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‎README.Rmd‎

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---
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output:
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md_document:
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variant: markdown_github
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output: github_document
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always_allow_html: yes
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bibliography: [vignettes/bibliography.bib]
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biblio-style: apalike
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link-citations: yes
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---
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<!-- README.md is generated from README.Rmd. Please edit that file -->
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# brokenstick
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<!-- badges: start -->
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[![Lifecycle: maturing](https://img.shields.io/badge/lifecycle-maturing-blue.svg)](https://www.tidyverse.org/lifecycle/#maturing)
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[![](https://img.shields.io/badge/github%20version-0.72.0-orange.svg)](https://github.com/stefvanbuuren/brokenstick)
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<!-- badges: end -->
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The broken stick model describes a set of individual curves by a linear mixed model using first order linear B-splines. The main use of the model is to align irregularly observed data to a user-specified grid of break ages.
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All fitting can done in the Z-score scale, so nonlinearities and irregular data can be treated as separate problems. This package contains functions for fitting a broken stick model to data, for exporting the parameters of the model for independent use outside this package, and for predicting broken stick curves for new data.
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`brokenstick()` | Fit a broken stick model to irregular data
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`predict()` | Predict broken stick estimates
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`plot()` | Plot observed and fitted trajectories
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## Resources
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### Background
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1. The name *broken stick* comes from @ruppert2003, page 59-61.
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2. As far as I know, @dekroon2010 is the first publication that uses the broken stick model without the intercept in a mixed modelling context. See [The Terneuzen birth cohort: BMI changes between 2 and 6 years correlate strongest with adult overweight](https://stefvanbuuren.name/publications/2010%20TBC%20Overweight%20-%20PLoS%20ONE.pdf).
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3. The model was formally defined and extended in [Flexible Imputation of Missing Data (second edition)](https://stefvanbuuren.name/fimd/sec-rastering.html#sec:brokenstick). See @vanbuuren2018.
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4. The evaluation by @anderson2019 concluded: "We recommend the use of the brokenstick model with standardised Z‐score data. Aside from the accuracy of the fit, another key advantage of the brokenstick model is that it is easier to fit and provides easily interpretable estimates of child growth trajectories."
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### Tutorials
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The [companion site](https://stefvanbuuren.name/brokenstick/) contains various articles that explain the model and the use of the software.
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### References

‎README.md‎

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<!-- README.md is generated from README.Rmd. Please edit that file -->
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brokenstick
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===========
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# brokenstick
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<!-- badges: start -->
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[![Lifecycle:
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maturing](https://img.shields.io/badge/lifecycle-maturing-blue.svg)](https://www.tidyverse.org/lifecycle/#maturing)
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[![](https://img.shields.io/badge/github%20version-0.72.0-orange.svg)](https://github.com/stefvanbuuren/brokenstick)
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<!-- badges: end -->
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The broken stick model describes a set of individual curves by a linear
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mixed model using first order linear B-splines. The main use of the
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exporting the parameters of the model for independent use outside this
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package, and for predicting broken stick curves for new data.
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Installation
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------------
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## Installation
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The `brokenstick` package can be installed from GitHub as follows:
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There is currently no CRAN version.
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Overview
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--------
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## Overview
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The *broken stick model* describes a set of individual curves by a
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linear mixed model using first order linear B-splines. The model can be
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used
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- to smooth growth curves by a series of connected straight lines;
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- to align irregularly observed curves to a common age grid;
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- to create synthetic curves at a user-specified set of break ages;
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- to estimate the time-to-time correlation matrix;
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- to predict future observations.
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- to smooth growth curves by a series of connected straight lines;
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- to align irregularly observed curves to a common age grid;
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- to create synthetic curves at a user-specified set of break ages;
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- to estimate the time-to-time correlation matrix;
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- to predict future observations.
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The user specifies a set of break ages at which the straight lines
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connect. Each individual obtains an estimate at each break age, so the
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The main assumptions of the broken stick model are:
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- The development between the break ages follows a straight line, and
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- The development between the break ages follows a straight line, and
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is generally not of particular interest;
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- Broken stick estimates follow a common multivariate normal
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- Broken stick estimates follow a common multivariate normal
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distribution;
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In order to conform to the assumption of multivariate normality, the
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user may fit the broken stick model on suitably transformed data that
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yield the standard normal (*Z*) scale. Unique feature of the broken
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yield the standard normal (\(Z\)) scale. Unique feature of the broken
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stick model are:
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- *Modular*: Issues related to nonlinearities of the growth curves in
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- *Modular*: Issues related to nonlinearities of the growth curves in
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the observed scale can be treated separately, i.e., outside the
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broken stick model;
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- *Local*: A given data point will contribute only to the estimates
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- *Local*: A given data point will contribute only to the estimates
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corresponding to the closest break ages;
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- *Exportable*: The broken stick model can be exported and reused for
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- *Exportable*: The broken stick model can be exported and reused for
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prediction for new data in alternative computing environments.
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The `brokenstick` package contains functions for
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- Fitting the broken stick model to data,
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- Plotting individual trajectories,
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- Predicting broken stick estimates for new data.
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- Fitting the broken stick model to data,
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- Plotting individual trajectories,
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- Predicting broken stick estimates for new data.
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Main functions
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--------------
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## Main functions
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The main functions in the `brokenstick` package are:
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| Function name | Description |
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|-----------------|--------------------------------------------|
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| --------------- | ------------------------------------------ |
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| `brokenstick()` | Fit a broken stick model to irregular data |
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| `predict()` | Predict broken stick estimates |
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| `plot()` | Plot observed and fitted trajectories |
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## Resources
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### Background
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1. The name *broken stick* comes from Ruppert, Wand, and Carroll
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([2003](#ref-ruppert2003)), page 59-61.
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2. As far as I know, Kroon et al. ([2010](#ref-dekroon2010)) is the
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first publication that uses the broken stick model without the
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intercept in a mixed modelling context. See [The Terneuzen birth
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cohort: BMI changes between 2 and 6 years correlate strongest with
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adult
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overweight](https://stefvanbuuren.name/publications/2010%20TBC%20Overweight%20-%20PLoS%20ONE.pdf).
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3. The model was formally defined and extended in [Flexible Imputation
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of Missing Data (second
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edition)](https://stefvanbuuren.name/fimd/sec-rastering.html#sec:brokenstick).
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See Buuren ([2018](#ref-vanbuuren2018)).
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4. The evaluation by Anderson et al. ([2019](#ref-anderson2019))
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concluded: “We recommend the use of the brokenstick model with
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standardised Z‐score data. Aside from the accuracy of the fit,
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another key advantage of the brokenstick model is that it is easier
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to fit and provides easily interpretable estimates of child growth
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trajectories.”
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### Tutorials
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The [companion site](https://stefvanbuuren.name/brokenstick/) contains
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various articles that explain the model and the use of the software.
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### References
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<div id="refs" class="references">
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<div id="ref-anderson2019">
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Anderson, C., R. Hafen, O. Sofrygin, L. Ryan, and HBGDki Community.
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2019. “Comparing Predictive Abilities of Longitudinal Child Growth
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Models.” *Statistics in Medicine* 38 (19): 3555–70.
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</div>
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<div id="ref-vanbuuren2018">
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Buuren, S. van. 2018. *Flexible Imputation of Missing Data. Second
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Edition*. Boca Raton, FL.: CRC Press.
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</div>
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<div id="ref-dekroon2010">
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Kroon, M.L.A. de, C.M. Renders, J.P. van Wouwe, S. van Buuren, and R.A.
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Hirasing. 2010. “The Terneuzen Birth Cohort: BMI Changes Between 2 and 6
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Years Correlate Strongest with Adult Overweight.” *PloS ONE* 5 (2):
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e9155.
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</div>
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<div id="ref-ruppert2003">
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Ruppert, D., M. P. Wand, and R. J. Carroll. 2003. *Semiparametric
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Regression*. Cambridge: Cambridge University Press.
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</div>
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</div>

‎inst/CITATION‎

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title = "{brokenstick}: Broken Stick Model for Irregular Longitudinal Data",
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author = personList(person("Stef", "van Buuren")),
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journal = "GitHub repository",
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year = "2017",
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year = "2020",
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publisher = "GitHub",
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url = "https://github.com/stefvanbuuren/brokenstick")
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textVersion =
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paste("Stef van Buuren (2017).",
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paste("Stef van Buuren (2020).",
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"brokenstick: Broken Stick Model for Irregular Longitudinal Data",
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"GitHub repository",
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"URL http://github.com/stefvanbuuren/brokenstick")

‎vignettes/bibliography.bib‎

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abstract = {},
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keywords = {}}
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@Article{dekroon2010,
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author = {de Kroon, M.L.A. and Renders, C.M. and van Wouwe, J.P. and van Buuren, S. and Hirasing, R.A.},
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title = {The Terneuzen birth cohort: BMI changes between 2 and 6 years correlate strongest with adult overweight},
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journal = {PloS ONE},
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volume = {5},
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number = {2},
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pages = {e9155},
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year = {2010},
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abstract = {},
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location = {},
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keywords = {}}
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@Article{anderson2019,
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author = {Anderson, C. and Hafen, R. and Sofrygin, O. and Ryan, L. and Community, HBGDki},
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title = {Comparing predictive abilities of longitudinal child growth models},
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journal = {Statistics in medicine},
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volume = {38},
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number = {19},
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pages = {3555--3570},
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year = {2019},
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location = {},
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keywords = {}}
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@Book{vanbuuren2018,
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author = {van Buuren, S.},
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title = {Flexible Imputation of Missing Data. Second Edition},
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volume = {},
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pages = {},
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editor = {},
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publisher = {CRC Press},
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address = {Boca Raton, FL.},
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year = {2018},
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abstract = {},
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keywords = {}}

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