Combating the Multicollinearity in Bell Regression Model: Simulation and Application

Shewa, G. A.; Ugwuowo, Fidelis Ifeayi

doi:10.46481/jnsps.2022.713

Cited by 6 publications

(3 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several authors have explored the use of this "Bell distribution", and its zero-inflated counterpart, in the context of regression analysis. For example, see Castellares et al (2018), Lemonte et al (2020), Abduljabbar and Algamal (2022), Abduljabbar et al (2022), Shewa and Ugwowo (2022), and Ertan et al (2023). While this application of the distribution is not our primary concern here, we present some results that relate to it.…”

Section: Introductionmentioning

confidence: 81%

The Performance of the Maximum Likelihood Estimator for the Bell Distribution for Count Data

David E. Giles

2024

JMASM

View full text Add to dashboard Cite

The single-parameter “Bell distribution” for discrete data allows for over-dispersion in the data. The maximum likelihood estimator for its parameter is downward-biased in finite samples. We consider various methods for reducing this bias. A simulation study shows that these are effective and also lead to a small improvement in the mean squared error of the estimator. The Cox-Snell correction is the recommended. choice among the options that are considered.

show abstract

Section: Introductionmentioning

confidence: 81%

The Performance of the Maximum Likelihood Estimator for the Bell Distribution for Count Data

David E. Giles

2024

JMASM

View full text Add to dashboard Cite

show abstract

“…For instance, literature has demonstrated multicollinearity, or the habitual existence of linear dependency among regressors [5]. The covariates have a propensity for perfect, strong, or moderate linear dependency [5,6]. When there is linear dependency among the covariates, the least squares technique is unbiased yet inefficient [7].…”

Section: Introductionmentioning

confidence: 99%

Robust weighted ridge regression based on S – estimator

Fayose,

Ayinde,

Alabi

et al. 2023

Afr. Sci. Rep.

View full text Add to dashboard Cite

Ordinary least squares (OLS) estimator performance is seriously threatened by correlated regressors often called multicollinearity. Multicollinearity is a situation when there is strong relationship between any two exogenous variables. In this case, the ridge estimator offers more reliable estimations when such scenario occurs. Outliers can have significant impact on the estimation of regression parameters leading to biased results. However, both OLS and Ridge estimators are sensitive to outlaying observations (outliers). The outlier – prone dataset in the endogenous variable has been efficiently solved utilizing the Robust M estimator in our recent paper. In recent studies, Robust M estimator has some drawbacks despite its efficient performances with outlier – prone dataset in the dependent (endogenous) variable hence the consideration of the Robust S estimator. The Robust S estimator is less sensitive to outliers in both endogenous and exogenous variables and utilizes standard deviation rather than the median in the case of Robust M estimator to handle outliers in the endogenous variable. The Robust ridge based on the S estimator was well suited to model dataset with multicollinearity and outliers problems in the endogenous variable. Also, it was noted in literature that outliers are one of the causes of heteroscedasticity and non – robust weighted least squares were initially employed to figure out for them. In this study, we introduced proposed Robust S weighted ridge estimator by adding a novel weighting method to address the three problems in a linear regression model. The selected Ridge estimators and Robust S estimator in two weighted versions (True weight (Wo) and suggested new weight (W1)) were combined to respectively develop the Robust S Ridge and Robust S Weighted Ridge estimators. Monte – Carlo simulation experiments were conducted on a linear regression model with three and six exogenous variables exhibiting different degrees of Multicollinearity, with heteroscedasticity structure of powers, size of outlier in endogenous variable and error variances and five levels of sample sizes. The Mean Square Error (MSE) was used as a criterion to evaluate the performances of the new and existing estimators. Simulation findings show categorically that the new approach is preferred over previous approach and hereby recommended.

show abstract

“…For instance, literature has shown that linear dependency frequently exists among regressors which are termed multicollinearity [5]. There is tendency for perfect or strong or moderate linear dependency among the regressors [5][6]. The method of least squares is unbiased but inefficient when there is linear dependency among the regressors [7].…”

Section: Introductionmentioning

confidence: 99%

M Robust Weighted Ridge Estimator in Linear Regression Model

Fayose,

Ayinde,

Alabi

2023

Afr. Sci. Rep.

View full text Add to dashboard Cite

Correlated regressors are a major threat to the performance of the conventional ordinary least squares (OLS) estimator. The ridge estimator provides more stable estimates in this circumstance. However, both OLS and Ridge estimators are sensitive to outlying observations. In previous studies, the robust ridge based on the M estimator suitably fit well to the model with multicollinearity and outliers in outcome variable. Since outlier is one of the sources of heteroscedasticity and the non – robust weighted least squares have been previously adopted to account for it. Therefore, this paper proposed and developed some novel estimators to handle three problems (multicollinearity, heteroscedasticity and outliers) simultaneously with the aim of identifying the most efficient (best) ones. The Ordinary Least Square (OLS) and M robust estimator in two weighted version (real weight (WO) and one estimated weight (W1)) were combined to respectively develop the M Robust Ridge and M Robust Weighted Ridge Estimators. Monte–Carlo simulation experiments were conducted on a linear regression model with three and six explanatory variables exhibiting different degrees of Multicollinearity, with heteroscedasticity structure of powers, magnitude of outlier in y direction and error variances and five levels of sample sizes. The Mean Square Error (MSE) was used as a criterion to evaluate the performances of the new and existing estimators. It is evident from the simulation results that the proposed estimators produced efficient estimates and hereby recommended.

show abstract

Combating the Multicollinearity in Bell Regression Model: Simulation and Application

Cited by 6 publications

References 24 publications

The Performance of the Maximum Likelihood Estimator for the Bell Distribution for Count Data

The Performance of the Maximum Likelihood Estimator for the Bell Distribution for Count Data

Robust weighted ridge regression based on S – estimator

M Robust Weighted Ridge Estimator in Linear Regression Model

Contact Info

Product

Resources

About