PartReg :   segmented linear regression with breakpoint and extended horizontal trend at the start or the end.
Totally free download of software

Summary:

The PartReg computer program (model) is designed to perform a partial segmented linear regression of one dependent variable (Y, e.g. plant growth, crop yield) on one (X) independent (explanatory) variable (predictors), e.g. crop growth factors like depth of water table and soil salinity with the aim to find the tolerance level or the "no effect" reach.

Details:

The segmentation is done by introducing a breakpoint and finding the stretch (at the beginning or at the end of the X-domain over which the Y-X relation can be considered horizontal, i.e. Y is not influenced by X. The regression coefficient (i.e. the slope of the line over the selected stretch) may not be significantly different from zero in statistical sense.
      Two types of functions (3 and 4) are used. In Type 3 the horizontal line is followed by a sloping line whereas in type 4 the sloping line is followed by a horizontal line.
      The horizontal line is found by partial regression over the head end or the tail end of the X domain.

Difference with SegReg:

The PartReg program is similar to SegReg. However, SegReg minimizes the deviations of the calculated values from the observed values over the entire domain and comes with a broken line fitting all data as well as possible. PartReg, on the other hand considers only that part of the domain over which the relation is horizontal. As a result the stretch over which the line is horizontal is usually longer than with SegReg, but the fit of the data in the sloping segment is not so good.
          An illustration of the difference follows. For more examples see this article on page 13 and following.


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Explanation of the difference between SegReg and PartReg

Example SegReg Type 3 :
wheat yield
              and soil salinity

Example PartReg Type 3 with extended horizontal line
using the same data as above
partial regression wheat and salt
The crop tolerates a soil salinity up to about ECe=7.1 dS/m
Example SegReg Type 4:
yield and depth
              watertable

Example PartReg Type 4 with extended horizontal line
using the same data as above
partial regression of
              crop yield and water level
The crop tolerates a watertable depth not shallower than 5 dm.
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