## What is the broken stick model?

The broken stick model describes a set of individual curves by a linear mixed model using second-order linear B-splines. 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 user-specified set of break ages;
• estimate the time-to-time 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
• 1-line model
• 2-line broken stick model
• 9-line broken stick model
• Prediction
• Subject-level 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
• Time-to-time correlations
• Profile analysis
• Curve interpolation
• Multiple imputation
• Curve matching
• Discussion
• Perfect model
• Properties of the perfect model
• Estimating time-to-time correlations
• Help for old friends
• Properties of the perfect model
• Estimating time-to-time correlations