There are several factors that are influencing a variable. We only know the extent of influence and the extent of correlation. How to prioritize these factors using mere these two attributes?
*These factors are represented in time series form.
Dear Saad,
welcome,
perhaps you can rank the different factor with the sensitivity of the parameter to the variations of the factor. Mathematically expressed,
the sensitivity S can be calculated from the formulation S= dy/y / dx/x, where y is the parameter and x is the factor. dy/y is the relative change in y due to the relative change in x. When S is larger means that the factor has more influence on the parameter y.
Best wishes
@Abdelhalim Zekry. Professor, thank you for the reply. Can you suggest me any paper where i can find this method?
Dear Saad,
please refer to the paper given in the link:https://deepblue.lib.umich.edu/bitstream/handle/2027.42/42691/10661_2004_Article_BF00547132.pdf?sequence=1
Best wisihes
@Abdelhalim Zekry
Dear Prof. I think this method is a kind of slope.
i.e., small slope = small influence of factor on the parameter.
larger slope = larger influence of factor on the parameter.
However slop method is usually for linear method and this differential analysis is for non-linear data as well. Since my data is non-linear, this method is preferable.
Now, i have a question, how can we use a data set to calculate differentiation? I am only familiar with calulating differentials of equaltions/relations. For example, I can manage y = 3x^3 + 4x^2 +5 but when
y = (1, 2, 3, 9, 12)
x1 = (1.1, 2.2, 5.6, 11, 13)
x2 = so on...
In this case how, would one calculate differtial?
For adiscrete series of values (like your examples), "differentiation" is as simple as calculating the differences:
dy = ( y[1] - y[0], y[2] - y[1], ..., y[k] - y[k-1] )
As for the calculation of the sensitivity S Prof. Zekry mentions:
S = dy/y ==> suggestion: S = ( y[n] - y[n-1] ) / ( ( y[n-1] + [y[n] ) / 2 )
@U. Dreher:
Thank you for your answer. Why are we dividing by 2 in denominator?
(a + b) / 2 results in the arithmetic mean value of a, b.
To calculate dy/y for discrete series, I feel that it might be better to use the mean value of the 2 points setting the difference than chosing either single point. Though - mathematically - you could as well decide to use either input value.
Writing this: be prepared to handle the case where both input values equal zero!
Adding to Dr. Dreher, you can directly calculate discrete values for the sensetivity as he showed. However, you can interpolate you data set to get an analytical function
Y= f(x) using interpolation tool box in matlab. Interpolation techniques belongs to the lessons of the numerical techniques.
After getting the analytic function you can analyse its sensitivity by straight forward partial differentiation.
Best wishes
OLS standardized beta coefficients are used to rank the strength of the variable using standard deviations, the higher value of a given variable the stronger impact it has on the dependent variable. In stata, just add beta after a normal regress command
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