AR(1) latent class models for longitudinal count data

• Published in: Statistics in medicine Vol. 37; no. 29; pp. 4441 - 4456
• Main Authors: Henderson, Nicholas C., Rathouz, Paul J.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 20.12.2018
• Subjects: Algorithms; Cluster Analysis; Data Interpretation, Statistical; discrete AR processes; finite mixture model; Humans; Latent Class Analysis; Likelihood Functions; Longitudinal Studies; Models, Statistical; negative binomial; Regression analysis; repeated measures; Treatment Outcome; Within-subjects design; discrete AR processes; negative binomial; finite mixture model; repeated measures
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.7931

In a variety of applications involving longitudinal or repeated‐measurements data, it is desired to uncover natural groupings or clusters that exist among study subjects. Motivated by the need to recover clusters of longitudinal trajectories of conduct problems in the field of developmental psychopathology, we propose a method to address this goal when the response data in question are counts. We assume the subject‐specific observations are generated from a first‐order autoregressive process that is appropriate for count data. A key advantage of our approach is that the class‐specific likelihood function arising from each subject's data can be expressed in closed form, circumventing common computational issues associated with random effects models. To further improve computational efficiency, we propose an approximate EM procedure for estimating the model parameters where, within each EM iteration, the maximization step is approximated by solving an appropriately chosen set of estimating equations. We explore the effectiveness of our procedures through simulations based on a four‐class model, placing a special emphasis on recovery of the latent trajectories. Finally, we analyze data and recover trajectories of conduct problems in an important nationally representative sample. The methods discussed here are implemented in the R package inarmix, which is available from the Comprehensive R Archive Network (http://cran.r-project.org).