The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses (original) (raw)
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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.
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The 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.
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The problem of multicollinearity is often encountered in time series data since explanatory variables included in the model often share a common trend. Various methods exist in literatures to handle this problem. Among them is the most widely used ridge regression estimator which depends on the ridge parameter. This estimator can be subdivided into either generalized ridge or ordinary ridge estimators. Variance inflation factor is introduced to replace eigenvalue in the generalized ridge estimator proposed by Lawless and Wang (1976). Through this modification some new generalized ridge parameters are proposed and investigated via simulation study. The performances of these proposed estimators are compared with the existing ones using mean square error. Results show that the proposed estimators perform better than the existing ones. It is evident that increasing the level of multicollinearity and number of regressors has positive effect on the MSE. Also, the performance of the estima...
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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.