In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew-normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM-type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new R package skewlmm.
The analysis of complex longitudinal data such as COVID-19 deaths is challenging due to several inherent features: (i) similarly-shaped profiles with different decay patterns; (ii) unexplained variation among repeated measurements within each country, possibly interpreted as clustered data since they are obtained from the same country at roughly the same time; and (iii) skewness, outliers or skewed heavy-tailed noises possibly embodied within response variables. This article formulates a robust nonlinear mixedeffects model based on the class of scale mixtures of skewnormal distributions to model COVID-19 deaths, which allows analysts to model such data in the presence of the above described features simultaneously. An efficient EM-type algorithm is proposed to carry out maximum likelihood estimation of model parameters. The bootstrap method is used to determine inherent characteristics of the individual nonlinear profiles, such as confidence intervals of the predicted deaths and fitted curves. The specific target is to model COVID-19 death curves from some Latin American countries since this region is the new epicenter of the disease. Moreover, since a mixed-effect framework borrows information from the population-average effects, in our analysis we include some countries from Europe and North America that are in a more advanced stage of the COVID-19 death curve.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.