standardized reg coefficients (, beta) for interaction

[Alexander Neuhaus]

Hello,

i have a question regarding the interpretation of standardized regression coefficients or beta coefficients in stata. I want to test the nonlinear effect of age on knowledge and i am able to interpret the unstandardized coefficients in models with interaction and also beta coefficients in models without interactions but i can´t get my head around the meaning of beta coefficients in models with interaction.

The syntax would be "reg knowledge c.age##c.age, beta".

Knowledge is 1-10

age is 18-95

How can i interpret a beta coefficient for c.age#c.age of lets say"0.22"?

[Clyde Schechter]

The difficulty you are having in interpreting this is quite understandable. It is rather complicated and I think it is an excellent example of why standardized regression coefficients should generally be avoided altogether. To interpret this coefficient you have to know not only what the standard deviation of age in your study sample is, but also the standard deviation of age^2 in that same sample. You then ahve to relate that to the standard deviation of the knowledge variable. Now, age has a natural metric of its own: years (or months for small children). A standardized age variable transforms a perfectly comprehensible concept into a mystery. Throw the quadratic term into the mix and you have a total obfuscation of what should be very simple.

It might be sensible to standardize the knowledge score, depending on how you measured it. If the measurement is in arbitrary units, or based on an instrument that most of your audience will be unfamiliar with. In that case the standardized version might at least provide the reader/listener with some context. But age? As far as I can tell, the only reason one could ever have for standardizing an age variable is to deliberately obfuscate the findings. Don't do it.

By the way, just to clear up part of the mystery for you, when you ask Stata to do a standardized regression with a quadratic term, it separately standardizes the linear and quadratic terms. It does not use the square of the standardized linear variable.