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.

scholarly journals Binomial Regression Models with a Flexible Generalized Logit Link Function

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 221 ◽  
Author(s):  
Rindang Bangun Prasetyo ◽  
Heri Kuswanto ◽  
Nur Iriawan ◽  
Brodjol Sutijo Suprih Ulama
Keyword(s):  
Model Performance ◽  
Cumulative Distribution ◽  
Logistic Distribution ◽  
Link Function ◽  
Linear Predictor ◽  
New Class ◽  
Link Functions ◽  
Generalized Logistic Distribution ◽  
Proposed Model ◽  
Binomial Regression

In binomial regression, a link function is used to join the linear predictor variables and the expectation of the response variable. This paper proposes a flexible link function from a new class of generalized logistic distribution, namely a flexible generalized logit (glogit) link. This approach considers both symmetric and asymmetric models, including the cases of lighter and heavier tails, as compared to standard logistic. The glogit is created from the inverse cumulative distribution function of the exponentiated-exponential logistic (EEL) distribution. Using a Bayesian framework, we conduct a simulation study to investigate the model performance compared to the most commonly used link functions, e.g., logit, probit, and complementary log–log. Furthermore, we compared the proposed model with several other asymmetric models using two previously published datasets. The results show that the proposed model outperforms the existing ones and provides flexibility fitting the experimental dataset. Another attractive aspect of the model are analytically tractable and can be easily implemented under a Bayesian approach.

scholarly journals A ballooned beta-logistic model

2015 ◽  
Author(s):  
◽  
Min Yi
Keyword(s):  
Regression Model ◽  
Logistic Model ◽  
Finite Interval ◽  
Extreme Values ◽  
Logistic Function ◽  
Enzyme Linked Immunosorbent Assay ◽  
Unknown Parameters ◽  
And Gender ◽  
Boundary Estimates ◽  
Flexible Model

The beta distribution is a simple and flexible model in which responses are naturally confined to the finite interval (0,1). Its parameters can be related to covariates such as dose and gender through a regression model. The Ballooned Beta-logistic (BBL) model expands the response boundaries from (0,1) to (L,U), where L and U are unknown parameters. Under the BBL model, expected responses follow a logistic function which can be made equal to that of the Four Parameter Logistic (4PL) model. But the distribution of responses differs from the classical 4PL model which has additive normal errors. In contrast, the BBL model naturally has bounded responses and inhomogeneous variance. The asymptotic normality of maximum likelihood estimators (MLEs) is obtained even though the support of this non-regular regression model depends on unknown parameters. We find MLEs converge faster to L and U than do extreme values at the minimum and maximum concentrations. Given enzyme-linked immunosorbent assay data from different plates, we study a motivating validation objective, which is to set suitability criteria for estimates of L and U; after this plates with boundary estimates outside these limits would be considered ”reference failures”. We show the BBL model has advantages over the 4PL model.

scholarly journals On the Usefulness of the Logarithmic Skew Normal Distribution for Describing Claims Size Data

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
E. Gómez–Déniz ◽  
E. Calderín-Ojeda
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Empirical Data ◽  
Lognormal Distribution ◽  
Empirical Distribution ◽  
Skew Normal Distribution ◽  
Response Variable ◽  
Explanatory Variables ◽  
The Right ◽  
Size Data

In this paper, the three-parameter skew lognormal distribution is proposed to model actuarial data concerning losses. This distribution yields a satisfactory fit to empirical data in the whole range of the empirical distribution as compared to other distributions used in the actuarial statistics literature. To the best of our knowledge, this distribution has not been used in insurance context and it might be suitable for computing reinsurance premiums in situations where the right tail of the empirical distribution plays an important role. Furthermore, a regression model can be simply derived to explain the response variable as a function of a set of explanatory variables.

The Skew Normal Distribution

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Normal Distribution ◽  
Information Matrix ◽  
Standard Theory ◽  
Parameter Estimates ◽  
Skew Normal Distribution ◽  
True Parameter ◽  
Folded Normal Distribution ◽  
Natural Parametrization ◽  
Special Case ◽  
Skew Normal

This chapter considers the univariate skew-normal distribution, a generalization of the normal that includes the normal as a special case. The most natural parametrization is non-standard. This is because the Fisher information matrix is then singular at the true parameter value when the true model is the normal special case. The log-likelihood is then particularly flat in a certain coordinate direction. Standard theory cannot then be used to calculate the asymptotic distribution of all the parameter estimates. This problem can be handled using an alternative parametrization. There is another special case: the half/folded normal distribution. This occurs in the usual parametrization when the shape parameter is infinite. This is not a problem computationally and is easily handled. There are many generalizations to skew-t distributions and to tractable multivariate forms and regression versions. A very brief review is included of these.

Using numerical methods to design simulations: revisiting the balancing intercept

2021 ◽  
Author(s):  
Sarah E Robertson ◽  
Issa J Dahabreh ◽  
Jon A Steingrimsson
Keyword(s):  
Regression Model ◽  
Logistic Model ◽  
Numerical Approximation ◽  
Basic Problem ◽  
Random Variable ◽  
Analytical Approximation ◽  
Simulation Studies ◽  
Linear Predictor ◽  
Binary Random Variable ◽  
A Value

Abstract We consider methods for generating draws of a binary random variable whose expectation conditional on covariates follows a logistic regression model with known covariate coefficients. We examine approximations for finding a “balancing intercept,” that is, a value for the intercept of the logistic model that leads to a desired marginal expectation for the binary random variable. We show that a recently proposed analytical approximation can produce inaccurate results, especially when targeting more extreme marginal expectations or when the linear predictor of the regression model has high variance. We describe and implement a numerical approximation based on Monte Carlo methods that appears to work well in practice. Our approach to the basic problem of the balancing intercept provides an example of a broadly applicable strategy for formulating and solving problems that arise in the design of simulation studies used to evaluate or teach epidemiologic methods.

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.

A log Birnbaum–Saunders regression model based on the skew-normal distribution under the centred parameterization

2020 ◽  
Vol 13 (3) ◽  
pp. 335-346
Author(s):  
Nathalia L. Chaves ◽  
Caio L. N. Azevedo ◽  
Filidor Vilca-Labra ◽  
Juvêncio S. Nobre
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Model Based ◽  
Skew Normal

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.

Sign in / Sign up

Export Citation Format

Share Document