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Title: Group based trajectory modelling with monotonicity constraints Authors:  Kevin Murray - University of Western Australia (Australia) [presenting]
Berwin Turlach - The University of Western Australia (Australia)
Michael Dymock - University of Western Australia (Australia)
Abstract: Existing methods for group based trajectory modelling have been developed over the past two decades with the addition of numerous extensions such as the ability to jointly analyse multiple trajectories as well as the handling of missing data. However, it is often known from underlying theory that a response trajectory will be monotonic and commonly used modelling techniques in group based trajectory modelling, such as polynomial regression, may fail to capture this behaviour. A new method for fitting group based trajectory models with monotonicity constraints is described in which an Expectation Maximisation algorithm is adopted in order to avoid the convergence issues commonly encountered by a Newton Raphson algorithm. Model selection and starting values are discussed and the methodology is described and implemented in R. Numerical experiments and an example on lung function data from the West Australian Busselton Health Study is used to illustrate the methodology.