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 Ridge-Type Estimator for the Gamma Regression Model

Scientifica ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Adewale F. Lukman ◽  
Issam Dawoud ◽  
B. M. Golam Kibria ◽  
Zakariya Y. Algamal ◽  
Benedicta Aladeitan
Keyword(s):  
Biological Activity ◽  
Regression Model ◽  
Mean Squared Error ◽  
Real Life ◽  
Regression Parameter ◽  
Likelihood Estimator ◽  
Response Variable ◽  
Explanatory Variables ◽  
Squared Error ◽  
The Mean

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

scholarly journals A new estimator for the multicollinear Poisson regression model: simulation and application

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adewale F. Lukman ◽  
Emmanuel Adewuyi ◽  
Kristofer Månsson ◽  
B. M. Golam Kibria
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Mean Squared Error ◽  
Model Simulation ◽  
Real Life ◽  
Poisson Regression Model ◽  
Squared Error ◽  
Damage Data ◽  
The Mean ◽  
Better Than

AbstractThe maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.

scholarly journals PMSE PERFORMANCE OF THE BIASED ESTIMATORS IN A LINEAR REGRESSION MODEL WHEN RELEVANT REGRESSORS ARE OMITTED

2002 ◽  
Vol 18 (5) ◽  
pp. 1086-1098 ◽  
Author(s):  
Akio Namba
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Positive Part ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Explicit Formulae ◽  
Biased Estimators

In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae for the predictive mean squared errors (PMSEs) of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the minimum mean squared error (MMSE) estimator, and the adjusted minimum mean squared error (AMMSE) estimator. It is shown analytically that the PSR estimator dominates the SR estimator in terms of PMSE even when there are omitted relevant regressors. Also, our numerical results show that the PSR estimator and the AMMSE estimator have much smaller PMSEs than the ordinary least squares estimator even when the relevant regressors are omitted.

scholarly journals Marginal quantile regression for longitudinal data analysis in the presence of time-dependent covariates

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
I-Chen Chen ◽  
Philip M. Westgate
Keyword(s):  
Parameter Estimation ◽  
Longitudinal Data ◽  
Quantile Regression ◽  
Mean Squared Error ◽  
Time Dependent ◽  
Regression Methods ◽  
Squared Error ◽  
Highly Correlated ◽  
Time Dependent Covariates ◽  
Independence Structure

AbstractWhen observations are correlated, modeling the within-subject correlation structure using quantile regression for longitudinal data can be difficult unless a working independence structure is utilized. Although this approach ensures consistent estimators of the regression coefficients, it may result in less efficient regression parameter estimation when data are highly correlated. Therefore, several marginal quantile regression methods have been proposed to improve parameter estimation. In a longitudinal study some of the covariates may change their values over time, and the topic of time-dependent covariate has not been explored in the marginal quantile literature. As a result, we propose an approach for marginal quantile regression in the presence of time-dependent covariates, which includes a strategy to select a working type of time-dependency. In this manuscript, we demonstrate that our proposed method has the potential to improve power relative to the independence estimating equations approach due to the reduction of mean squared error.

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 Dynamic Regression and Filtered Data Series: A Laplace Approximation to the Effects of Filtering in Small Samples

1996 ◽  
Vol 12 (3) ◽  
pp. 432-457 ◽  
Author(s):  
Eric Ghysels ◽  
Offer Lieberman
Keyword(s):  
Regression Model ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
Small Sample ◽  
Data Series ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Lagged Dependent Variable ◽  
Dynamic Regression Model

It is common for an applied researcher to use filtered data, like seasonally adjusted series, for instance, to estimate the parameters of a dynamic regression model. In this paper, we study the effect of (linear) filters on the distribution of parameters of a dynamic regression model with a lagged dependent variable and a set of exogenous regressors. So far, only asymptotic results are available. Our main interest is to investigate the effect of filtering on the small sample bias and mean squared error. In general, these results entail a numerical integration of derivatives of the joint moment generating function of two quadratic forms in normal variables. The computation of these integrals is quite involved. However, we take advantage of the Laplace approximations to the bias and mean squared error, which substantially reduce the computational burden, as they yield relatively simple analytic expressions. We obtain analytic formulae for approximating the effect of filtering on the finite sample bias and mean squared error. We evaluate the adequacy of the approximations by comparison with Monte Carlo simulations, using the Census X-11 filter as a specific example

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 Analysis of SF-6D Health State Utility Scores: Is Beta Regression Appropriate?

Healthcare ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 525
Author(s):  
Samer A Kharroubi
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Random Effects ◽  
Regression Models ◽  
Mean Squared Error ◽  
Health State Utility ◽  
Beta Regression ◽  
Health State ◽  
Linear Regression Models ◽  
Utility Scores

Background: Typically, modeling of health-related quality of life data is often troublesome since its distribution is positively or negatively skewed, spikes at zero or one, bounded and heteroscedasticity. Objectives: In the present paper, we aim to investigate whether Bayesian beta regression is appropriate for analyzing the SF-6D health state utility scores and respondent characteristics. Methods: A sample of 126 Lebanese members from the American University of Beirut valued 49 health states defined by the SF-6D using the standard gamble technique. Three different models were fitted for SF-6D via Bayesian Markov chain Monte Carlo (MCMC) simulation methods. These comprised a beta regression, random effects and random effects with covariates. Results from applying the three Bayesian beta regression models were reported and compared based on their predictive ability to previously used linear regression models, using mean prediction error (MPE), root mean squared error (RMSE) and deviance information criterion (DIC). Results: For the three different approaches, the beta regression model was found to perform better than the normal regression model under all criteria used. The beta regression with random effects model performs best, with MPE (0.084), RMSE (0.058) and DIC (−1621). Compared to the traditionally linear regression model, the beta regression provided better predictions of observed values in the entire learning sample and in an out-of-sample validation. Conclusions: Beta regression provides a flexible approach to modeling health state values. It also accounted for the boundedness and heteroscedasticity of the SF-6D index scores. Further research is encouraged.

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