Regressograms and Mean-Covariance Models for Incomplete Longitudinal Data

Longitudinal studies are prevalent in biological and social sciences where subjects are measured repeatedly over time. Modeling the correlations and handling missing data are among the most challenging problems in analyzing such data. There are various methods for handling missing data, but data-based and graphical methods for modeling the covariance matrix of longitudinal data are relatively new. We adopt an approach based on the modified Cholesky decomposition of the covariance matrix which handles both challenges. It amounts to formulating parametric models for the regression coefficients of the conditional mean and variance of each measurement given its predecessors. We demonstrate the roles of profile plots and regressograms in formulating joint mean-covariance models for incomplete longitudinal data. Applying these graphical tools to the Fruit Fly Mortality (FFM) data, which has 22% missing values, reveals a logistic curve for the mean function and two different models for the two factors of the modified Cholesky decomposition of the sample covariance matrix. An expectation-maximization algorithm is proposed for estimating the parameters of the mean-covariance models; it performs well for the FFM data and in a simulation study of incomplete longitudinal data.