Robust Estimation Methods And Outlier Detection In Mediation Models

Mediation models refer to the relationships among three variables: an independent variables (IV), a potential mediating variable (M), and a dependent variable (DV). When the relationship between the dependent variable (DV) and an independent variables (IV) can be accounted for by an intermediate...

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Main Author:	Fitrianto, Anwar
Format:	Thesis
Language:	English English
Published:	2010
Subjects:	Robust statistics Outliers (Statistics) Mediation (Statistics)
Online Access:	http://psasir.upm.edu.my/id/eprint/12439/1/FS_2010_24A.pdf
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spelling	my-upm-ir.124392013-05-27T07:52:15Z Robust Estimation Methods And Outlier Detection In Mediation Models 2010-03 Fitrianto, Anwar Mediation models refer to the relationships among three variables: an independent variables (IV), a potential mediating variable (M), and a dependent variable (DV). When the relationship between the dependent variable (DV) and an independent variables (IV) can be accounted for by an intermediate variable M, mediation is said to occur. Simple mediation model consists of three regression equations. The Ordinary Least Squares (OLS) method is often use to estimate the parameters of the mediation model. However, due to the fact that outliers have an unduly effect on the OLS estimates, we propose to incorporate robust M and MM estimator which are not easily affected by outliers, in the estimation of the mediation model which is called RobSim1 and RobSim2, respectively. The numerical example indicates that various types of contamination in the simulated data have arbitrarily large effect on the OLS estimates and the Sobel test. The MM-estimator incorporated in RobSim2 has improved the precision of the indirect effect of mediation model. The overall analysis clearly shows that the Simple Mediation Model based on RobSim2 is prominently the most excellent result, because it is able to withstand various contamination in the m , x , and y - axes (direction). There is also concern not only when the data contain observations that are extreme in the response variable but also in the regressor space, namely the leverage points. A new measure for the identification of high-leverage point is called Diagnostic Robust Generalized Potentials (DRGP) which is proposed previously. The DRGP procedures incorporated the Robust Mahanalobis Distance (RMD) based on the minimum volume ellipsoid (MVE) for identifying the set of cases ‘remaining’ (R) and a set of cases ‘deleted’(D), and then diagnostic approach is used to confirm the suspected values. The DRGP procedure uses MAD as its cutoff points. We suggest an alternative method for identification of high leverage points in the mediation model. A modification is made to the DRGP procedure. It was verified that both MAD and n Q have the same breakdown point that is 50%. Nonetheless, the efficiency of the n Q is higher (86%) than the MAD (37%). This work inspired us to incorporate the n Q instead of the MAD in the proposed algorithm. We refer the above new method of identifying potential outliers in mediation analysis as ModDRGP1 where the MAD is incorporated in the second step of the ModDRGP1 algorithm. In this thesis we also propose another DRGP, which has modified step 2 and step 4 for identifying potential outliers in mediation model. We called the second proposed method as ModDRGP2. Robust statistics Outliers (Statistics) Mediation (Statistics) 2010-03 Thesis http://psasir.upm.edu.my/id/eprint/12439/ http://psasir.upm.edu.my/id/eprint/12439/1/FS_2010_24A.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Robust statistics Outliers (Statistics) Mediation (Statistics) Faculty Of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Robust statistics Outliers (Statistics) Mediation (Statistics)
spellingShingle	Robust statistics Outliers (Statistics) Mediation (Statistics) Fitrianto, Anwar Robust Estimation Methods And Outlier Detection In Mediation Models
description	Mediation models refer to the relationships among three variables: an independent variables (IV), a potential mediating variable (M), and a dependent variable (DV). When the relationship between the dependent variable (DV) and an independent variables (IV) can be accounted for by an intermediate variable M, mediation is said to occur. Simple mediation model consists of three regression equations. The Ordinary Least Squares (OLS) method is often use to estimate the parameters of the mediation model. However, due to the fact that outliers have an unduly effect on the OLS estimates, we propose to incorporate robust M and MM estimator which are not easily affected by outliers, in the estimation of the mediation model which is called RobSim1 and RobSim2, respectively. The numerical example indicates that various types of contamination in the simulated data have arbitrarily large effect on the OLS estimates and the Sobel test. The MM-estimator incorporated in RobSim2 has improved the precision of the indirect effect of mediation model. The overall analysis clearly shows that the Simple Mediation Model based on RobSim2 is prominently the most excellent result, because it is able to withstand various contamination in the m , x , and y - axes (direction). There is also concern not only when the data contain observations that are extreme in the response variable but also in the regressor space, namely the leverage points. A new measure for the identification of high-leverage point is called Diagnostic Robust Generalized Potentials (DRGP) which is proposed previously. The DRGP procedures incorporated the Robust Mahanalobis Distance (RMD) based on the minimum volume ellipsoid (MVE) for identifying the set of cases ‘remaining’ (R) and a set of cases ‘deleted’(D), and then diagnostic approach is used to confirm the suspected values. The DRGP procedure uses MAD as its cutoff points. We suggest an alternative method for identification of high leverage points in the mediation model. A modification is made to the DRGP procedure. It was verified that both MAD and n Q have the same breakdown point that is 50%. Nonetheless, the efficiency of the n Q is higher (86%) than the MAD (37%). This work inspired us to incorporate the n Q instead of the MAD in the proposed algorithm. We refer the above new method of identifying potential outliers in mediation analysis as ModDRGP1 where the MAD is incorporated in the second step of the ModDRGP1 algorithm. In this thesis we also propose another DRGP, which has modified step 2 and step 4 for identifying potential outliers in mediation model. We called the second proposed method as ModDRGP2.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Fitrianto, Anwar
author_facet	Fitrianto, Anwar
author_sort	Fitrianto, Anwar
title	Robust Estimation Methods And Outlier Detection In Mediation Models
title_short	Robust Estimation Methods And Outlier Detection In Mediation Models
title_full	Robust Estimation Methods And Outlier Detection In Mediation Models
title_fullStr	Robust Estimation Methods And Outlier Detection In Mediation Models
title_full_unstemmed	Robust Estimation Methods And Outlier Detection In Mediation Models
title_sort	robust estimation methods and outlier detection in mediation models
granting_institution	Universiti Putra Malaysia
granting_department	Faculty Of Science
publishDate	2010
url	http://psasir.upm.edu.my/id/eprint/12439/1/FS_2010_24A.pdf
_version_	1747811366706610176

Robust Estimation Methods And Outlier Detection In Mediation Models

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