Interpretation of marginal effects in an ordered probit model for a z-transformed variable

[Daniel Weimar]

Hi everyone,

I am trying to find out, how I could interpret z-transformed variables in an ordered probit model with marginal effects. My independent variable is a distance measure, which is a global z-score out of three different distance measures (GlobalZDistance). The dependent variable is of ordinal nature ranging from 1 to 7 (Support). I am only interested in the effects on the highest category (7). I use an ordinal probit model. The average marginal effect of GlobalZDistance on Support (7) is 0.054.

In a simple linear model, this value should indicate that if GlobalZDistance changes by 1SD, then Support increases by 0.054 SD, right? But what is the right interpretation for my marginal effects?

[Clyde Schechter]

In a simple linear model, this value should indicate that if GlobalZDistance changes by 1SD, then Support increases by 0.054 SD, right?

No, even this much would only hold if Support is also standardized. (I'm ignoring the causality issues here, which would make the statement in general false no matter what you did with the variables.)

With GlobalZDistance being standardized, and Support being simply an ordinal variable ranging from 1 to 7, the interpretation would be that a difference of 1 SD in GlobalZDistance is associated with a 0.054 increase in the probability of Support being 7, all else equal and adjusted to the observed distribution of values of other variables in your data.

By the way, it is not a good idea to refer to standardized variables as "z-transformed." There is a function known as the Fisher z-transformation, which has nothing to do with standardization. Initially it sounded like you were referring to that.

[Richard Williams]

You might want to check out Long and Freese's listcoef command (findit spost13_ado). It offers different kinds of standardization. I think what you have actually done is X-Standardization, but what you describe is Full-Standardization. For interpretation, best is to read their book:

http://www.stata.com/bookstore/regre...ent-variables/

But for a brief discussion of listcoef, see

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

I think coefficients in logit and ologit models are hard enough to understand as is without standardizing the X's too. You might want to look at how spost13 commands like mtable and mchange can make life easier:

http://www3.nd.edu/~rwilliam/xsoc73994/Margins05.pdf

[Daniel Weimar]

Thank you very much for your thoughts. What I have done is a global standardization with GlobalZDistance=SD(SD(feet distance)+SD(road distance) + SD(distance public transport in Minute)) with SD=(x-mean)/Standard error