Recently medical and public health research has focused on the development of models for longitudinal studies that aim to identify individuals at risk for obesity by tracking childhood weight gain. The National Longitudinal Surveys of Youth 79 (NLSY79), which includes a random sample of women with biometric information on their biological children collected biennially, has been considered. A mixed model with three levels of clustered random effects has been proposed for the estimation of child-specific weight trajectories while accounting the nested structure of the dataset. Included in this model is a regression equation approach to address any remaining heterogeneity in the within-child variances. Specifically, a model has been implemented to fit the log of the within-child variances as a function of time. This allows for more flexibility in modeling residual variances that appear to be increasing over time. Using the EM algorithm with a Newton-Raphson update all the parameters of the model are estimated simultaneously.
A second aspect to the research that is presented is the analysis of missing data. Extensive exploratory analysis revealed that intermittent missingness was prevalent in the relevant subset of the NLSY79 dataset. Starting with the assumptions of MCAR and MAR selection models are built up to appropriately account for the missing mechanism at play. A factorization of the multinomial distribution as a product of dependent binary observations is applied to model intermittent missingness. Logit models for dependent binary observations are used to fit selection models for missingness under the assumptions of MAR and MCAR. The NMAR case for clustered longitudinal data is discussed as an area for future research.