Meta analysis of regression: a review and new approach with application to linear-circular regression model
Abstract In a usual meta analysis of regression, it is assumed that co-variance among studies are zero. However, the main utility of a meta analysis is to provide an estimated overall effect by combining the results from related small studies. Therefore, incorporating co-variance among those small studies is essential, and in our earlier work, it was shown to improve the estimates obtained from the proposed generalized least square approach. In this paper, we provide a review of meta analysis of regression, then present an improved weighed least square approach to meta analysis that takes account into an appropriate co-variance structure among related studies. We illustrate our proposed method in a linear-circular regression setting with application to forecasting problem in Environmental Sciences, and compare the different approaches presented in this paper using the mean square prediction error (MSPE).