Comparing the influences of different IVs is tricky, and to my opinion usually pointless, as it seems the wrong question.

As you said, the coefficients depend on the units of the IVs, and those are arbitrary (I can give time in min, h, day or whatever; I can give mass in µg, g, kg, etc etc).

The standardized coeffs are unitless, what at a first glance looks like an advantage. But what do these values mean? It's already a problem to interpret the value of a coefficient given the unit, but now we have a ratio that contains this value and a measure of the variation (in the same unit). Just because the unit cancels out it does not mean that the value of the ratio will be easier to interpret than the individual values (mean and sd of the raw coeff). Clearly, one can see which IV would have the largest impact relative to its sd, but as the variances of the different IVs have different meanings, it remains unclear what we learn from that conclusion.

As a solution, I would refer the changes to a common ground. For instance, that could be money. How much would it cost to change the value of an IV to get one unit change of the DV? This way, all the influences are measured in the same unit (not unitless!) and can be compared.

Comparing the influences of different IVs is tricky, and to my opinion usually pointless, as it seems the wrong question.

As you said, the coefficients depend on the units of the IVs, and those are arbitrary (I can give time in min, h, day or whatever; I can give mass in µg, g, kg, etc etc).

The standardized coeffs are unitless, what at a first glance looks like an advantage. But what do these values mean? It's already a problem to interpret the value of a coefficient given the unit, but now we have a ratio that contains this value and a measure of the variation (in the same unit). Just because the unit cancels out it does not mean that the value of the ratio will be easier to interpret than the individual values (mean and sd of the raw coeff). Clearly, one can see which IV would have the largest impact relative to its sd, but as the variances of the different IVs have different meanings, it remains unclear what we learn from that conclusion.

As a solution, I would refer the changes to a common ground. For instance, that could be money. How much would it cost to change the value of an IV to get one unit change of the DV? This way, all the influences are measured in the same unit (not unitless!) and can be compared.

Hi John-Kåre. I agree with Jochen. If you need a reference to support what he says about standardized regression coefficients (which are viewed by many as the solution to this problem), perhaps this note I wrote when reading John Fox's book on regression and GLM will be useful to you. HTH.

--- Start of note ---

John Fox, author of "Applied Regression Analysis and Generalized Linear Models" (2008, Sage) is very cautious about the use of standardized regression coefficients. He gives this interesting example. When two variables are measured on the same scale (e.g., years of education, and years of employment), the relative impact of the two can be compared directly. But suppose those two variables differ substantially in the amount of spread. In that case, comparison of the standardized regression coefficients would likely yield a very different story than comparison of the raw regression coefficients. Fox then says:

"If expressing coefficients relative to a measure of spread potentially distorts their comparison when two explanatory variables are commensurable, then why should the procedure magically allow us to compare coefficients [for variables] that are measured in different units?" (p. 95)

That is an excellent question!

Hello John-Kåre,

If you want to compare relative emphasis given to individual variables in a model (e.g., for the full model regardless of whether you forced all independent variables (IVs) in simultaneously or in stages), then the standardized regression coefficients will convey this information.

If, on the other hand, you'd like to know which independent variable adds the most to explanatory power, given the other IVs, you could run a set of reduced models, each omitting one IV at a time, and compare their R-squared values to that for the full model (with all IVs). The omitted variable that yields the biggest change (from exclusion to inclusion) is the one that adds the most explanatory power (for your set of IVs, with your sample) for the dependent variable.

Of course, if you have a rationale for a specific staging/sequence of IV entry in a hierarchical regression, it may be easiest just to inspect standardized regression coefficients for the IVs in the model at any given stage and compare those.

Good luck with your work.

Thanks for your comments, they are much appreciated!!

Best

John-Kåre

Prof Wilhelm's answer is quite good in some situations. For predictive models there are other choices depending on what you mean by your question. See the attached papers. Best, David Booth