Abstract: Correlation structure contains important information about longitudinal data. Existing sufficient dimension reduction approaches assuming independence may lead to substantial loss of efficiency. We apply the quadratic inference function to incorporate the correlation information and apply the transformation method to recover the central subspace. The proposed estimators are shown to be consistent and more efficient than the ones assuming independence. In addition, the estimated central subspace is also efficient when the correlation information is taken into account. We compare the proposed method with other dimension reduction approaches through simulation studies, and apply this new approach to longitudinal data for an environmental health study.

Key words and phrases: Correlation structure, eigen-decomposition, quadratic inference function, slice inverse regression, transformation method.