Dr. Sehar Saleem completed her PhD in June, 2021 from University of the Punjab in the subject of Statistics. Her research supervisor was Associate Prof. Dr. Rehan Ahmad Khan Sherwani. Her research topic was “Optimal Score Functions for Robust Estimation of Multilevel Models in the Presence of Outliers”.
The brief summary of her research work is given asIn the era of modern sciences, several fields of behavioral and social studies deal with complex inherent hierarchical data to conclude the results for the concerned authorities. However, multilevel models in a domain of regression are quite interesting to incorporate hierarchical structure to provide analysis of several individual and cross-levels variables. In such cases, presence of outliers at level-1 in multilevel data actually violates the assumption of normality leading towards the biased estimates, inflated Standard Error (SE) and spurious analysis of fixed and random effects in the model. Robust rank-based estimation method is proposed in the literature to resolve the issue of normality of error term occurred due to the presence of outliers and considered as an alternative of likelihood-based/ least squares methods in the presence of outliers. The efficiency of rank-based analyses is particularly based on appropriate selection of score function to depend on probability distribution of error term. In presented study, score selection schemes are explored and compared under several error distributions in the context of multilevel models via Monte Carlo simulation. Furthermore, different estimates of bias, variance, Mean Square Error (MSE) and precision are computed for different combination of sample sizes to address different error distributions.
It is concluded in presented study that Kloke’s scheme outperformed efficiently than Hogg’s scheme for skewed error distributions. In all simulation scenarios, modified version of Hogg’s scheme is proposed to overcome the deficiency for symmetric and asymmetric heavy, moderate and light tailed error distribution. Subsequently, a score function is proposed for Weibull distribution of level-1 and level-2 error terms in multilevel models. The estimates of bias, MSE and precision of Weibull score function are also compared with Wilcoxon score function and traditional method Restricted Maximum Likelihood (REML) for efficiency. It is also concluded that Weibull score function produced efficient analysis than Wilcoxon and REML in all combination of sample sizes with small number of covariates in the multilevel model. Weibull and Wilcoxon score function concluded as equally precise and more efficient than REML for large number of covariates. Practically, the empirical economic and financial characteristics often contain outliers causing the non-normality in the error terms. The proposed methods produce valid and efficient results than the existing methods for the non-normal and skewed data caused by the presence of outliers.
