Segmented relationships in regression models with breakpoints / changepoints estimation
Estimation and Inference of Regression Models with piecewise linear relationships having a fixed number of break-points. The estimation method is described in Muggeo (2003) <doi: 10.1002/sim.1545>.
segmented is aimed to estimate linear and generalized linear models (and virtually any regression model)
having one or more segmented relationships in the linear predictor. Estimates of the slopes and
breakpoints are provided along with standard errors. The package includes testing/estimating
functions and methods to print, summarize and plot the results.
The algorithm used by
segmented is not grid-search. It is an iterative procedure (Muggeo, 2003)
that needs starting values only for the breakpoint parameters and therefore it is quite efficient even
with several breakpoints to be estimated. Moreover since version 0.2-9.0,
the bootstrap restarting (Wood, 2001) to make the algorithm less sensitive to starting values.
Since version 0.5-0.0 a default method
segmented.default has been added. It may be employed to include segmented relationships
in general regression models where specific methods do not exist. Examples include quantile and Cox regressions. See
Since version 1.0-0 the estimating algorithm has been slight modified and it appears to be much stabler (in examples with noisy segmented relationhips and flat log likelihoods) then previous versions.
Hypothesis testing (about the existence of the breakpoint) and confidence intervals are performed via appropriate methods and functions.
A tentative approach to deal with unknown number of breakpoints
is also provided, see option
Muggeo, V.M.R. (2017) Interval estimation for the breakpoint in segmented regression: a smoothed score-based approach. Australian & New Zealand Journal of Statistics 59, 311--322.
Muggeo, V.M.R. (2016) Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling. J of Statistical Computation and Simulation 86, 3059--3067.
Davies, R.B. (1987) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74, 33--43.
Seber, G.A.F. and Wild, C.J. (1989) Nonlinear Regression. Wiley, New York.
Bacon D.W., Watts D.G. (1971) Estimating the transistion between two intersecting straight lines. Biometrika 58: 525 -- 534.
Muggeo, V.M.R. (2003) Estimating regression models with unknown break-points. Statistics in Medicine 22, 3055--3071.
Muggeo, V.M.R. (2008) Segmented: an R package to fit regression models with broken-line relationships. R News 8/1, 20--25.
Muggeo, V.M.R., Adelfio, G. (2011) Efficient change point detection in genomic sequences of continuous measurements. Bioinformatics 27, 161--166.
Wood, S. N. (2001) Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting. Biometrics 57, 240--244.
Muggeo, V.M.R. (2010) Comment on `Estimating average annual per cent change in trend analysis' by Clegg et al., Statistics in Medicine; 28, 3670-3682. Statistics in Medicine, 29, 1958--1960.