# Getting started

#### 2020-10-23

## 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