Adaptive Hierarchical Bayes Estimation of Small Area Proportions

2017 ◽  
Vol 69 (2) ◽  
pp. 150-164 ◽  
Author(s):  
Benmei Liu ◽  
Partha Lahiri
Keyword(s):  
Random Effects ◽  
Small Area ◽  
Probability Distributions ◽  
Random Effect ◽  
Real Data ◽  
Hierarchical Bayes ◽  
Bayes Estimation ◽  
Proposed Model ◽  
Exponential Power ◽  
Power Class

Unit-level logistic regression models with mixed effects have been used for estimating small area proportions in the literature. Normality is commonly assumed for the random effects. Nonetheless, real data often show significant departures from normality assumptions of the random effects. To reduce the risk of model misspecification, we propose an adaptive hierarchical Bayes estimation approach in which the distribution of the random effect is chosen adaptively from the exponential power class of probability distributions. The richness of the exponential power class ensures the robustness of our hierarchical Bayes approach against departure from normality. We demonstrate the robustness of our proposed model using both simulated and real data. The results suggest that the proposed model works reasonably well to incorporate potential kurtosis of the random effects distribution.

scholarly journals PENERAPAN MODEL SPATIAL LOGIT-NORMAL PADA SMALL AREA ESTIMATION DENGAN METODE HIERARCHICAL BAYES

2020 ◽  
Vol 2019 (1) ◽  
pp. 59-66
Author(s):  
Taly Purwa
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Small Area ◽  
Small Area Estimation ◽  
Random Effect ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Hierarchical Bayes ◽  
Area Estimation ◽  
Spatial Random Effect

Penelitian ini menerapkan model Spatial Logit-normal pada Small Area Estimation (SAE) untuk estimasi proporsi penduduk dengan asupan kalori minimum di bawah 1.400 kkal/kapita/hari pada level kecamatan di Provinsi Bali Tahun 2014 yang merupakan indikator 2.1.2(A) pada tujuan ke-2 SDGs dalam rangka mengukur capaian dan mendukung tercapainya target SDGs pada level lebih tinggi. Terdapat tiga model SAE yang digunakan dengan spesifikasi random effect yang berbeda, yaitu model dengan random effect yang bersifat saling bebas (independen), spatial random effect (iCAR) serta model dengan kedua jenis random effect sekaligus (BYM). Penggunaan unsur spatial random effect diharapkan dapat meningkatkan efisiensi hasil estimasi. Metode estimasi menggunakan pendekatan Hierarchical Bayes (HB) dengan metode Markov Chain Monte Carlo (MCMC) algoritma Gibbs Sampling. Estimasi parameter pada ketiga model menunjukkan hasil yang relatif tidak berbeda dimana hanya ada satu variabel prediktor yang memiliki pengaruh signifikan, yaitu proporsi keluarga pertanian, pada model dengan random effect independen dan model BYM. Sedangkan pada model iCAR tidak ada satu pun variabel prediktor yang berpengaruh signifikan. Berdasarkan nilai Deviance Information Criterion (DIC), model terbaik adalah model BYM. Akan tetapi penambahan unsur spatial random effect bersamaan dengan random effect independen tidak secara signifikan dapat meningkatkan efisiensi hasil estimasi akibat dari minimnya nilai dependensi spasial Moran’s I. Secara visual, pemetaan hasil estimasi dengan model terbaik tidak menunjukkan adanya pola persebaran atau pengelompokan tertentu pada level kecamatan.

scholarly journals The quasi xgamma-geometric distribution with application in medicine

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5291-5330 ◽  
Author(s):  
Subhradev Sen ◽  
Ahmed Afify ◽  
Hazem Al-Mofleh ◽  
Mohammad Ahsanullah
Keyword(s):  
Hazard Rate ◽  
Geometric Distribution ◽  
Probability Distributions ◽  
Real Data ◽  
Data Generation ◽  
Unknown Parameters ◽  
Monte Carlo Simulation Study ◽  
Proposed Model ◽  
Life Distributions

In this paper, a new probability distribution, which is synthesized based on the quasi xgamma[26] and geometric distributions, is proposed and studied. The proposed distribution so synthesized is basically a family of positively skewed probability distributions and possesses increasing and decreasing hazard rate properties depending on the values of the unknown parameters. Different important distributional and survival and/or reliability properties are also studied. A unique characterization of the distribution is presented based on reversed hazard rate. Seven different frequentist methods of estimating unknown parameters are proposed and the methods are justified with Monte-Carlo simulation study. Flexible data generation algorithm eases the utility of the proposed model in survival and/or reliability application which is accomplished by real data analyses and by comparing with other competitive life distributions.

scholarly journals The Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression Modeling

2019 ◽  
Vol 8 (2) ◽  
pp. 70 ◽  
Author(s):  
Mustafa C. Korkmaz ◽  
Emrah Altun ◽  
Haitham M. Yousof ◽  
G.G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Simulation Studies ◽  
Proposed Model ◽  
Family Of Distributions

In this study, a new flexible family of distributions is proposed with its statistical properties as well as some useful characterizations. The maximum likelihood method is used to estimate the unknown model parameters by means of two simulation studies. A new regression model is proposed based on a special member of the proposed family called, the log odd power Lindley Weibull distribution. Residual analysis is conducted to evaluate the model assumptions. Four applications to real data sets are given to demonstrate the usefulness of the proposed model.

Using Extremes to Design Products and Segment Markets

1995 ◽  
Vol 32 (4) ◽  
pp. 392-403 ◽  
Author(s):  
Greg M. Allenby ◽  
James L. Ginter
Keyword(s):  
Product Design ◽  
Random Effects ◽  
Market Segmentation ◽  
Credit Card ◽  
Hierarchical Bayes ◽  
Random Effects Model ◽  
Product Attributes ◽  
Proposed Model ◽  
Depth Study

Current marketing methodologies used to study consumers are inadequate for identifying and understanding respondents whose preferences for a product offering are most extreme. These “extreme respondents” have important implications for product design and market segmentation decisions. The authors develop a hierarchical Bayes random-effects model and apply it to a conjoint study of credit card attributes. Their proposed model facilitates an in-depth study of respondent heterogeneity, especially of extreme respondents. The authors demonstrate the importance of characterizing extremes in identifying product attributes and predicting the success of potential products.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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