brokenstick

Data on multiple individuals through time are often sampled at times that differ between persons. Irregular observation times can severely complicate the statistical analysis of the data. The broken stick model approximates each subject’s trajectory by one or more connected line segments. The times at which segments connect (breakpoints) are identical for all subjects and under control of the user. A well-fitting broken stick model effectively transforms individual measurements made at irregular times into regular trajectories with common observation times. Specification of the model requires three variables: time, measurement and subject. The model is a special case of the linear mixed model, with time as a linear B-spline and subject as the grouping factor. The main assumptions are: subjects are exchangeable, trajectories between consecutive breakpoints are straight, random effects follow a multivariate normal distribution, and unobserved data are missing at random. The package contains functions for fitting the broken stick model to data, for predicting curves in new data and for plotting broken stick estimates. The package supports two optimization methods, and includes options to structure the variance-covariance matrix of the random effects. The analyst may use the software to smooth growth curves by a series of connected straight lines, to align irregularly observed curves to a common time grid, to create synthetic curves at a user-specified set of breakpoints, to estimate the time-to-time correlation matrix and to predict future observations. See doi:10.18637/jss.v106.i07 for additional documentation on background, methodology and applications.