scholarly journals A Class of Exponentiated Regression Model for Non Negative Censored Data with an Application to Antibody Response to Vaccine

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1419
Author(s):  
Guillermo Martínez-Flórez ◽  
Sandra Vergara-Cardozo ◽  
Roger Tovar-Falón
Keyword(s):  
Regression Model ◽  
Information Matrix ◽  
Continuous Distribution ◽  
Score Function ◽  
Negative Data ◽  
Proposed Model ◽  
Discrete Part ◽  
Bernoulli Distributions ◽  
Best Fit ◽  
Maximum Method

In this paper, an asymmetric regression model for censored non-negative data based on the centred exponentiated log-skew-normal and Bernoulli distributions mixture is introduced. To connect the discrete part with the continuous distribution, the logit link function is used. The parameters of the model are estimated by using the likelihood maximum method. The score function and the information matrix are shown in detail. Antibody data from a study of the measles vaccine are used to illustrate applicability of the proposed model, and it was found the best fit to the data with respect to an others models used in the literature.

scholarly journals Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1989
Author(s):  
Guillermo Martínez-Flórez ◽  
Hector W. Gomez ◽  
Roger Tovar-Falón
Keyword(s):  
Regression Model ◽  
Logistic Model ◽  
Information Matrix ◽  
Link Function ◽  
Skew Normal Distribution ◽  
Linear Predictor ◽  
Response Variable ◽  
Proposed Model ◽  
Flexible Model ◽  
Skew Normal

Rate or proportion data are modeled by using a regression model. The considered regression model can be used for studying phenomena with a response on the (0, 1), [0, 1), (0, 1], or [0, 1] intervals. To connect the response variable with the linear predictor in the regression model, we use a logit link function, which guarantees that the obtained prediction ranges between zero and one in the cases inflated at zero or one (or both). The model is complemented with the assumption that the errors follow a power-skew-normal distribution, resulting in a very flexible model, and with a non-singular information matrix, constituting an advantage over other existing models in the literature. To explain the probability of point mass at the values zero and/or one (inflated part), we used a polytomic logistic model with covariates. The results of two illustrations showed that the proposed model is a better alternative compared to widely known models in the literature.

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.

Regression model of assessment of customer solvency and banking risks in the process of lending

2019 ◽  
pp. 69-73
Author(s):  
Zoryna Yurynets ◽  
Rostyslav Yurynets ◽  
Nataliya Kunanets ◽  
Ivanna Myshchyshyn
Keyword(s):  
Logistic Regression ◽  
Discriminant Analysis ◽  
Regression Model ◽  
Likelihood Ratio ◽  
Credit Scoring ◽  
Bank Loans ◽  
Management Decisions ◽  
Computer Data ◽  
Proposed Model ◽  
Loan Risk

In the current conditions of economic development, it is important to pay attention to the study of the main types of risks, effective methods of evaluation, monitoring, analysis of banking risks. One of the main approaches to quantitatively assessing the creditworthiness of borrowers is credit scoring. The objective of credit scoring is to optimize management decisions regarding the possibility of providing bank loans. In the article, the scientific and methodological provisions concerning the formation of a regression model for assessing bank risks in the process of granting loans to borrowers has been proposed. The proposed model is based on the use of logistic regression tools, discriminant analysis with the use of expert evaluation. During the formation of a regression model, the relationship between risk factors and probable magnitude of loan risk has been established. In the course of calculations, the coefficient of the individual's solvency has been calculated. Direct computer data preparation, including the calculation of the indicators selected in the process of discriminant analysis, has been carried out in the Excel package environment, followed by their import into the STATISTICA package for analysis in the “Logistic regression” sub-module of the “Nonlinear evaluation” module. The adequacy of the constructed model has been determined using the Macfaden's likelihood ratio index. The calculated value of the Macfaden's likelihood ratio index indicates the adequacy of the constructed model. The ability to issue loans to new clients has been evaluated using a regression model. The conducted calculations show the possibility of granting a loan exclusively to the second and third clients. The offered method allows to conduct assessment of client's solvency and risk prevention at different stages of lending, facilitates the possibility to independently make informed decisions on credit servicing of clients and management of a loan portfolio, optimization of management decisions in banks. In order for a loan-based model to continue to perform its functions, it must be periodically adjusted.

scholarly journals L2,1-norm regularized multivariate regression model with applications to genomic prediction

2021 ◽  
Author(s):  
Alain J Mbebi ◽  
Hao Tong ◽  
Zoran Nikoloski
Keyword(s):  
Variable Selection ◽  
Regression Model ◽  
Multivariate Regression ◽  
Statistical Testing ◽  
Supplementary Information ◽  
Nucleotide Polymorphisms ◽  
Multiple Traits ◽  
Multivariate Regression Model ◽  
Proposed Model ◽  
Iterative Optimization Algorithm

AbstractMotivationGenomic selection (GS) is currently deemed the most effective approach to speed up breeding of agricultural varieties. It has been recognized that consideration of multiple traits in GS can improve accuracy of prediction for traits of low heritability. However, since GS forgoes statistical testing with the idea of improving predictions, it does not facilitate mechanistic understanding of the contribution of particular single nucleotide polymorphisms (SNP).ResultsHere, we propose a L2,1-norm regularized multivariate regression model and devise a fast and efficient iterative optimization algorithm, called L2,1-joint, applicable in multi-trait GS. The usage of the L2,1-norm facilitates variable selection in a penalized multivariate regression that considers the relation between individuals, when the number of SNPs is much larger than the number of individuals. The capacity for variable selection allows us to define master regulators that can be used in a multi-trait GS setting to dissect the genetic architecture of the analyzed traits. Our comparative analyses demonstrate that the proposed model is a favorable candidate compared to existing state-of-the-art approaches. Prediction and variable selection with datasets from Brassica napus, wheat and Arabidopsis thaliana diversity panels are conducted to further showcase the performance of the proposed model.Availability and implementation: The model is implemented using R programming language and the code is freely available from https://github.com/alainmbebi/L21-norm-GS.Supplementary informationSupplementary data are available at Bioinformatics online.

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

scholarly journals PREDICTION FOR THE 2012 UNITED STATES PRESIDENTIAL ELECTION USING MULTIPLE REGRESSION MODEL

2012 ◽  
Vol 6 (2) ◽  
pp. 77-97
Author(s):  
Pankaj Sinha ◽  
Aastha Sharma Aastha Sharma ◽  
Harsh Vardhan Singh
Keyword(s):  
Regression Model ◽  
Unemployment Rate ◽  
Presidential Election ◽  
Voting Behavior ◽  
Presidential Elections ◽  
Multiple Regression Model ◽  
Economic Factors ◽  
Gdp Growth Rate ◽  
Proposed Model ◽  
Midterm Elections

This paper investigates the factors responsible for predicting 2012 U.S. Presidential election. Though contemporary discussions on Presidential election mention that unemployment rate will be a deciding factor in this election, it is found that unemployment rate is not significant for predicting the forthcoming Presidential election. Except GDP growth rate, various other economic factors like interest rate, inflation, public debt, change in oil and gold prices, budget deficit/surplus and exchange rate are also not significant for predicting the U.S. Presidential election outcome. Lewis-Beck and Rice (1982) proposed Gallup rating, obtained in June of the election year, as a significant indicator for forecasting the Presidential election. However, the present study finds that even though there exists a relationship between June Gallup rating and incumbent vote share in the Presidential election, the Gallup rating cannot be used as the sole indicator of the Presidential elections. Various other non-economic factors like scandals linked to the incumbent President and the performance of the two parties in the midterm elections are found to be significant. We study the influence of the above economic and non-economic variables on voting behavior in U.S. Presidential elections and develop a suitable regression model for predicting the 2012 U.S. Presidential election. The emergence of new non-economic factors reflects the changing dynamics of U.S. Presidential election outcomes. The proposed model forecasts that the Democrat candidate Mr. Barack Obama is likely to get a vote percentage between 51.818 % - 54.239 %, with 95% confidence interval.

Study of Donor Centres in n-InSb due to the Temperature Annealing

2005 ◽  
Vol 480-481 ◽  
pp. 197-200
Author(s):  
Y. Sayad ◽  
A. Nouiri
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Annealing Time ◽  
Annealing Temperature ◽  
Theoretical Study ◽  
Donor Concentration ◽  
Model Based ◽  
Proposed Model ◽  
Kinetics Of ◽  
Best Fit

An increasing of donor centres has been detected in n-InSb when it was submitted to anneal/quench with various annealing temperature (450 °C - 850 °C) and various annealing time (5 - 100 hours). A theoretical study of the kinetics of the conduction conversion of n-InSb at temperature annealing above 250 °C has been made. The present analysis indicates that the donor concentration increases with increasing of annealing time. In order to study this variation and to give a model for donor centres generated, a proposed model based on the simple kinetic is used to fit the variation of donor concentration as a function of annealing time. However, from the best fit of experimental data using the proposed model, the activation energy is determined.

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

A Physically-Based Anisotropic Discrete Fiber Model for Fibrous Soft Tissues

2010 ◽  
Author(s):  
C. Flynn ◽  
M. B. Rubin ◽  
P. M. F. Nielsen
Keyword(s):  
Soft Tissues ◽  
Mechanical Response ◽  
Continuous Distribution ◽  
Collagen Fibers ◽  
Fiber Bundles ◽  
Parameter Study ◽  
Rabbit Skin ◽  
Pig Skin ◽  
Proposed Model ◽  
Physically Based

Physically-based fibrous soft tissue models often consider the tissue to be a collection of fibers with a continuous distribution function to represent their orientations. This study proposes a simple model for the response of fibrous connective tissues in terms of a discrete number of fiber bundles. The proposed model consists of six weighted fiber bundles orientated such that they pass through opposing vertices of an icosahedron. A novel aspect of the proposed model is the use of a simple analytical function to represent the undulation distribution of the collagen fibers. The mechanical response of the elastin fiber is represented by a neo-Hookean hyperelastic equation. A parameter study was performed to analyze the effect of each parameter on the overall response of the model. The proposed model accurately simulated the uniaxial stretching of pig skin with an 8% error-of-fit for stretch ratios up to 1.8. The model also accurately simulated the biaxial stretching of rabbit skin with a 10% error-of-fit for stretch ratios up to 1.9. The stiffness of the collagen fibers determined by the model was about 100 MPa for the rabbit skin and 900 MPa for the pig skin, which are comparable with values reported in the literature. The stiffness of the elastin fibers in the model was about 2 kPa.

scholarly journals Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions

2016 ◽  
Vol 5 (3) ◽  
pp. 1 ◽  
Author(s):  
Aerambamoorthy Thavaneswaran ◽  
Saumen Mandal ◽  
Dharini Pathmanathan
Keyword(s):  
Closed Form ◽  
Information Matrix ◽  
Score Function ◽  
Function Approach ◽  
Closed Form Expression ◽  
Characteristic Functions ◽  
Model Parameters ◽  
Estimating Function ◽  
Method Of Moment ◽  
Poisson Distributions

There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.

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