Upper Vistula catchment (Poland)

2018 ◽  
Vol 23 ◽  
pp. 00001
Author(s):  
Katarzyna Baran-Gurgul
Keyword(s):  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Low Flow ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Flow Duration ◽  
Distribution Parameters ◽  
Anderson Darling ◽  
Parameter Estimation Methods

Based on 30-year 24-hour flow sequences at 69 water gauging stations in the Upper Vistula catchment, it was determined that the probability distributions of the low flow duration and its maximum annual deficit can be described by the gamma distribution with the estimated parameters by the methods: MOM, the method of moments, LMOM, the method of linear moments, and MLE, the method of maximum likelihood. The stationarity of the time series was tested by the Mann-Kendall correlation using the Hamed and Rao variance correction. The low flows were defined by the SPA method, with the limit flow Q70%. The quality of the match was tested by the Anderson-Darling goodness of fit test. This test allowed accepting the gamma distribution in all analysed cases, regardless of the method used to estimate the distribution parameters, since the pv (p-values) values were greater than 5% (over 18% for Tmax and 7.5% for Vmax). The highest pv values for individual water gauging stations, as well as the highest 90% Tmax and Vmax quantiles were noted using LMOM to estimate the gamma distribution parameters. The highest 90% Tmax and Vmax quantiles were observed in the uppermost part of the studied area.

scholarly journals Statistical Inference of Odd Fréchet Inverse Lomax Distribution with Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Ramadan A. ZeinEldin ◽  
Muhammad Ahsan ul Haq ◽  
Sharqa Hashmi ◽  
Mahmoud Elsehety ◽  
M. Elgarhy
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Information Criterion ◽  
Value Theory ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Monte Carlo Simulation Study ◽  
Lifetime Distributions ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution

In this article, we propose and study a new three-parameter distribution, called the odd Fréchet inverse Lomax (OFIL) distribution, derived by combining the odd Fréchet-G family and the inverse Lomax distribution. Since Fréchet is a continuous distribution with wide applicability in extreme value theory, the new model contains these properties as well as the characteristics of the inverse Lomax distribution which make it more flexible and provide a good alternative for some well-known lifetime distributions. We initially present a linear representation of its functions and discussion on density and hazard rate function. Then, we study its various mathematical properties. Different estimation methods are used to estimate parameters of OFIL. The Monte Carlo simulation study is carried out to compare the efficiencies of different methods of estimation. The maximum likelihood estimation (MLE) method is used to estimate the OFIL parameters by considering three practical data applications. We show that the related model is the best in comparisons based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and other goodness-of-fit measures.

scholarly journals Impact of 3-year changes in fasting insulin and insulin resistance indices on incident hypertension: Tehran lipid and glucose study

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Aidin Baghbani-Oskouei ◽  
Maryam Tohidi ◽  
Mitra Hasheminia ◽  
Fereidoun Azizi ◽  
Farzad Hadaegh
Keyword(s):  
Insulin Resistance ◽  
Goodness Of Fit ◽  
Density Lipoprotein ◽  
Information Criteria ◽  
Model Assessment ◽  
Fasting Insulin ◽  
Incident Hypertension ◽  
Discrimination Ability ◽  
Glucose Ratio ◽  
Incident Cases

Abstract Background To examine the association between changes in fasting insulin, homeostasis model assessment of insulin resistance (HOMA-IR), and insulin-glucose ratio (IGR) levels, over approximately 3 years with incident hypertension. Methods A total of 2814 Iranian participants (1123 men) without hypertension and known diabetes at baseline and the first examination were followed for a median of 6.32 years. The associations between quartiles of changes in fasting insulin and IR indices with incident hypertension were assessed using multivariate Cox proportional hazard regression analyses with first quartile as reference. The models were adjusted for baseline values of insulin or each IR index, and age, sex, smoking, physical activity, educational levels, marital status, history of cardiovascular diseases, baseline levels of systolic and diastolic blood pressures, estimated glomerular filtration rate, triglycerides, total cholesterol, high-density lipoprotein cholesterol, fasting plasma glucose (only for insulin change) and both body mass index (BMI) per se, and its change. Akaike’s information criteria (AIC) was applied as indicator for goodness of fit of each predictive model. The discrimination ability of models was calculated using the Harrell’s C statistic. Results During the study, 594 incident cases of hypertension (253 men) were identified. The 4th quartile of changes in insulin, HOMA-IR, and IGR showed hazard ratios (95% confidence interval) of 1.31 (1.01–1.69), 1.18 (0.92–1.52), and 1.53 (1.18–1.98) for hypertension, respectively, in fully-adjusted models. Changes in fasting insulin levels and IR indices showed significant increasing trends for incident hypertension, moving from 1st to 4th quartiles (all P-values < 0.05). Focusing on model fitness, no superiority was found between changes in fasting insulin, HOMA-IR, and IGR to predict incident hypertension. The discriminatory powers of changes in fasting insulin and IR indices as assessed by C index were similar (i.e. about 80%). Conclusion Changes in fasting insulin and IR indices were significantly associated with developing hypertension among normotensive population even after considering BMI changes.

Estimation of the average wage in Polish small companies using the robust approach

2020 ◽  
Vol 66 (3) ◽  
pp. 200-213
Author(s):  
Grażyna Dehnel ◽  
Łukasz Wawrowski
Keyword(s):  
Small Firms ◽  
Estimation Methods ◽  
Average Wage ◽  
Small Companies ◽  
Auxiliary Variables ◽  
Robust Approach ◽  
Business Statistics ◽  
Economic Statistics ◽  
Robust Version ◽  
Level Of Aggregation

There is a growing demand for multivariate economic statistics for crossclassified domains. In business statistics, this demand poses a particular challenge given the specific character of the population of enterprises, which necessitates searching for methods of analysis that would represent the robust approach to estimation, where auxiliary variables could be utilised. The adoption of new solutions in this area is expected to increase the scope of statistical output and improve the precision of estimates. The study presented in the paper furthers this goal, as it is focused on testing the application of a robust version of the Fay-Herriot model, which makes it possible to meet the assumption of normality of random effects under the presence of outliers. These alternative models are supplied to estimate the parameters of small firms operating in 2012. Variables from administrative registers were used as auxiliary variables, which made the estimation process more comprehensive. The paper refers to small area estimation methods. The variables of interest are estimated at a low level of aggregation represented by the crosssection province and NACE sections.

Determination of Yearly Wind Energy Potential and Extraction of Wind Energy Using Wind Turbine for Coastal Cities of Baluchistan, Pakistan

2019 ◽  
Vol 10 (3) ◽  
pp. 56-63
Author(s):  
Muhammad Shoaib ◽  
Imran Siddiqui ◽  
Saif Ur Rehman
Keyword(s):  
Wind Energy ◽  
Goodness Of Fit ◽  
Estimation Methods ◽  
Energy Potential ◽  
Goodness Of Fit Test ◽  
Wind Speeds ◽  
Energy Assessment ◽  
Weibull Pdf ◽  
Parameter Estimation Methods ◽  
Two Parameters

04 March, 2019 Accepted: 24 April, 2019Abstract: Wind energy assessment of Ormara, Gwadar and Lasbela wind sites which are located in provinceBaluchistan is presented. The daily averaged wind speed data for the three sites is recorded for a period of four yearsfrom 2010-2013 at mast heights 7 m, 9.6 m and 23 m. Measured wind data are extrapolated to heights 60 m (Ormara),80 m (Gwadar) and 60 m (Lasbela). Yearly averaged wind speeds are modeled using a two parameters Weibullfunction whose shape (k) and scale (c) parameters are computed using seven well known numerical iterative methods.Reliability of the fitting process is assessed by employing three goodness-of-fit test statistics, namely, RMSE, R2 and χ2tests. Tests indicate that MLE, MLM and EPFM outperformed other Weibull parameter estimation methods for a betterfit behavior. Yearly Weibull pdf and cdf are obtained and Weibull wind characteristics are determined. Wind turbinesEcotecnia 60/1.67 MW and Nordex S77 1500 kW are used to extract wind energy on yearly basis. Estimated yearlyWeibull power densities are in the range 623.00 - 700.13 W/m2, 276.04 – 307.55 W/m2 and 66.85 – 75.93 W/m2 forOrmara, Gwadar and Lasbela respectively. Extracted wind energy values for Ormara and Gwadar using wind turbinesare reported as ca. 8623 kWh and ca. 4622 kWh, respectively.

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