Combining Regression Slopes from Studies with Different Models in Meta-Analysis

Primary studies are using complex models more and more. Slopes from multiple regression analyses are reported in primary studies, but few scholars have dealt with how to combine multiple regression slopes. One of the problems in combining multiple regression slopes is that each study may use a different regression model. The purpose of this research is to propose a method for combining partial regression slopes from studies with different regression models. The method combines comparable covariance matrices to obtain a synthetic partial slope. The proposed method assumes the population is homogeneous, and that the different regression models are nested. Elements in the sample covariance matrix are not independent of each other, so missing elements should be imputed using conditional expectations. The Bartlett decomposition is used to decompose the sample covariance matrix into a parameter component and a sampling error component. The proposed method treats the sample-size weighted average as a parameter matrix and applies Bartlett’s decomposition to the sample covariance matrices to get their respective error matrices. Since missing elements in the error matrix are not correlated, missing elements can be estimated in the error matrices and hence in the parameter matrices. Finally the partial slopes can be computed from the combined matrices. Simulation shows the suggested method gives smaller standard errors than the listwise-deletion method and the pairwise-deletion method. An empirical examination shows the suggested method can be applied to heterogeneous populations.