Habshah Midi

Collinearity diagnostics of binary logistic regression model

Abstract Multicollinearity is a statistical phenomenon in which predictor variables in a logistic regression model are highly correlated. It is not uncommon when there are a large number of covariates in the model. Multicollinearity has been the thousand pounds monster in statistical modeling. Taming this monster has proven to be one of the great challenges of statistical modeling research. Multicollinearity can cause unstable estimates and inaccurate variances which affects confidence intervals and hypothesis tests. The existence of collinearity inflates the variances of the parameter estimates, and consequently incorrect inferences about relationships between explanatory and response variables. Examining the correlation matrix may be helpful to detect multicollinearity but not sufficient. Much better diagnostics are produced by linear regressionwith the option tolerance, Vif, condition indices and variance proportions. For moderate to large sample sizes, the approach to drop one of the correlated variables was established entirely satisfactory to reduce multicollinearity. On the light of different collinearity diagnostics, we may safely conclude that without increasing sample size, the second choice to omit one of the correlated variables can reduce multicollinearity to a great extent.

Preliminary estimators for robust non-linear regression estimation

In this paper, the robustness of weighted non-linear least-squares estimation based on some preliminary estimators is examined. The preliminary estimators are the Lnorm estimates proposed by Schlossmacher, by El-Attar et al., by Koenker and Park, and by Lawrence and Arthur. A numerical example is presented to compare the robustness of the weighted non-linear least-squares approach when based on the preliminary estimators of Schlossmacher (HS), El-Attar et al. (HEA), Koenker and Park (HKP), and Lawrence and Arthur (HLA). The study shows that the HEA estimator is as robust as the HKP estimator. However, the HEA estimator posed certain computational problems and required more storage and computing time.

Robust Multivariate Control Charts to Detect Small Shifts in Mean

The classical multivariate CUSUM and EWMA charts are commonly used to detect small shifts in the mean vectors. It is now evident that those charts are easily affected by outliers which may be due to small or moderate changes in the mean vector. In this paper, we propose a robust multivariate CUSUM and Robust multivariate EWMA charts to remedy the problem of small changed in scatter outliers. Both the empirical and simulation results indicate that the proposed robust multivariate CUSUM and EWMA charts offer substantial improvement over other multivariate CUSUM and EWMA charts. This article also discussed the robustness of the proposed charts, when there is a small or moderate sustained shift in the data set.

The performance of robust two-stage estimator in nonlinear regression with autocorrelated error.

Some statistics practitioners often ignore the underlying assumptions when analyzing a real data and employ the Nonlinear Least Squares (NLLS) method to estimate the parameters of a nonlinear model. In order to make reliable inferences about the parameters of a model, require that the underlying assumptions, especially the assumption that the errors are independent, are satisfied. However, in a real situation, we may encounter dependent error terms which prone to produce autocorrelated errors. A two-stage estimator (CTS) has been developed to remedy this problem. Nevertheless, it is now evident that the presence of outliers have an unduly effect on the least squares estimates. We expect that the CTS is also easily affected by outliers since it is based on the least squares estimator, which is not robust. In this article, we propose a Robust Two-Stage (RTS) procedure for the estimation of the nonlinear regression parameters in the situation where autocorrelated errors come together with the existence of outliers. The numerical example and simulation study signify that the RTS is more efficient than the NLLS and the CTS methods.

Robust Wild Bootstrap for Stabilizing the Variance of Parameter Estimates in Heteroscedastic Regression Models in the Presence of Outliers

Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, physics, meteorology, medicine, biology, and chemistry. In this paper, the robustness of Wu (1986) and Liu (1988)s Wild Bootstrap techniques is examined. The empirical evidences indicate that these techniques yield efficient estimates in the presence of heteroscedasticity problem. However, in the presence of outliers, these estimates are no longer efficient. To remedy this problem, we propose a Robust Wild Bootstrap for stabilizing the variance of the regression estimates where heteroscedasticity and outliers occur at the same time. The proposed method is based on the weighted residuals which incorporate the MM estimator, robust location and scale, and the bootstrap sampling scheme of Wu (1986) and Liu (1988). The results of this study show that the proposed method outperforms the existing ones in every respect.

An Improvement of the Hotelling Statistic in Monitoring Multivariate Quality Characteristics

The Hotelling statistic is the most popular statistic used in multivariate control charts to monitor multiple qualities. However, this statistic is easily affected by the existence of more than one outlier in the data set. To rectify this problem, robust control charts, which are based on the minimum volume ellipsoid and the minimum covariance determinant, have been proposed. Most researchers assess the performance of multivariate control charts based on the number of signals without paying much attention to whether those signals are really outliers. With due respect, we propose to evaluate control charts not only based on the number of detected outliers but also with respect to their correct positions. In this paper, an Upper Control Limit based on the median and the median absolute deviation is also proposed. The results of this study signify that the proposed Upper Control Limit improves the detection of correct outliers but that it suffers from a swamping effect when the positions of outliers are not taken into consideration. Finally, a robust control chart based on the diagnostic robust generalised potential procedure is introduced to remedy this drawback.

Robust regression imputation for analyzing missing data

Missing data arises in many statistical analyses which lead to biased estimates. In order to rectify this problem, single imputation and multiple imputation methods are put forward. However, it is found that both single and multiple imputation methods are easily affected by outliers and give poor estimates. This article proposes simple but very interesting robust single imputation technique which gives more accurate estimates over the classical single imputation technique in the presence of outliers. The proposed method is basically the robust version of the classical random regression imputation (RRI) which we call robust random regression imputation (RRRI). By examining the real life data, results show that the RRRI method is more resistance in the presence of outliers.

On the Performance of the Measure for Diagnosing Multiple High Leverage Collinearity-Reducing Observations

There is strong evidence indicating that the existing measures which are designed to detect a single high leverage collinearity-reducing observation are not effective in the presence of multiple high leverage collinearity-reducing observations. In this paper, we propose a cutoff point for a newly developed high leverage collinearity-influential measure and two existing measures ( and ) to identify high leverage collinearity-reducing observations, the high leverage points which hide multicollinearity in a data set. It is important to detect these observations as they are responsible for the misleading inferences about the fitting of the regression model. The merit of our proposed measure and cutoff point in detecting high leverage collinearity-reducing observations is investigated by using engineering data and Monte Carlo simulations.

Bayesian elastic net single index quantile regression

ABSTRACT Single index model conditional quantile regression is proposed in order to overcome the dimensionality problem in nonparametric quantile regression. In the proposed method, the Bayesian elastic net is suggested for single index quantile regression for estimation and variables selection. The Gaussian process prior is considered for unknown link function and a Gibbs sampler algorithm is adopted for posterior inference. The results of the simulation studies and numerical example indicate that our propose method, BENSIQReg, offers substantial improvements over two existing methods, SIQReg and BSIQReg. The BENSIQReg has consistently show a good convergent property, has the least value of median of mean absolute deviations and smallest standard deviations, compared to the other two methods.

Polynomial Spline Approach for Double Integrals with Algebraic Singularity

In this note, cubature formulas are constructed to evaluate the double integrals on the rectangle with algebraic singularity by replacing the density function f(x,y) with the S?(P) modified spline function interpolation of type (0,2). Rate of convergence are obtained in the classes of function f(x,y) C2,?(D).