Using Margins when model has squared terms

[Zuhura Anne]

Hello statlisters,

I am using a probit model to carry out my estimation. My explanatory variables comprise squared, continuous and dummy variables.
After running my probit model, and then the margins command, I realized that the probit model has the squared terms but the output from margins does not have them.

Is there a way I can ensure that I have the squared terms in the output?

probit y  i.x1  i.x2  x3  c.x3#c.x3 i.x4 i.x5 x6 x7 c.x7#c.x7, cluster(id)

margins, dydx(*)post

[daniel klein]

See Vince Wiggin's discussion of the problem.

Best
Daniel

[Phil Bromiley]

The short answer is that the derivative is with respect to x, not x-squared. x is what really changes and you can't change x-squared independent of x. Because you use factor notation, Stata handles that for you so the dy/dx includes both linear and squared terms.

[Mari Meir]

Besides Vince Wiggin's discussion on the theme suggested by Daniel, I also suggest the following readings:

Buis, M. L. (2010). Interpretation of interactions in non-linear models. The Stata Journal, 10 (2), 305-308.
Greene, W. (2010). Testing hypotheses about interaction terms in nonlinear models. Economics Letters, 107, 291–296.
Hoetker, G. (2007). The Use of Logit and Probit Models in Strategic Management Research: Critical Issues. Strategic Management Journal. (28),4, pp. 331-343
Karaca-Mandic, P., Norton, E. C., and Dowd, B. Interaction Terms in Nonlinear Models. Health Service Research, 47(1), 255-274.
Williams, R. (2012). Using the margins command to estimate and interpret adjusted predictions and marginal effects. The Stata Journal, 12(2), 308-331.

[Zuhura Anne]

Thank you all so much.

[Mahnoor Sohail]

Zuhura Anne hi, so how did you present the quadratic term with the results? i want to present margins but i also want to show that the relationship is non linear.

[Richard Williams]

Graphics can help. I am a big fan of the mcp command, which you can get from the Stata Journal files (findit mcp). Example:

webuse nhanes2f, clear
reg health c.weight
mcp weight, var1(30) plotopts(name(Linear, replace))
reg health c.weight c.weight#c.weight
mcp weight, var1(30) plotopts(name(NonLinear, replace))

Or, if you prefer not to use mcp,

margins, at (weight = (30(5)175))
marginsplot, noci

A summary of mcp can be found at

https://www3.nd.edu/~rwilliam/stats3/Margins03.pdf

[Mahnoor Sohail]

Richard Williams Thanks a lot sir!!