reports & cases
reports & cases
(1) - An amplification application of the SegReg calculator permitting expression of preference for a certain type of segmentation, or of the wish to exclude a certain type, can be downloaded from SegRegA. It also gives the option to select an S-curve, power function, or a generalized third degree polynoom, see: S-curves, Cubic, Power or, Polynome.
(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 difference between SegReg and PartReg. The first minimizes the deviations of the model values from the observed ones over the entire domain, whereas the second calculates the maximum part (range) 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 segmented regression article on page 13 and following, the tolerance paper on soil salinity tolerance of crops, or the sensitivity paper on sensitivity of crops to shallow watertables.
Segreg permits the analysis of one dependent and two independent variables. This case is called polynomial. See the screen print of the input menu for such a case in Part 2 of the illustrations below. Some results are also shown there.
Relations of crop yield and depth of water table: crop-watertable .
Yearly average day temperatures in the Netherlands and global warming: average temperatures .
Yearly maximum day temperatures in the Netherlands and global warming: maximum temperatures .
Segmented and probability analysis: segments and probability.
Comparing the regressions of Y-X data by means of the amplified power function using Solver in Excel and SegRegA with graphics.
Testing the statistical significance of the improvement of cubic regression compared to quadratic regression using analysis of variance (ANOVA): testing.
Part 1 of the illustrations for 1 dependent and one
variable (Y and X respectively).|
(Part 2 for the polynomal case of 1 dependent
variable (Y) and 2 independent variables (X and Z)
can be seen further down)|
Introduction screen of SegReg calculator program:
The model comes with various explanations like programmed function types, calculation methods, and application of
Example Type 3:
The SegReg model is designed for segmented (piecewise) linear regression with breakpoint (threshold). The application program
can be used for salt tolerance of crops or the tolerance to shallow watertables.
The calculator clarifies the crop response and demonstrates the resistance to high soil salinity or water level. This Type 3 is similar to the Maas-Hoffman model.
Example Type 3 with extended horizontal line using the same data as above in the PartReg software application.
instead of SegReg.
According to this calculator model, the salt tolerance of mustard is almost ECe=8 dS/m. After this threshold the yield reduces.
In other words, form this application program it can be deduced that the crop resists salinity up to 8 dS/m while up to 8 dS/m there is no negative effect.
Example Type 4:
The crop tolerates a depth of the water table of 7 dm.
The Segreg software calculator is an application (app) made to detect different segmented models, like Type 4 in the above figure.
This type is an inverted Type 3 or an inverted Maas-Hoffman model
Example Type 5:
In year 9 (1976) a dam was contstructed in the river
The Segreg application (app) is a calculator made to program different segmented models, for example Type 5 in the figure.
Part 2 for the polynomal case of 1 dependent variable (Y) and 2 independent variables (X and Z)
Screen print of the input menu for the polynomial case (1 dependent variable (Y) and 2 independent variables (X and Z).
The SegReg program found that the 1st independent variable (X) has a higher coefficient of explanation than the second (Z). Therefore the first segemented regression is made for X.
The the residuals of Y after the regression on X are used with a segmented regression on the second variable (Z).
The mathematical combination of the first and second analysis yields equations of the type Y = A.X + B.Z + C (polynomial)