Free software for partial z-shape (plateau type) segmented regression

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 (predictor), e.g. crop growth factors like depth of water table and soil salinity with the aim to find the water table and salt tolerance level, also called the "no effect" range or plateau.

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 (plateau) is followed by a sloping line whereas in type 4 the sloping line is followed by a horizontal line (plateau).
The horizontal line (plateau) is found by partial regression over the head end (Type 3) or the tail end (Type 4) of the X domain.

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.

          At the bottom of this page an example is shown of the ability of PartReg to use three segments, instead of two, in which the first and the last segments show horizontal lines.

The salt tolerance (or response) of field crops under farming conditions in irrigated lands is analyzed in this tolerance paper for cases in Egypt, India, and Pakistan.

          The sensitivity of field crops under farming conditions for shallow water tables is analyzed in this sensitivity paper analyzing the tolerance of banana, cotton, sugarcane and wheat too elevated watertables.

          An article entitled "Salt tolerance of crops, statistical analysys of data measured in farm Lands" on the use of PartReg as one of the methods for the assesement of crop tolerance to soil salinity has been published in the International Journal of Agriculltural Science, which can be found on this website.

          The Salt Farm Texel has published a paper on a methodology to evaluate crop salt tolerance from field trials, which I find unacceptable. My comments on this paper can be found in: this report.

Examples of the range of no effect of an influential variable on a response variable is to be seen in this paper.