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Abstract:
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In the analysis of longitudinal data, it is common to characterize the relationship between (repeated) response measures and the covariates. However, when the covariates do vary over time (time-dependent covariates) there is extra relation due to the delayed effects that need to be accounted for. Moreover, it is not uncommon that these studies often consist of simultaneous responses on the subject. However, a joint likelihood function of the simultaneous responses is impossible to afford maximum likelihood estimates as the observations are correlated. We present a simultaneous modeling approach of multiple responses with a hierarchical working correlation matrix while using Bayesian regression estimates on the partitioning of the data matrix. We conduct a simulation study demonstrating the benefits of this model. We demonstrate its fit using studies with a single response and studies with simultaneous responses. We provide code in R and a SAS macro while revisiting two numerical examples, Chinese Quality of Health survey data and Add Heath survey data.
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