SegReg :   segmented linear regression with breakpoint and confidence intervals
Totally free download of software

The SegReg computer program (model) is designed to perform a segmented (piecewise) linear regression (in splines) of one dependent variable (Y, e.g. plant growth, crop yield) on one (X) or two (X and Z) independent (explanatory) variables (predictors), e.g. crop growth factors like depth of water table and soil salinity.

The segmentation is done by introducing a breakpoint (break-point, threshold, switching point). Thus one can obtain a broken, discontinuous, line. Seven types of functions (0 to 6) are used. Examples are given.
      The selection of the best function type and breakpoint is based on maximizing the statistical coefficient of explanation (determination) and performing the test of significance.
      The 90% confidence interval (belt) is given as well as an Anova table for variance analysis.
In December 2008, an amplified version (SegRegA) was made permitting the use of weight factors, preferred regression type or type exclusion. Although it can lead to manipulation, it is available on request.
      More details are found in the program itself.

The mathematical model starts clicking on SegReg.Exe.

A paper on the statistical principles of segmented regression with break-point, including the determination of its confidence interval, can be inspected in here.
      The construction of confidence intervals of the regression segments separated by the breakpoint, and of the breakpoint itself, is described in this confidence paper, which also gives an example. The intervals are made with Student's t-distribution, see the t-test program.
      The principles of regression analysis in general can be found in this lecture note.
Furter, the analysis of variance (Anova) and the F-test for segmented linear regression with break-point, as used in SegReg, is briefly discussed in this paper.
      A lecture note on statistical analysis with examples of SegReg applications is found in a document called Data Analysis.
Se here a list of articles and publications using SegReg.

In September 2010, the SegReg program was provided with new functionalities thanks to a request by Kirsten Otis.
      In March 2011 the confidence belts were improved thanks to questions raised by Linda Jung.
In October 2012 the confidence block of the breakpoint for type 2 functions was improved thanks to questions raised by John Schukman.
      In March 2013 the use of a second independent variable was updated thanks to comments made by Barbara Mahler.
In November 2013 the calculation of the standard error and confidence interval of the breakpoint (BP), as well as of the Y value at BP, was standardized for the different types of segmented regression. A description of the mathematics involved, with examples, can be seen in this confidence paper. These changes were motivated by suggestions put forward by Dawn Noren and Wenhuai Li.
      In January 2014 the conditions for Type 2, 3, 4 and 5 were made more strict thanks to an example provided by John Shukman.


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(in Spanish,
 en Español)

reports & cases

reports & cases

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(1) - An amplification of SegReg permitting expression of preference for a certain type or of wish to exclude a certain type can be downloaded from SegRegA
(2) - A different version of SegReg, called PartReg has been developed with the aim to detect the largest possible horizontal stretch in Type 3 and Type 4 relations. This has been done to find the maximum tolerance (or "no effect" reach of the dependent variable (e.g. crop yield) for changes in the dependent variable (e.g. soil salinity or depth of the water table).
      Download PartReg with this link
See the figures below to appreciate the diffrence bteween SegReg and PartReg. The first minimizes the deviations of the model values from the observed ones over the entire domain, whereas the second detects the maximum part of the domain over which the regression coefficient (i.e. the slope of the regression line) can be taken equal to zero.
      For more examples see this article on page 13 and following.

Introduction screen SegReg program:
introdcution to segreg

  Example Type 3:
yield of mustard versus
              soil salinity

Example Type 3 with extended horizontal line using
the same data as above in the PartReg program
instead of SegReg.
Mustard and salinity with partial regression

            The salt tolerance of mustard is almost ECe=8 dS/m

Example Type 4:
example segreg type 4

  Example Type 5:
segmented regression type 5

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