Developing a Liu‐type estimator in beta regression model

2021 ◽  
Author(s):  
Zakariya Yahya Algamal ◽  
Mohamed R. Abonazel
Keyword(s):  
Regression Model ◽  
Beta Regression ◽  
Beta 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.

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.

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 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.

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>

APPLICATION OF THE BETA REGRESSION MODEL ON THE NEUTRALIZATION INDEX OF POWER EQUIPMENT INSULATING OIL

2015 ◽  
Vol 35 (2) ◽  
Author(s):  
Charlene de C. Silva ◽  
Maria R. Madruga ◽  
Héliton R. Tavares ◽  
Terezinha F. de Oliveira ◽  
Augusto e C.F. Saraiva
Keyword(s):  
Regression Model ◽  
Beta Regression ◽  
Power Equipment ◽  
Insulating Oil ◽  
Neutralization Index ◽  
Beta Regression Model

scholarly journals Longitudinal assessment of utilities in patients with migraine: an analysis of erenumab randomized controlled trials

2019 ◽  
Vol 17 (1) ◽  
Author(s):  
Gian Luca Di Tanna ◽  
Joshua K. Porter ◽  
Richard B. Lipton ◽  
Anthony J. Hatswell ◽  
Sandhya Sapra ◽  
...  
Keyword(s):  
Regression Model ◽  
Linear Mixed Effect Model ◽  
Beta Regression ◽  
Response Model ◽  
Mixed Effect ◽  
Utility Values ◽  
Effect Model ◽  
Fractional Response ◽  
Probit Link ◽  
Beta Regression Model

Abstract Background Cost-effectiveness analyses in patients with migraine require estimates of patients’ utility values and how these relate to monthly migraine days (MMDs). This analysis examined four different modelling approaches to assess utility values as a function of MMDs. Methods Disease-specific patient-reported outcomes from three erenumab clinical studies (two in episodic migraine [NCT02456740 and NCT02483585] and one in chronic migraine [NCT02066415]) were mapped to the 5-dimension EuroQol questionnaire (EQ-5D) as a function of the Migraine-Specific Quality of Life Questionnaire (MSQ) and the Headache Impact Test (HIT-6™) using published algorithms. The mapped utility values were used to estimate generic, preference-based utility values suitable for use in economic models. Four models were assessed to explain utility values as a function of MMDs: a linear mixed effects model with restricted maximum likelihood (REML), a fractional response model with logit link, a fractional response model with probit link and a beta regression model. Results All models tested showed very similar fittings. Root mean squared errors were similar in the four models assessed (0.115, 0.114, 0.114 and 0.114, for the linear mixed effect model with REML, fractional response model with logit link, fractional response model with probit link and beta regression model respectively), when mapped from MSQ. Mean absolute errors for the four models tested were also similar when mapped from MSQ (0.085, 0.086, 0.085 and 0.085) and HIT-6 and (0.087, 0.088, 0.088 and 0.089) for the linear mixed effect model with REML, fractional response model with logit link, fractional response model with probit link and beta regression model, respectively. Conclusions This analysis describes the assessment of longitudinal approaches in modelling utility values and the four models proposed fitted the observed data well. Mapped utility values for patients treated with erenumab were generally higher than those for individuals treated with placebo with equivalent number of MMDs. Linking patient utility values to MMDs allows utility estimates for different levels of MMD to be predicted, for use in economic evaluations of preventive therapies. Trial registration ClinicalTrials.gov numbers of the trials used in this study: STRIVE, NCT02456740 (registered May 14, 2015), ARISE, NCT02483585 (registered June 12, 2015) and NCT02066415 (registered Feb 17, 2014).

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