Robust Estimation Methods And Outlier Detection In Mediation Models - Fitrianto, Anwar (2010)

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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.