Longitudinal models for analysis of respiratory function

We compare the results of fitting three longitudinal models, two autoregressive models (the serial correlation model and a damped autoregressive model) and a compound symmetry model, to data on a cohort of 1154 adult men in Boston. The serial correlation model assumes that the error terms are autocorrelated with correlation of the form lambda t for visits t years apart while the damped autoregressive assumes that the correlation between error terms of observations t years apart is of the form lambda t theta. The compound symmetry model assumes that the errors are correlated, with the same correlation regardless of how far apart observations are in time. These three models are all related in that the serial correlation and compound symmetry models are particular cases of the damped autoregressive models (that is, theta = 1 corresponds to the serial correlation model and theta = 0 corresponds to the compound symmetry model). For current smokers, the damped autoregressive model provided a significantly better fit than either of the other two models (p < 0.001); for never smokers the damped autoregressive and compound symmetry models were almost identical with both providing a significantly better fit than the serial correlation model (p < 0.001).