Standardized regression coefficients with categorical independent variables.

[Glenn Abilene]

Hi Statalisters,

I am running some simple regressions with a continuous dependent variable and several continuous, ordinal, and dichotomous variables. I was previously standardizing the continuousand ordinal variables. The colleague recommended that I use the ", beta" command to standardize all coefficients. However, as I understand it, this will also standardize the categorical variables I am employing, which will not provide intuitive results.

For example,
sysuse auto
egen STDprice=std(price)
xi: reg STDprice mpg foreign rep78
xi: reg STDprice mpg foreign rep78, beta

I'm using Stata 12, however I don't think its relevant to this example.

While the standardize coefficients are easily interpretable for the continuous "mpg" and reasonably interpretable for the (assumed to be) ordinal variable "rep78", the beta for "foreign" doesn't make sense. Without the standardized dummy variable, the coef can be interpreted as: on average foreign cars cost .347 std. more than domestic cars holding all else constant.
However, if "foreign" is standardized, how would this be interpreted? A 1 standard deviation in "foreignness" doesn't make sense to me.
Therefore, is it technically or practically inadvisable to use the ", beta" command? Would there be any advantages to standardizing cat. vars?

Thanks in advance,

Glenn

[Marcos Almeida]

Hello, Glenn,

It's up to you to make a choice, and sometimes it can be a matter of taste. But I gather the standardized coefficients allow us to compare different predictors under a sole scale. You don't need to worry about the original measurement anymore. What is more, it provides sort of "effect size", "correlation-like", so to speak.

Best,

Marcos

[Clyde Schechter]

Therefore, is it technically or practically inadvisable to use the ", beta" command? Would there be any advantages to standardizing cat. vars?

There is no technical obstacle at all. Just add the -beta- option and, voila!

Practically speaking, your own arguments against standardizing a categorical variable make perfect sense and standardizing it makes no sense. The only thing I can say in favor of the practice is that in certain disciplines, particularly behavioral sciences, the practice of standardizing everything is widespread--to the point of being almost a social norm. [There is some basis for this in that many of the variables in this domain have arbitrary scales, so putting those variables into standard scaling makes sense.]

Your observation that it renders the regression coefficients uninterpretable is correct, with one exception. If the primary research question is to compare the relative strength of association to the outcome of the different independent variables, then standardizing them all makes sense so that effects of scale are eliminated. (Actually, there are some arguments against the practice even in this situation, but let's not go there.) But that is seldom the actual goal of the research.

I get into these discussions with my behavioral science collaborators from time to time and I'm usually able to persuade them not to standardize these variables. Just hang in there!