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Abstract |
Missing responses and measurement errors are very common to be seen in practice. We develop new estimating equations, which can simultaneously estimate the mean and covariance under the partially linear model for longitudinal data with missing responses and covariate measurement errors. Specifically, we propose a novel approach to handle measurement errors by using the independence among replicated measures. Comparing with the existing methods, the proposed method needs less assumptions, such as those conditions in classical structural approaches or correction methods for measurement errors, and estimating the probability of being observed or imputing missing responses based on assumed models for missing responses. Additionally, the estimating equations of the proposed method is easy to implement in most popular statistical softwares by applying existing algorithms for the standard generalized estimating equations. We establish the asymptotic properties of proposed estimators under regularity conditions, and the simulation studies demonstrate desired properties. Finally, we investigate the Lifestyle Education for Activity and Nutrition (LEAN) study and confirm the effective of intervention in producing weight loss after nine month. |
