Local Influence Analysis For Generalized Cochran's Q-statistic In The Meta Regression Model

Meta analysis is a kind of research method for systematic evaluation and quantitative analysis of multiple research results which have the same purpose and are independent of each other.Many scholars at home and abroad have done a lot of research on Meta analysis.Meta analysis has been widely used in various fields,such as social science(including pedagogy,psychology and social decision science),medicine,ecology,management science,and Economics,etc.According to the existing literature,there are many methods for estimating heterogeneity in Meta regression analysis,and scholars have also applied these methods.On the other hand,the problem of identifying outliers and influence points in Meta analysis is also discussed by some scholars.Viechtbauer W and Cheung W-L(2010)apply the diagnostic methods in linear regression analysis to the Meta analysis model,the outliers and influence points in the Meta analysis model are identified.Shi Lei et al.(2017)made impact diagnosis for Meta regression analysis model,studied the diagnostic theory of impact points in Meta random effect model under the framework of data deletion and local impact analysis.Although this paper gives a likelihood-based local impact analysis,other commonly used statistic s in Meta regression model,such as generalized Cochran's Q-statistics,have not been involved.Therefore,how to analyze the local impact based on generalized Cochran's Q-statistics and other non-likelihood statistics is still a problem to be discussed.Based on the theoretical framework of the local impact analysis of generalized influence function and generalized Cook statistics,this paper considers the two estimation methods of generalized Cochran's Q-statistics and Paule and Mandel(PM)in the meta-regression model,derives the diagnostic statistics of heterogenous variance estimation respectively,and then uses individual weighted perturbation scheme and dependent variable weighted perturbation scheme to make local shadow.The effectiveness of the method is proved by an example.Through an example analysis,it can be concluded that the results obtained by using non-likelihood statistics for local impact analysis are consistent with those obtained by using likelihood-based local impact analysis.And the influence points or outliers identified by different statistics are different;for the same statistics,the influence points or outliers identified by different disturbance modes are also different.