A study of quadratic inference functions with alternative weighting matrices

ABSTRACT

Quadratic inference function (QIF) is an alternative methodology to the popular generalized estimating equations (GEE) approach, it does not involve direct estimation of the correlation parameter, and thus remains optimal even if the working correlation structure is misspecified. The idea is to represent the inverse of the working correlation matrix by a linear combination of some basis matrices. In this article, we present a modification of QIF with a robust variance estimator of the extended score function. Theoretical and numerical results show that the modified QIF attains better efficiency and achieves better small sample performance than the original QIF method.

Keywords:

• Longitudinal data
• QIF
• Sandwich variance estimator
• Small sample size

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F12
• 62H12
• 62H20
• 62E20

Funding

This research is supported by the NSFC (No. 11301569, No. 11401059), National Social Science Foundation of China (No. 13CTJ016), Science Foundation of Ministry of Education of China (No. 13xjc910001), and Educational Commission of Chongqing (KJ130719, KJ130730).