Lifecycle: maturing

The broken stick model describes a set of individual curves by a linear mixed model using second-order linear B-splines. The main use of the model is to align irregularly observed data to a user-specified grid of break ages.

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.


The brokenstick package can be installed from GitHub as follows:


There is currently no CRAN version.


The broken stick model describes a set of individual curves by a linear mixed model using linear B-splines. The model can be used

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.

The main assumptions of the broken stick model are:

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. Unique feature of the broken stick model are:

The brokenstick package contains functions for



  1. I took the name broken stick from Ruppert, Wand, and Carroll (2003), page 59-61, but it is actually much older.
  2. As far as I know, de Kroon et al. (2010) 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.
  3. The model was formally defined and extended in Flexible Imputation of Missing Data (second edition). See van Buuren (2018).
  4. The evaluation by Anderson et al. (2019) 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.

Instructive materials


Anderson, C., R. Hafen, O. Sofrygin, L. Ryan, and HBGDki Community. 2019. “Comparing Predictive Abilities of Longitudinal Child Growth Models.” Statistics in Medicine 38 (19): 3555–70.

de Kroon, M. L. A., C. M. Renders, J. P. van Wouwe, S. van Buuren, and R. A. Hirasing. 2010. “The Terneuzen Birth Cohort: BMI Changes Between 2 and 6 Years Correlate Strongest with Adult Overweight.” PloS ONE 5 (2): e9155.

Ruppert, D., M. P. Wand, and R. J. Carroll. 2003. Semiparametric Regression. Cambridge: Cambridge University Press.

van Buuren, S. 2018. Flexible Imputation of Missing Data. Second Edition. Boca Raton, FL.: CRC Press.