scholarly journals Estimation of Beta Regression Model with Applied Study

2016 ◽  
Vol 12 (11) ◽  
pp. 6773-6777
Author(s):  
Hanaa Abd El Reheem Salem
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Regression Model ◽  
Bayesian Method ◽  
Numerical Study ◽  
Regression Coefficients ◽  
Beta Regression ◽  
Applied Study ◽  
The Mean ◽  
Beta Regression Model

This paper proposes a regression model where the dependent variable is beta distributed. Therefore the observations of the dependent variable must fall within (0,1) interval. This beta regression model produces two regression coefficients: one for the model of the mean and one for the model of the dispersion. Parameter estimation is performed by maximum likelihood and Bayesian method. Finally, numerical study is presented.

Flexible quasi-beta regression models for continuous bounded data

2018 ◽  
Vol 19 (6) ◽  
pp. 617-633 ◽  
Author(s):  
Wagner H Bonat ◽  
Ricardo R Petterle ◽  
John Hinde ◽  
Clarice GB Demétrio
Keyword(s):  
Regression Model ◽  
Regression Models ◽  
Beta Regression ◽  
Estimating Function ◽  
Dispersion Parameters ◽  
Linear Predictor ◽  
Mean And Variance ◽  
The Mean ◽  
Bounded Data ◽  
Beta Regression Model

We propose a flexible class of regression models for continuous bounded data based on second-moment assumptions. The mean structure is modelled by means of a link function and a linear predictor, while the mean and variance relationship has the form [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the mean, dispersion and power parameters respectively. The models are fitted by using an estimating function approach where the quasi-score and Pearson estimating functions are employed for the estimation of the regression and dispersion parameters respectively. The flexible quasi-beta regression model can automatically adapt to the underlying bounded data distribution by the estimation of the power parameter. Furthermore, the model can easily handle data with exact zeroes and ones in a unified way and has the Bernoulli mean and variance relationship as a limiting case. The computational implementation of the proposed model is fast, relying on a simple Newton scoring algorithm. Simulation studies, using datasets generated from simplex and beta regression models show that the estimating function estimators are unbiased and consistent for the regression coefficients. We illustrate the flexibility of the quasi-beta regression model to deal with bounded data with two examples. We provide an R implementation and the datasets as supplementary materials.

Skewness of maximum likelihood estimators in the varying dispersion beta regression model

2018 ◽  
Vol 48 (17) ◽  
pp. 4250-4260 ◽  
Author(s):  
Tiago M. Magalhães ◽  
Denise A. Botter ◽  
Mônica C. Sandoval ◽  
Gustavo H. A. Pereira ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Regression Model ◽  
Maximum Likelihood Estimators ◽  
Beta Regression ◽  
Varying Dispersion ◽  
Beta Regression Model

scholarly journals ESTIMATION OF THE BINARY LOGISTIC REGRESSION MODEL PARAMETER USING BOOTSTRAP RE-SAMPLING

2018 ◽  
Vol 48 (3) ◽  
pp. 199-204 ◽  
Author(s):  
R. LI ◽  
J. ZHOU ◽  
L. WANG
Keyword(s):  
Logistic Regression ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Regression Model ◽  
Logistic Regression Model ◽  
Binary Logistic Regression ◽  
Parametric Bootstrap ◽  
Binary Logistic Regression Model ◽  
Bayesian Bootstrap ◽  
Non Parametric

In this paper, the non-parametric bootstrap and non-parametric Bayesian bootstrap methods are applied for parameter estimation in the binary logistic regression model. A real data study and a simulation study are conducted to compare the Nonparametric bootstrap, Non-parametric Bayesian bootstrap and the maximum likelihood methods. Study results shows that three methods are all effective ways for parameter estimation in the binary logistic regression model. In small sample case, the non-parametric Bayesian bootstrap method performs relatively better than the non-parametric bootstrap and the maximum likelihood method for parameter estimation in the binary logistic regression model.

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.

scholarly journals Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1738
Author(s):  
Selvi Mardalena ◽  
Purhadi Purhadi ◽  
Jerry Dwi Trijoyo Purnomo ◽  
Dedy Dwi Prastyo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Poisson Regression ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Count Response ◽  
The Mean ◽  
Gaussian Regression ◽  
Response Variables

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors.

scholarly journals Contingent Valuation Method and the beta model: an accounting economic vision for environmental damage in Atlântico Sul Shipyard

2018 ◽  
Vol 29 (77) ◽  
pp. 266-282
Author(s):  
Silvana Karina de Melo Travassos ◽  
José Carlos de Lacerda Leite ◽  
Jose Isidio de Freitas Costa
Keyword(s):  
Regression Model ◽  
Contingent Valuation ◽  
Contingent Valuation Method ◽  
Measurement Techniques ◽  
Point Of View ◽  
Environmental Damage ◽  
Beta Regression ◽  
Accounting Measurement ◽  
Valuation Method ◽  
Beta Regression Model

ABSTRACT The objective of this paper is to apply the beta model as an alternative to the Valuation Method in order to estimate the environmental asset Willingness to Pay (WTP) so that the Tribunal de Contas do Estado de Pernambuco (TCE/PE) can supervise the Atlântico Sul Shipyard (ASS) as a negative environmental externality, which is discussed here from an accounting perspective. Our methodology is exploratory, and the beta regression model was used in the contingent valuation to estimate the environmental asset. The results allowed estimating the value of the Ipojuca mangrove at US$ 134,079,793.50, and the value of the environmental damage caused by the shipyard to the public asset was valued at US$ 61,378,155.37. This latter value is object of interest to the inspection body. However, the final estimated value of the Ipojuca mangrove prompts a discussion about the implications from an accounting point of view, such as the attribution of monetary value to a public asset that does not have a financial value, problems regarding the conceptualization and valuation of public assets for governmental patrimony. It is concluded that the beta regression model to estimate the WTP for contingent valuation will serve as a contribution to the research on accounting measurement techniques for public assets.

scholarly journals A new modified ridge-type estimator for the beta regression model: simulation and application

2021 ◽  
Vol 7 (1) ◽  
pp. 1035-1057
Author(s):  
Muhammad Nauman Akram ◽  
◽  
Muhammad Amin ◽  
Ahmed Elhassanein ◽  
Muhammad Aman Ullah ◽  
...  
Keyword(s):  
Regression Model ◽  
Mean Squared Error ◽  
Model Simulation ◽  
Beta Regression ◽  
Explanatory Variables ◽  
Squared Error ◽  
The Matrix ◽  
Biased Estimators ◽  
Highly Correlated ◽  
Beta Regression Model

<abstract> <p>The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.</p> </abstract>

scholarly journals A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2768
Author(s):  
Luis Sánchez ◽  
Víctor Leiva ◽  
Helton Saulo ◽  
Carolina Marchant ◽  
José M. Sarabia
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Quantile Regression ◽  
Regression Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Distributed Data ◽  
Quantile Regression Model ◽  
The Mean ◽  
Asymmetrically Distributed

Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.

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