Search

The study proposed and compared the biased estimators for the Poisson-Inverse Gaussian regression model to deal with correlated regressors. The limitations of each biased estimator are also discussed. Additionally, some biasing parameters for the Stein estimator are proposed. The performance of estimators is evaluated with the help of a simulation study and a real-life application based on the minimum mean squared error criterion. The simulation and application findings favor the ridge estimator with specific biasing parameters because it provides less variation than others.

The Zero-inflated negative binomial (ZINB) regression models are commonly used for count data that shows an over-dispersion and extra zeros. Multicollinearity is considered to be a significant issue in the estimation of parameters in the ZINB regression model. Thus, to alleviate the negative effects of multicollinearity, a new estimator called ZINB modified ridge type (ZINBMRT) estimator is proposed. Furthermore, we proposed some new approaches to estimate the shrinkage parameters for the ZINBMRT estimator. A Monte Carlo simulation study and illustrative example are given to show the superiority of the proposed ZINBMRT estimator over some of the existing estimation methods. Based on the findings of simulation study and example, it is observed that the proposed ZINBMRT estimator under different suggested parameters give a better performance over the other competitive estimators. [ABSTRACT FROM AUTHOR]

AbstractThis study focuses on parameter estimation in the presence of multicollinearity for the count response that follows the Waring distribution. The Waring regression model deals with over-dispersion. So, this study proposed the Waring ridge regression (WRR) model as a solution for multicollinearity with over-dispersion. We conducted a theoretical comparison between the ridge estimator and the maximum likelihood estimators using matrix and scalar mean squared error as a performance evaluation criterion. Several ridge parameters are considered for the WRR estimator. The performance of these parameters is numerically evaluated using a Monte Carlo simulation study and a real application. The results of the simulation and application demonstrate the superiority of the WRR model with different ridge parameters over the maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

The logistic regression model is applied in situations when the response variable is of binary nature and follows the Bernoulli distribution. The maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the logistic regression. However, in the presence of multicollinearity, MLE is not a reliable estimation method due to its large variance and high standard errors. To overcome this problem, we consider the logistic ridge regression estimator (LRRE) under different link functions. Moreover, we also propose some ridge parameters for the LRRE and compare the performance of these ridge parameters with the available best ones. A Monte Carlo simulation study and a real dataset are considered for the evaluation of LRRE using scalar mean squared error as performance evaluation criteria. The simulation results indicate the superiority of the LRRE with a specified link function over the MLE in the presence of multicollinearity. From the simulation and real data application results, it is observed that the LRRE with ridge parameters k_8 and k_9 under logit and probit link functions is superior to the other ridge parameters with other link functions. [ABSTRACT FROM AUTHOR]

One of the flexible count data models for dealing with over and under-dispersion with extra zeroes is the zero-inflated Conway–Maxwell Poisson (ZICOMP). The ZICOMP regression coefficients are generally estimated using the maximum likelihood estimator (MLE). In the ZICOMP regression model, when the explanatory variables are correlated, the MLE does not give efficient results. To overcome the effect of multicollinearitymode in the ZICOPM regression, we proposed the ridge regression estimator. To evaluate the performance of the estimator, we use mean squared error (MSE) as the performance evaluation criteria. A theoretical comparison of the ridge estimator with MLE is made to show the superiority of the estimator. The proposed estimator is evaluated with the help of a simulation study and a real application. The results of the simulation study and real application show the superiority of the proposed estimator because it produces a smaller MSE as compared to the MLE. [ABSTRACT FROM AUTHOR]

The quasi-Poisson regression model is used for count data and is preferred over the Poisson regression model in the case of over-dispersed count data. The quasi-likelihood estimator is used to estimate the regression coefficients of the quasi-Poisson regression model. The quasi-likelihood estimator gives sub-optimal estimates if regressors are highly correlated—multicollinearity issue. Biased estimation methods are often used to overcome the multicollinearity issue in the regression model. In this study, we explore the ridge estimator for the quasi-Poisson regression model to mitigate the multicollinearity issue. Furthermore, we propose various ridge parameter estimators for this model. We derive the theoretical properties of the ridge estimator and compare its performance with the quasi-likelihood estimator in terms of matrix and scalar mean squared error. We further compared the proposed estimator numerically through a Monte Carlo simulation study and a real-life application. We found that both the simulation and application results show the superiority of the ridge estimator, particularly with the best ridge parameter estimator, over the quasi-likelihood estimator in the presence of multicollinearity issue. [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]

The ridge regression estimator (RRE) is a widely used estimation method for the multiple linear regression model when the explanatory variables are correlated. The situation becomes problematic for the RRE when the data set contains outliers in the y-direction. The use of the RRE in the presence of outliers may have some adverse effects on parameter estimates. To address this issue, the robust ridge estimators based on M-estimator are available in the literature which are less sensitive to the presence of outliers. It is a well-known fact that the selection of ridge parameter k is very crucial while using the RRE and the same phenomenon may happen in the case of robust ridge estimators. This study proposes some robust ridge estimators for the ridge parameter k. The performance of proposed estimators is evaluated with the help of the Monte Carlo simulations and a real application where the mean squared error (MSE) is considered as a performance evaluation criterion. Results show a better performance of the proposed robust ridge estimators as compared to the RRE, least square and M-estimation methods. While for modified ridge M-estimator, different ridge parameters found to be better for different conditions. [ABSTRACT FROM AUTHOR]

The gamma regression model (GRM) is commonly used if the response variable is continuous and positively skewed. In the existence of multicollinearity problem, maximum likelihood estimator (MLE) is inadequate for estimating the GRM coefficients. To avoid this issue, well-known estimators such as, ridge and Liu are generally used. In this study, we propose the generalized class of biased estimators, namely generalized ridge, and generalized Liu estimators for the GRM with correlated explanatory variables. The standard properties of the proposed estimators are derived and illustrated using Monte Carlo simulation study and two real applications where mean squared error is considered as an assessment criterion. Based on the findings of simulation and empirical applications, we found that the performance of the generalized gamma ridge regression estimator is better as compared to MLE, and generalized gamma Liu estimator. [ABSTRACT FROM AUTHOR]

In multiple linear regression models, the explanatory variables should be uncorrelated within each other but this assumption is violated in most of the cases. Generally, ordinary least square (OLS) estimator produces larger variances when explanatory variables are highly multicollinear. So, in this paper, we propose some new ridge parameters under Bayesian perspective relative to different loss functions, using Tierney and Kadane (T-K) approximation technique to overcome the effect of multicollinearity. We conduct the simulation study to compare the performance of the proposed estimators with OLS estimator and ordinary ridge estimator with some available best ridge parameters using mean squared error as the performance evaluation criterion. A real application is also consider to show the superiority of proposed estimators against competitive estimators. Based on the results of simulation and real application, we conclude that Bayesian ridge parameter estimated under general entropy loss function is better as compared to the OLS estimator and ordinary ridge estimator, when explanatory variables are small. This statement is also true for larger explanatory variables with small sample size. While for larger sample sizes and explanatory variables, the ordinary ridge estimator with best ridge parameter gives the better performance as others. [ABSTRACT FROM AUTHOR]

Influential observations influence the Poisson regression model (PRM) inferences. There are the situations in the PRM, where the explanatory variables are correlated and influential observations occurs simultaneously. So the Poisson ridge regression model (PRRM) is proposed to reduce the effect of multicollinearity. This study proposes some influence diagnostics for the PRRM to identify the influential observations. The performance of proposed PRRM diagnostic methods is evaluated through Monte Carlo simulation study and two real applications. The simulation and real applications results show the superiority of proposed diagnostic methods over maximum likelihood estimation based diagnostic methods. [ABSTRACT FROM AUTHOR]

The two-parameter estimator (TPE) was proposed for the Poisson regression model. It has the limitation of a single parameter. Contrary to this, count data models often exhibit the problems of dispersion and multicollinearity. The Conway–Maxwell–Poisson regression model (COMPRM) is suitable to handle both the dispersion and the multicollinearity issues simultaneously. The TPE for COMPRM is proposed to overcome these issues. In order to estimate the COMPRM co-efficient, the method of iterative reweighted least square (IRLS) is used. The efficiency of the estimator is evaluated in terms of mean square error (MSE) through a Monte Carlo simulation study. In the presence of multicollinearity, mostly the Asar and Genc's two-parameter estimator (AGTPE) gives more efficient results for COMPRM as compared to the maximum likelihood (MLE), the Ridge estimator, the Liu estimator and the TPE by Huang and Yang (HYTPE). The proposed estimator is also being studied for real-life application. [ABSTRACT FROM AUTHOR]

The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in the interval (0, 1), such as rates, proportions, percentages and fractions. Generally, the parameters of the BRM are estimated by the method of maximum likelihood estimation (MLE). However, the MLE does not offer accurate and reliable estimates when the explanatory variables in the BRM are correlated. To solve this problem, the ridge and Liu estimators for the BRM were proposed by different authors. In the current study, the James Stein Estimator (JSE) for the BRM is proposed. The matrix mean squared error (MSE) and the scalar MSE properties are derived and then compared to the available ridge estimator, Liu estimator and MLE. The performance of the proposed estimator is evaluated by conducting a simulation experiment and analyzing two real-life applications. The MSE of the estimators is considered as a performance evaluation criterion. The findings of the simulation experiment and applications indicate the superiority of the suggested estimator over the competitive estimators for estimating the parameters of the BRM. [ABSTRACT FROM AUTHOR]

The Gamma Regression Model (GRM) has a variety of applications in medical sciences and other disciplines. The results of the GRM may be misleading in the presence of multicollinearity. In this article, a new biased estimator called James-Stein estimator is proposed to reduce the impact of correlated regressors for the GRM. The mean squared error (MSE) properties of the proposed estimator are derived and compared with the existing estimators. We conducted a simulation study and employed the MSE and bias evaluation criterion to judge the proposed estimator's performance. Finally, two medical dataset are considered to show the benefit of the proposed estimator over existing estimators. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation for the inverse Gaussian regression model (IGRM) in the presence of multicollinearity. The inverse Gaussian modified ridge-type estimator (IGMRTE) is developed for efficient parameter estimation and compared with other estimation methods such as the maximum likelihood estimator (MLE), ridge and Liu estimator. We derived the properties of the proposed estimator and conducted a theoretical comparison with some of the existing estimators using the matrix mean squared error and mean squared error criterions. Furthermore, the statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation study under different conditions. The findings of the simulation study demonstrate that the proposed IGMRTE showed a much more robust behavior in the presence of severe multicollinearity. A real life example is also analyzed to evaluate the effectiveness of the estimators under study. Both the simulation and the application results confirm the use of IGMRTE for the estimation of unknown regression coefficients of the IGRM when the explanatory variables are highly correlated. [ABSTRACT FROM AUTHOR]

The Poisson Inverse Gaussian Regression model (PIGRM) is used for modeling the count datasets to deal with the issue of over-dispersion. Generally, the maximum likelihood estimator (MLE) is used to estimate the PIGRM estimates. In the PIGRM, when the explanatory variables are correlated, the MLE does not provide efficient results. To overcome this problem, we propose a ridge estimator for the PIGRM. The matrix mean square error (MSE) and the scalar MSE properties are derived and then compared with the MLE. In the ridge estimator, ridge parameter play a significant role, so, this study also proposes different ridge parameter estimators for the PIGRM. The performance of the proposed estimator is evaluated with the help of a simulation study and a real-life application using MSE as a performance evaluation criterion. The simulation study and the real-life application results show the superiority of the proposed parameter estimators as compared to the MLE. [ABSTRACT FROM AUTHOR]

The bell regression is used, when the response variable is in the form of counts with over dispersion. The bell regression coefficients are generally estimated using the maximum likelihood estimator (MLE). It is known that the performance of the traditional MLE is very sensitive to multicollinearity. Therefore, we propose a Bell ridge regression (BRR) as a solution to the multicollinearity problems. For the assessment of BRR, we conduct a Monte Carlo simulation study to monitor the performance of the proposed estimator where the mean squared error (MSE) is considered as an evaluation criterion. Also, two real examples are included to show the superiority of the BRR estimator. [ABSTRACT FROM AUTHOR]

The binary logistic regression model (LRM) is practical in situations when the response variable (RV) is dichotomous. The maximum likelihood estimator (MLE) is generally considered to estimate the LRM parameters. However, in the presence of multicollinearity (MC), the MLE is not the correct choice due to its inflated standard deviation (SD) and standard errors (SE) of the estimates. To combat MC, commonly used biased estimators, i.e., the Ridge estimators (RE) and Liu estimators (LEs), are preferred. However, most of the time, the traditional LE attains a negative value for its Liu parameter (LP), which is considered to be a major drawback. Therefore, to overcome this issue, we proposed a new adjusted LE for the binary LRM. Owing to numerical evaluation purposes, Monte Carlo simulation (MCS) study is performed under different conditions where bias and mean squared error are the performance criteria. Findings showed the superiority of our proposed estimator in comparison with the other estimation methods due to the existence of high but imperfect multicollinearity, which clearly means that it is consistent when the regressors are multicollinear. Furthermore, the findings demonstrated that whenever there is MC, the MLE is not the best choice. Finally, a real application is being considered to be evidence for the advantage of the intended estimator. The MCS and the application findings pointed out that the considered adjusted LE for the binary logistic regression model is a more efficient estimation method whenever the regressors are highly multicollinear. [ABSTRACT FROM AUTHOR]

Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this study, we proposed the Logistic Kibria-Lukman estimator (LKLE) to handle multicollinearity for the logistic regression model. We theoretically established the superiority condition of this new estimator over the MLE, the logistic ridge estimator (LRE), the logistic Liu estimator (LLE), the logistic Liu-type estimator (LLTE) and the logistic two-parameter estimator (LTPE) using the mean squared error criteria. The theoretical conditions were validated using a real-life dataset, and the results showed that the conditions were satisfied. Finally, a simulation and the real-life results showed that the new estimator outperformed the other considered estimators. However, the performance of the estimators was contingent on the adopted shrinkage parameter estimators. [ABSTRACT FROM AUTHOR]

The inverse Gaussian regression model (IGRM) is frequently applied in the situations, when the response variable is positively skewed and well fitted to the inverse Gaussian distribution. The maximum likelihood estimator (MLE) is generally used to estimate the unknown regression coefficients of the IGRM. The performance of the MLE method is better if the explanatory variables are uncorrelated with each other. But the presence of multicollinearity generally inflates the variance and standard error of the MLE resulting the loss of efficiency of estimates. So, for the estimation of unknown regression coefficients of the IGRM, the MLE is not a trustworthy method. To combat multicollinearity, we propose two parameter estimators (TPE) for the IGRM to improve the efficiency of estimates. Moreover, mean squared error criterion is taken into account to compare the performance of TPE with other biased estimators and MLE using Monte Carlo simulation study and a real example. Based on the results of Monte Carlo simulation study and a real example, we may suggest that the TPE based on Asar and Genç method for the IGRM is better than the other competitive estimators. [ABSTRACT FROM AUTHOR]

In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods. [ABSTRACT FROM AUTHOR]

The Poisson regression model (PRM) aims to model a counting variable y, which is usually estimated by using maximum likelihood estimation (MLE) method. The performance of MLE is not satisfactory in the presence of multicollinearity. Therefore, we propose a Poisson James-Stein estimator (PJSE) as a solution to the problems of inflated variance and standard error of MLE with multicollinear explanatory variables. For assessing the superiority of proposed estimator, we present a theoretical comparison based on the matrix mean squared error (MMSE) and scalar mean squared error (MSE) criterions. A Monte Carlo simulation study is performed under different conditions in order to investigate the performance of the proposed estimator where MSE is considered as an evaluation criterion. In addition, an aircraft damage data is also considered to assess the superiority of proposed estimator. Based on the results of simulation and real data application, it is shown that the PJSE outperforms the classical MLE and other biased estimation methods in a sense of minimum MSE criterion. [ABSTRACT FROM AUTHOR]

The Zero‐inflated negative binomial (ZINB) regression models are mainly applied for count data that shows over‐dispersion and extra zeros. Multicollinearity is considered to be a significant problem in the estimation of parameters in the ZINB regression model. Thus, in order to alleviate the serious effects of multicollinearity, a new estimator is proposed which is called ZINB Stein estimator (ZINBSE). We also proposed various biasing parameters for the ZINBSE. A theoretical comparison is also conducted with some existing estimators in the literature. A Monte Carlo simulation study has been considered in order to judge the superiority of the proposed and other estimators, where the estimated mean squared error and mean absolute error are the evaluation criterion. An empirical application is also considered for illustration purposes. Based on the simulation and application results, it is observed that the new ZINBSE with proposed biasing parameters are superior over the other competitors' estimators. [ABSTRACT FROM AUTHOR]

The beta regression model (BRM) is appropriate when the response variable is continuous and is in the form of ratios and proportions. For the estimation of the BRM, the maximum likelihood estimation (MLE) method is used with a specific link function. However, the MLE provides unstable results when the explanatory variables are correlated. In this study, we consider some ridge parameters for the beta ridge regression estimator (BRRE) under different link functions. However, mostly the researchers do not pay much attention to the suitable link function. So, we consider five link functions to see the performance of ridge parameters in the BRRE. For the performance assessment of ridge parameters and different link functions, a Monte Carlo simulation and a real application are considered, where mean squared error is used as the evaluation criterion. Both the simulation and example findings demonstrate that the BRRE with the log–log link function provides efficient results. [ABSTRACT FROM AUTHOR]

The maximum likelihood estimator (MLE) is generally used to estimate the Conway Maxwell Poisson regression model (COMPRM). When the explanatory variables are highly correlated, then the MLE results are not valid. In this study, we proposed a modified one-parameter Liu estimator in the presence of multicollinearity among the regressors for the COMPRM. The theoretical properties of the proposed estimator are derived and compared it with the available biased estimators as well as the MLE based on the matrix mean squared error (MSE) and scalar MSE criteria. To investigate the efficiency of the proposed estimator, a Monte Carlo simulation analysis was performed under various controlled conditions. Finally, two real applications are considered in the superiority of the proposed estimator. The simulation and real applications results show that the proposed estimator outperforms the classical MLE and other biased estimators in terms of the minimum MSE and mean absolute error criterion. [ABSTRACT FROM AUTHOR]

The inverse Gaussian regression model (IGRM) is applied when the response variable y is continuous, positively skewed and well fitted to the inverse Gaussian distribution. In the presence of multicollinearity, the maximum likelihood estimation (MLE) is not a right choice. Therefore, we proposed a new estimator called the principal component ridge estimator for the IGRM which combines the principal component estimator and the ridge estimator. We also consider a two-parameter estimator (TPE) and other biased estimators to see a clear image of our proposed estimator. A Monte Carlo simulation study is also presented to examine the performance of the proposed estimators. Furthermore, we analysed a dataset to assess the superiority of the proposed estimator. Based on the simulation and application results, it is evident that the proposed estimator dominates the classical MLE, and other considered biased estimation methods. [ABSTRACT FROM AUTHOR]

This article introduces the almost unbiased gamma ridge regression estimator (AUGRRE) estimator based on the gamma ridge regression estimator (GRRE). Furthermore, some shrinkage parameters are proposed for the AUGRRE. The performance of the AUGRRE by using different shrinkage parameters is compared with the existing GRRE and maximum likelihood estimator. A Monte Carlo simulation is carried out to assess the performance of the estimators where the bias and mean squared error performance criteria are used. We also used a real-life dataset to demonstrate the benefit of the proposed estimators. The simulation and real-life example results show the superiority of AUGRRE over the GRRE and the maximum likelihood estimator for the gamma regression model with collinear explanatory variables. [ABSTRACT FROM AUTHOR]

In linear regression modeling, the presence of multicollinearity among the explanatory variables has undesirable effects on the maximum likelihood estimator (MLE). To overcome this effect, we proposed some new ridge parameters under Bayesian paradigm. Moreover, we also compare these ridge parameters with Bayesian approach under different loss functions. To access the performance of new ridge parameters, we conduct a Monte Carlo simulation study where mean squared error (MSE) is considered as an evaluation criterion. In addition, a real life example is also provided to assess the superiority of the proposed estimators on the basis of MSE and cross-validation approaches. The simulation and real application results show that the Bayesian ridge parameter estimated under Precautionary loss function is better as compared to the other loss functions as well as the MLE and ordinary ridge regression estimator. [ABSTRACT FROM AUTHOR]

In this article, we propose a restricted gamma ridge regression estimator (RGRRE) by combining the gamma ridge regression (GRR) and restricted maximum likelihood estimator (RMLE) to combat multicollinearity problem for estimating the parameter β in the gamma regression model. The properties of the new estimator are discussed, and its superiority over the GRR, RMLE and traditional maximum likelihood estimator is theoretically analysed under different conditions. We also suggest some estimating methods to find the optimal value of the shrinkage parameter. A Monte Carlo simulation study is conducted to judge the performance of the proposed estimator. Finally, an empirical application is analysed to show the benefit of RGRRE over the existing estimators. [ABSTRACT FROM AUTHOR]

The Gamma ridge regression estimator (GRRE) is commonly used to solve the problem of multicollinearity, when the response variable follows the gamma distribution. Estimation of the ridge parameter estimator is an important issue in the GRRE as well as for other models. Numerous ridge parameter estimators are proposed for the linear and other regression models. So, in this study, we generalized these estimators for the Gamma ridge regression model. A Monte Carlo simulation study and two real-life applications are carried out to evaluate the performance of the proposed ridge regression estimators and then compared with the maximum likelihood method and some existing ridge regression estimators. Based on the simulation study and real-life applications results, we suggest some better choices of the ridge regression estimators for practitioners by applying the Gamma regression model with correlated explanatory variables. [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]

Recently, the Bell regression model (BRM) is proposed to model a count variable. The BRM is generally preferred over the Poisson regression model to overcome the restriction that the mean is equal to the variance. The BRM is usually estimated using the maximum likelihood estimator (MLE). It is a well-known phenomenon that the MLE is very sensitive to multicollinearity. We propose a Bell Liu regression (BLR) estimator to circumvent the problem of multicollinearity associated with the BRM. Moreover, some new Liu parameters are proposed for the BLR estimator. To evaluate the performance of the proposed estimators, we conduct a Monte Carlo simulation study where the mean squared error is considered as an evaluation criterion. In addition, a real application is also included to show the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In data analysis, count data modeling contributing a significant role. The Conway‐Maxwell Poisson (COMP) is one of the flexible count data models to deal over and under dispersion. In the COMP regression model, when the explanatory variables are correlated, then the maximum likelihood estimator does not give efficient results due to the large standard error (SE) of the estimates. To overcome the effect of multicollinearity, we have proposed some ridge regression estimators in the COMP regression model by introducing dispersion parameter in the context of overdispersion, equidispersion, and underdispersion. The Iterative reweighted least method is used for the estimation of ridge regression coefficients in the COMP regression model. To evaluate the performance of the proposed estimators, we use mean squared error (MSE) as the performance evaluation criteria. Theoretical comparison of the proposed estimators with the competitor estimators is made and conditions of efficiency have been derived. The proposed estimator is evaluated with the help of a simulation study and two real applications. The results of the simulation study and real applications show the superiority of the proposed estimator because the proposed estimator produces smaller MSE and SEs of the COMP regression estimates with multicollinearity. [ABSTRACT FROM AUTHOR]

Summary: The Poisson regression model (PRM) is usually applied in the situations when the dependent variable is in the form of count data. For estimating the unknown parameters of the PRM, maximum likelihood estimator (MLE) is commonly used. However, its performance is suspected when the regressors are multicollinear. The performance of MLE is not satisfactory in the presence of multicollinearity. To mitigate this problem, different biased estimators are discussed in the literature, that is, ridge and Liu. However, the drawback of using the traditional Liu estimator is that in most of the times, the shrinkage parameter d, attains a negative value which is the major disadvantage of traditional Liu estimator. So, to overcome this problem, we propose a new adjusted Poisson Liu estimator (APLE) for the PRM which is the robust solution to the problem of multicollinear explanatory variables. For assessment purpose, we perform a theoretical comparison with other competitive estimators. In addition, a Monte Carlo simulation study is conducted to show the superiority of the new estimator. At the end, two real life applications are also considered. From the findings of simulation study and two empirical applications, it is observed that the APLE is the most robust and consistent estimation method as compared to the MLE and other competitive estimators. [ABSTRACT FROM AUTHOR]

There is a long history of interest in modeling Poisson regression in different fields of study. The focus of this work is on handling the issues that occur after modeling the count data. For the prediction and analysis of count data, it is valuable to study the factors that influence the performance of the model and the decision based on the analysis of that model. In regression analysis, multicollinearity and influential observations separately and jointly affect the model estimation and inferences. In this article, we focused on multicollinearity and influential observations simultaneously. To evaluate the reliability and quality of regression estimates and to overcome the problems in model fitting, we proposed new diagnostic methods based on Sherman–Morrison Woodbury (SMW) theorem to detect the influential observations using approximate deletion formulas for the Poisson regression model with the Liu estimator. A Monte Carlo method is done for the assessment of the proposed diagnostic methods. Real data are also considered for the evaluation of the proposed methods. Results show the superiority of the proposed diagnostic methods in detecting unusual observations in the presence of multicollinearity compared to the traditional maximum likelihood estimation method. [ABSTRACT FROM AUTHOR]

The influential observation affects the regression model inferences. Literature has shown that the problems of multicollinearity and influential observations can jointly exist in a model. The ridge regression estimator has been developed to handle the challenge of multicollinearity. The detection of influential observations with multicollinearity and its impact on the ridge estimates is necessary for better decision making. In this article, we proposed some influence diagnostics for the inverse Gaussian ridge regression model (IGRRM). The proposed diagnostics are evaluated with the help of a simulation study and two chemometric‐related data sets. We found that the covariance ratio (CVR) method is better than other methods for the detection of influential observations under smaller dispersion. While for larger dispersion, all the IGRRM diagnostics perform equally well for the identification of influential observations. This study focuses on the proposal of influence diagnostic methods for the inverse Gaussian ridge regression model. Monte Carlo simulation study and two chemometric data sets are considered for the evaluation of proposed influence diagnostic methods. Results show that the covariance ratio method gives the better performance as compared with the other methods under smaller dispersion. [ABSTRACT FROM AUTHOR]

This article introduces some Liu parameters in the linear regression model based on the work of Shukur, Månsson, and Sjölander. These methods of estimating the Liu parameter d increase the efficiency of Liu estimator. The comparison of proposed Liu parameters and available methods has done using Monte Carlo simulation and a real data set where the mean squared error, mean absolute error and interval estimation are considered as performance criterions. The simulation study shows that under certain conditions the proposed Liu parameters perform quite well as compared to the ordinary least squares estimator and other existing Liu parameters. [ABSTRACT FROM AUTHOR]

The Inverse Gaussian Regression Model (IGRM) is used when the response variable is positively skewed and follows the inverse Gaussian distribution. In this article, we propose a Liu-type estimator to combat multicollinearity in the IGRM. The variance of the Maximum Likelihood Estimator (MLE) is overstated due to the presence of severe multicollinearity. Moreover, some estimation methods are suggested to estimate the optimal value of the shrinkage parameter. The performance of the proposed estimator is compared with the MLE and some other existing estimators in the sense of mean squared error through Monte Carlo simulation and different real-life applications. Under certain conditions, it is concluded that the proposed estimator is superior to the MLE, ridge, and Liu estimator. [ABSTRACT FROM AUTHOR]

In this article, we proposed some influence diagnostics for the gamma regression model (GRM) and the gamma ridge regression model (GRRM). We assess the impact of influential observations on the GRM and GRRM estimates by extending the work of Pregibon [Logistic regression diagnostics. Ann Stat. 1981;9:705-724] and Walker and Birch [Influence measures in ridge regression. Technometrics. 1988;30:221-227]. Comparison of both models is made and demonstrated with the help of a simulation study and a real data set. We report some momentous results in detecting the influential observations and their effects on the GRM and GRRM estimates. [ABSTRACT FROM AUTHOR]

The maximum likelihood (ML) method is used to estimate the unknown Gamma regression (GR) coefficients. In the presence of multicollinearity, the variance of theMLmethod becomes overstated and the inference based on the ML method may not be trustworthy. To combat multicollinearity, the Liu estimator has been used. In this estimator, estimation of the Liu parameter d is an important problem. A few estimation methods are available in the literature for estimating such a parameter. This study has considered some of these methods and also proposed some new methods for estimation of the d. The Monte Carlo simulation study has been conducted to assess the performance of the proposed methods where the mean squared error (MSE) is considered as a performance criterion. Based on the Monte Carlo simulation and application results, it is shown that the Liu estimator is always superior to the ML and recommendation about which best Liu parameter should be used in the Liu estimator for the GR model is given. [ABSTRACT FROM AUTHOR]

In agriculture and related fields many relationships exist that need to be identified in quantitative way. Regression modeling plays an important role for the determination of such relationships and also the isolation of factors that greatly affect the target or response variable. For reliable and valid results, one has to check the regression assumptions like influential observations, multicollinearity etc. In this study, we have fitted the regression models with and without satisfying the some regression assumptions for the identification of cotton yield factors. For the analysis purposes, the required data was collected from the district Khanewal. It was observed when regression assumptions were satisfied, model goodness (r²) was improved from 68% to 92%, r² (adjusted) was improved from 62% to 90%) and standard error of the estimates reduced from 8.298 to 2.348. These better results indicated that the pesticide used for seed, all type of fertilizers (DAP, potash and Ganwara), water frequency, and previously sown crops were the significant factors for cotton yield with p-values as less than 0.05. So cotton yield was 90% explained by these factors. [ABSTRACT FROM AUTHOR]