Search

The Bell regression model (BRM), a member of the generalized linear models (GLMs), can be used when the dependent variable consists of overdispersed count data. The maximum likelihood estimator (MLE) is generally used to estimate unknown regression coefficients. The major drawback of the MLE is an inflated variance when multicollinearity problems occur. In this study, we proposed a new biased estimator to cope with the multicollinearity in the BRM. The simulation study is conducted to illustrate the performance of the proposed estimator over the MLE and Bell ridge estimator (BRE). Also, we give real data examples to approve the applicability of the proposed estimator in real data problems. [ABSTRACT FROM AUTHOR]

Count regression models, particularly negative binomial regression (NBR), are widely used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely when dealing with count data, and NBR has gained attention as an effective tool to address this challenge. However, multicollinearity among covariates and the presence of outliers can lead to inflated confidence intervals and inaccurate predictions in the model. This study proposes a comprehensive approach integrating robust and regularization techniques to handle the simultaneous impact of multicollinearity and outliers in the negative binomial regression model (NBRM). We investigate the estimators' performance through extensive simulation studies and provide analytical comparisons. The simulation results and the theoretical comparisons demonstrate the superiority of the proposed robust hybrid KL estimator (M-NBKLE) with predictive accuracy and stability when multicollinearity and outliers exist. We illustrate the application of our methodology by analyzing a forestry dataset. Our findings complement and reinforce the simulation and theoretical results. [ABSTRACT FROM AUTHOR]

The regression model is one of the important quantitative structure-activity relationship (QSAR) model tools that is used chiefly in chemometrics studies. In chemometrics, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, then the inverse Gaussian regression model (IGRM) is a better choice QSAR model. Multicollinearity in the IGRM affects the IGRM estimation and inferences. To overcome the effect of multicollinearity, biased estimators such as ridge and Liu are discussed in the literature. However, the disadvantage of using the traditional Liu estimator is that the shrinkage parameter, d, returns a negative value that severely affects the estimator's performance. To mitigate this problem, we propose a new improved Liu estimator for the IGRM. The new estimator's performance is compared with the maximum likelihood estimator (MLE) and the other biased estimators. A Monte Carlo simulation study is conducted to assess the newly proposed estimator's performance under different parametric conditions. A QSAR chemometric application is also considered to see the clear picture of the proposed estimator. The simulation and QSAR application findings demonstrate that the newly proposed estimator consistently dominates the other competitive estimators in all the evaluated conditions. [ABSTRACT FROM AUTHOR]

Multicollinearity and unusual observations pose threats to the performance of maximum likelihood estimator in the gamma regression model. Literature has shown that both problems can exist simultaneously in a model. Researchers have paid little attention to the detection of influential observation in the gamma regression model with multicollinearity. This study aims to develop statistics for the detection of unusual observation in a multicollinear gamma regression model using gamma modified ridge-type estimator. The performance of the statistics was examined through a Monte Carlo simulation study and two real applications. The results show that gamma modified ridge-type estimator copes with unusual observations by reducing their influence. [ABSTRACT FROM AUTHOR]

Most studies on local rice in Nigeria were centred on increasing production, consumption or competitiveness with very few of them addressing the determinants of the price of rice in an economy. Filling this gap requires a study on the various factors that influence the price of rice. Food price instability is a frequent forerunner of macroeconomic shocks and political turmoil that can discourage long-run investment and curtail growth. In this study, secondary data were employed. The study used descriptive statistics tools to analyse the pattern of price variation over the period of 42 years in the study area. Similarly, various factors affecting price variation of rice were examined. The following recommendations were made: appropriate tax collection measures on producers should be implemented so as to curtail farmers from exploiting the masses by making excessive gains. Since the decrease in export results in an increase in price, the government should keep a balance between import and export to maintain the price of rice at a reasonable level. The price of rice can be reduced by the government when they implement measures to control the inflation rate in the economy. The government should put measures to regulate the quantity of land used by rice producers as well as to control the price of rice, since they both have a positive relationship.

Linear regression models with correlated regressors can negatively impact the performance of ordinary least squares estimators. The Stein and ridge estimators have been proposed as alternative techniques to improve estimation accuracy. However, both methods are non-robust to outliers. In previous studies, the M-estimator has been used in combination with the ridge estimator to address both correlated regressors and outliers. In this paper, we introduce the robust Stein estimator to address both issues simultaneously. Our simulation and application results demonstrate that the proposed technique performs favorably compared to existing methods. [ABSTRACT FROM AUTHOR]

A new two-parameter estimator was developed to combat the threat of multicollinearity for the linear regression model. Some necessary and sufficient conditions for the dominance of the proposed estimator over ordinary least squares (OLS) estimator, ridge regression estimator, Liu estimator, KL estimator, and some two-parameter estimators are obtained in the matrix mean square error sense. Theory and simulation results show that, under some conditions, the proposed two-parameter estimator consistently dominates other estimators considered in this study. The real-life application result follows suit. [ABSTRACT FROM AUTHOR]

The modified ridge-type estimator has been shown to cushion the effects of multicollinearity in the linear regression model. Recent studies have shown the adverse effects of multicollinearity in the gamma regression model (GRM). We proposed a gamma modified ridge-type estimator to tackle this problem. We derived the properties of this estimator and conducted a theoretical comparison with some of the existing estimators. A real-life example and simulation study show that the proposed estimator gains an advantage over other estimators in terms of the mean square error. [ABSTRACT FROM AUTHOR]

The Poisson regression model (PRM) is employed in modelling the relationship between a count variable (y) and one or more explanatory variables. The parameters of PRM are popularly estimated using the Poisson maximum likelihood estimator (PMLE). There is a tendency that the explanatory variables grow together, which results in the problem of multicollinearity. The variance of the PMLE becomes inflated in the presence of multicollinearity. The Poisson ridge regression (PRRE) and Liu estimator (PLE) have been suggested as an alternative to the PMLE. However, in this study, we propose a new estimator to estimate the regression coefficients for the PRM when multicollinearity is a challenge. We perform a simulation study under different specifications to assess the performance of the new estimator and the existing ones. The performance was evaluated using the scalar mean square error criterion and the mean squared error prediction error. The aircraft damage data was adopted for the application study and the estimators' performance judged by the SMSE and the mean squared prediction error. The theoretical comparison shows that the proposed estimator outperforms other estimators. This is further supported by the simulation study and the application result. [ABSTRACT FROM AUTHOR]

This study introduces a new biased estimator called the K‐L estimator for the linear mixed model to overcome the effect of multicollinearity. We derived the mean squared error property of the proposed estimator and made a theoretical comparison with other methods. For the assessment of the K‐L estimator, we use the mean squared error criterion as a performance evaluation criterion. Moreover, we defined some shrinkage parameters for the proposed estimator. For numerical evaluation, we use a Monte Carlo simulation study and a real example. The result shows the supremacy of the K‐L estimator as compared to the available methods under certain conditions. [ABSTRACT FROM AUTHOR]