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title: "Getting started"
date: "`r Sys.Date()`"
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vignette: >
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## 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](https://growthcharts.org/brokenstick/reference/index.html) 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](mainfunctions.html)
    + 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](brokenstick-article.html)
    + 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](perfectmodel.html)
    + Properties of the perfect model
    + Estimating time-to-time correlations

* [Help for old friends](oldfriends.html)
    + Properties of the perfect model
    + Estimating time-to-time correlations



