# How to interpret coefficients (and R²) of an -oprobit- model (STATA 13)?

I'm fitting a "oprobit" model in STATA 13 and I can't wrap my head around how to interpret the coefficients.

This is the model that I'm running:

oprobit enforce depth_index TransitionalFlex numberms ns us eu g20 asia americas africa wto_max Democratization m_mean yr*, robust


This is what my (main) variables look like:

• enforce (Y): 0-9 (with lots of 0s)
• depth_index: 0-7
• TransitionalFlex: 0-25
• numberms: 2-91

I'm controling for time effects ("yr*") but I'm not directly reporting any time effects at this point. Also, I use robust S.E.s as this is probably the default approach.

Now my output looks like this:

Obviously, the coefficients cannot be interpreted the same way as in a simple OLS regression: coefficient of X1 * range of X1 = maximum substantial effect of X1 on Y.

I guess the main reason for that is that "nonlinearity" plays a central role in an oprobit model while OLS assumes perfect linearity. Right?

Also, I learned that -margins- should be a really helpful tool to interpret the oprobit output (e.g. as explained here), but so far I couldn't wrap my head around how this works exactly. Especially, I was wondering if there is a way to interpret the maximum effect of one variable on another (Y) additionally to the marginal effect of a change from one value on X to another. Should I take the average of all marginals effects of one variable or add them all together...?

Thus, I would really appreciate if someone could provide me with (very simple) instructions: how should I interpret the effects of my main variables?

And how does the Pseudo R² correspond to a normal OLS model R²? Lower? Higher? More reliable? Less reliable?

Hope others can benefit from a once-and-for-all simple explanation of these things as well.

• Concerning Pseudo-$R^2$'s, check this answer to another question: stats.stackexchange.com/a/3562/109647 – T.E.G. Aug 9 '17 at 3:00
• Thank you! All this criticism regarding Pseudo-R²s makes me wonder whether there is any good alternative at all. It seems that out of fear that Pseudo-R²s would mislead, nothing is reported at all but the mere coefficients, S.E.s etc. (which is at least my impression from several articles that I have read in which they fitted [ordered] logit and [ordered] probit models...). – Fabian Habersack Aug 9 '17 at 8:36
• You might some of this post helpful. – Dimitriy V. Masterov Aug 11 '17 at 16:44