As a junior engineer I worked with an experienced and talented technician to interpret test results from a rotating kiln cold model investigating a range of feed materials and operating conditions. He used the following procedure to develop simple relationships to describe the data.
· The dependent variable (y) is plotted against each independent variable of interest (say x and z) to determine which achieves the best fit. A simple relationship (power, exponential, logarithmic, etc) was then used to describe the fit (say a x2 for variable x).
· The dependent variable was then divided by this relationship and the values for the modified dependent variable (y/a x2) plotted against the remaining independent variable again to find the simple relationship that best described the fit (say b EXP(c z)).
· The final relationship was y = a b x2 EXP(c z).
· The relationships developed for the cold model seemed reliable and were used to support improvements to an under-performing commercial dryer.
I have used this approach on a number of occasions to identify the form of knowledge-based relationship to be used in a statistical regression package. It appears a successful screening tool but I can find no reference to the approach in the literature. Does anyone know if there is a basis for the approach? What other screening approaches might be used?
Hello,
For me is the first time that I see this estimation procedure, but I have notes :
1- what about the relationships between the independent variabels (x,z) ?? because your method don't allow us to test the independenc bewteen them.
2- Why you are divded the original data (y) on the predicitve one (^y) and not did the difference -which is the reference in econometric (i.e) it represent the residuals)
3- I think (and especialy- in the second step, you've changed the scale of the dependent variable .
Best whishes
This only works for one model, probably the one he knew he was working with. If you want to do this for any model see the attached. Best, David Booth
Gentlemen, Thank you for your replies and Dr. Booth for the course materials “Regression Modeling Strategies”. I am sure that readers in addition to myself will find the information of great value.
As an indication of how long ago I was a junior engineer, all calculations were carried out using slide rules. The technician had a well-worn 18-inch wooden model, far superior to my 10-inch plastic Thornton. As addition and subtraction are not possible on these admirable devices, it was easier to develop models in which the functions describing the variables were multiplied together. As far as the model selection procedure, it may have originated during the time the technician was serving in the Royal Ordnance during WW2.
When used on the rotating kiln cold model, the variables were not randomly selected but those found by others to be significant: no consideration was given to statistics. When I use the approach now, the model developed is subjected to a range of statistical tests to verify that the analysis is valid. It works best when the influence of one variable predominates with lesser effects for the others. All I can say is that the approach generally gives relationships that provide some insight into how a system works. I would, however, feel more comfortable using it if I could find some reference to its use elsewhere, hence my question.
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