What is the broken stick model?
The broken stick model describes a set of individual curves by a linear mixed model using secondorder linear Bsplines. The model can be used to
 smooth growth curves by a series of connected straight lines;
 align irregularly observed curves to a common age grid;
 create synthetic curves at a userspecified set of break ages;
 estimate the timetotime correlation matrix;
 predict future observations.
The user specifies a set of break ages at which the straight lines connect. Each individual obtains an estimate at each break age, so the set of estimates of the individual form a smoothed version of the observed trajectory.
What are the main model assumptions?
The main assumptions of the broken stick model are:
 The development between the break ages follows a straight line;
 Broken stick estimates follow a common multivariate normal distribution;
In order to conform to the assumption of multivariate normality, the user may fit the broken stick model on suitably transformed data that yield the standard normal (\(Z\)) scale.
Why should I want to use the broken stick model?
Three unique features of the broken stick model are:

Modular: Issues related to nonlinearities of the growth curves in the observed scale can be treated separately, i.e., outside the broken stick model;

Local: A given data point will contribute only to the estimates corresponding to the closest break ages;

Exportable: The broken stick model can be exported and reused for prediction for new data in alternative computing environments.
What is in the package?
The brokenstick
package contains functions to fit, predict and plot data. See the reference page for an overview.
Acknowledgement
Development of the brokenstick
package was kindly supported by the Healthy Birth Growth and Development knowledge integration (HBGDki) program of the Bill & Melinda Gates Foundation.
Further reading

Main functions
 Plot trajectories
 Orginal scale and \(Z\)score scale
 1line model
 2line broken stick model
 9line broken stick model
 Prediction
 Subjectlevel analysis

Broken Stick Model for Irregular Longitudinal Data
 Irregular observation times
 Literature overview
 Definition of the model
 Interpretation of the model
 Estimation by
lmer
and kr
methods
 Software overview

brokenstick()
for model fitting

predict()
for trajectory plotting
 Conversion back and forth to the \(Z\)score scale
 Predict growth curve of new subjects
 Assess the quality of the model
 Knot placement strategies
 Critical periods
 Timetotime correlations
 Profile analysis
 Curve interpolation
 Multiple imputation
 Curve matching
 Discussion

Perfect model
 Properties of the perfect model
 Estimating timetotime correlations

Help for old friends
 Properties of the perfect model
 Estimating timetotime correlations