Robust maximum Lq-likelihood estimation of joint mean–covariance models for longitudinal data

Abstract A comprehensive longitudinal data analysis requires screening for unusual observations. Outliers or measurement errors might lead to considerable efficiency loss or even misleading results in longitudinal data inference. Via joint mean–covariance modelings (Pourahmadi, 2000; Zhang et al., 2015) and q -order entropy theory (Ferrari, 2010), we propose a maximum L q -likelihood estimation for longitudinal data, which can yield robust and consistent estimators of the mean regression coefficients. An EM type algorithm is introduced to achieve both efficient and stable computation. The asymptotic properties of the proposed estimators are provided. Simulation studies and an application to Turkish anesthesiology data are used to show the effectiveness of the new approach.