Sunday, April 1, 2007

Don't standardize the parameters

If you are doing a linear regression, it is recommended that you interpret unstandardized coefficients (betas) rather than standardized ones (Mendenhall, Sincich, 2003). By standardizing the coefficients, you are losing the weights of independent variables on the dependent variable. Also, you are trying to compare non-comparable variables.

For example, let's say that you have two independent variables "age" and "education" (both in years) explaining a dependent variable, say, salary. If betas associated with the two dependent variables are 1,000 and 10,000 respectively, you interpret the betas as follows:

One unit of increase in age increases the salary by 1,000 units, keeping education constant. Similarly, one unit of increase in education increases the salary by 10,000 units, keeping age constant.

As seen in this example, one unit of education is more influential on salary than age. If you standardize the coefficients, you may lose this information. Furthermore, standardization makes one unit of age equal to one unit of education. However, one unit of age is never equal to one unit of education.

That is why some of the statistical software packages like SAS do not report standardized betas in their output...

References:
Mendenhall, W., Sincich, T., "A Second Course in Statistics: Regression Analysis", 6th ed. Upper Saddle River, N.J.: Prentice Hall, 2003.
ISBN-10: 0130223239

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