Parameter estimates scaled by SD

[Rob Keith]

Hello Forum,

Does anybody has an idea how to approach to get parameter estimates scaled by the standard deviation of an underlying variable?

Best,
Keith

[Clyde Schechter]

If you are referring specifically to the -regress- command, if you add the -beta- option to the command it will give you coefficients that are scaled to the standard deviations of all of the explanatory and outcome variables. If you only want some of the variables scaled that way, or if you are using any other estimation command, then you have to rescale the variables themselves before running the estimation command:

foreach v of varlist list_of_variables_for_standardization {
    quietly summ `v'
    gen `v'_std = (`v'-r(mean))/r(std)
}

Then use the *_std variables in the estimation command in place of the original ones.

That said, do you really want to do this? It's usually a bad idea. It never makes sense at all to standardize a discrete variable. And even for continuous variables, if they have a natural scale of their own, you should use that so that your results will be readily understandable. If I were to tell you that Y increases by z amount with a 1 SD increase in, say, a person's height, you would probably, and rightly, feel that I'm obfuscating the result. How big, after all, is 1 SD of height. And even if I were to tell you it is, say, 2.3 inches, you would rightly wonder why I would express a result per 2.3 inches instead of just telling you the results per inch. The only time standardizing this way is really helpful is when the variable in question has no natural scale (or the natural scale is so exotic that most of your intended audience would be unfamiliar with it anyway).

[Richard Williams]

I pretty much agree with Clyde. In this handout (see especially the last page) I basically argue that standardized coefficients are often the work of Satan:

https://www3.nd.edu/~rwilliam/stats2/l71.pdf

On the other hand though, in this handout I show how different types of standardization (Full Standardization, X-Standardization, and Y-Standardization) can be easily done with Long & Freese's listcoef command:

https://www3.nd.edu/~rwilliam/xsoc73994/L04.pdf

So, if you really really want to use standardized variables, Long & Freese's listcoef command (findit spost13_ado) is probably the easiest way to go, But, if you go that route, consider using X-standardization rather than full-standardization. X-Standardization achieves the goals that most people want to achieve with standardized variables while still providing semi-intuitive results.

[Richard Williams]

Having said all that, I wonder if we misunderstand the Q. What do you mean by "an underlying variable?" Do you mean a latent variable, perhaps something like the Y* variable in a logit or probit model? Or what?