Assessing the Impact of Square Root Transformation on Weibull-Distributed Error Component of a Multiplicative Error Model
Issue:
Volume 9, Issue 4, August 2021
Pages:
94-105
Received:
8 July 2021
Accepted:
19 July 2021
Published:
27 July 2021
Abstract: This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality and non-equality. Considering the possibility that the error component of a Multiplicative Error Model (MEM) can be a Weibull distribution (W (σ, n)); σ and n are shape and scale parameters respectively) and the need for data transformation as a popular remedial measure to stabilize the variance of a data set prior to statistical modeling, this paper investigates the impact of the square root transformation on the mean and variance of a Weibull-distributed error component of a MEM. The mean and variance of W (σ, n) and those of the square root transformed distributions are calculated for σ= 6, 7,.., 99, 100 with the corresponding values of n for which the mean of the untransformed distribution is equal to one. The fitted MEM (2,0) under the square root transformation gave a better fit than the original fitted MEM (2,0). The paper concludes that the square-root transformation would yield better results as they reveal constancy in variance when using MEM with a Weibull-distributed error component and where data transformation is deemed necessary to stabilize the variance of the data set.
Abstract: This paper aims at determining if the assumed fundamental structure of the error component (unit mean and constant variance) is maintained after the square root transformation of a Weibull-distributed error component of a multiplicative model and also to investigate what happens to variance of the transformed and untransformed in terms of equality ...
Show More
On the Restricted Poisson Ridge Regression Estimator
Issue:
Volume 9, Issue 4, August 2021
Pages:
106-112
Received:
2 August 2021
Accepted:
19 August 2021
Published:
26 August 2021
Abstract: For modeling count data, the Poisson regression model is widely used in which the response variable takes non-negative integer values. However, the presence of strong correlation between the explanatory variables causes the problem of multicollinearity. Due to multicollinearity, the variance of the maximum likelihood estimator (MLE) will be inflated causing the parameters estimation to become unstable. Multicollinearity can be tackled by using biased estimators such as the ridge estimator in order to minimize the estimated variance of the regression coefficients. An alternative approach is to specify exact linear restrictions on the parameters in addition to regression model. In this paper, the restricted Poisson ridge regression estimator (RPRRE) is suggested to handle multicollinearity in Poisson regression model with exact linear restrictions on the parameters. In addition, the conditions of superiority of the suggested estimator in comparison to some existing estimators are discussed based on the mean squared error (MSE) matrix criterion. Moreover, a simulation study and a real data application are provided to illustrate the theoretical results. The results indicate that the suggested estimator, RPRRE, outperforms the other existing estimators in terms of scalar mean squared error (SMSE). Therefore, it is recommended to use the RPRRE for the Poisson regression model when the problem of multicollinearity is present.
Abstract: For modeling count data, the Poisson regression model is widely used in which the response variable takes non-negative integer values. However, the presence of strong correlation between the explanatory variables causes the problem of multicollinearity. Due to multicollinearity, the variance of the maximum likelihood estimator (MLE) will be inflate...
Show More
