Statistical Modelling 14 (4) (2014), 293–313

Segmented mixed models with random changepoints: a maximum likelihood approach with application to treatment for depression study

Vito MR Muggeo
Dipartimento di Scienze Statistiche e Matematiche “S. Vianelli”,
Universita di Palermo,
Italy
e-mail: vito.muggeo@unipa.it

David C Atkins
Dept. of Psychiatry and Behavioural Science,
University of Washington - Seattle,
WA,
USA


Robert J Gallop
Dept. of Mathematics,
Applied Statistics Program,
West Chester University,
West Chester,
PA, USA


Sona Dimidjian
Dept. of Psychology and Neuroscience,
University of Colorado at Boulder,
CO, USA


Abstract:

We present a simple and effective iterative procedure to estimate segmented mixed models in a likelihood based framework. Random effects and covariates are allowed for each model parameter, including the changepoint. The method is practical and avoids the computational burdens related to estimation of nonlinear mixed effects models. A conventional linear mixed model with proper covariates that account for the changepoints is the key to our estimating algorithm. We illustrate the method via simulations and using data from a randomized clinical trial focused on change in depressive symptoms over time which characteristically show two separate phases of change.

Keywords:

changepoint; mixed segmented regression; nonlinear mixed models; random changepoints; psychiatric longitudinal data

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