mtable after probit analysis

[Miguel A. Duran]

I am running a probit analysis. The dependent variable, Y, is a (0,1) dummy variable, and the regressors are both continuous and (0,1) indicator variables. I would like to know Prob(Y=1) according to the estimation. In line with the recommendations by Richard Williams, I am using the command mtable. After reading Stata's help for this command, there is one thing that is still not completely clear to me. Does the comannd "mtable" (without any at() specification) generate the AVERAGE, predicted probability of Y = 1 according to the results obtained in the probit analysis? Thanks in advance.

[Richard Williams]

To be clear, mtable is a user-written command and is part of Long and Freese's spost13 package (findit spost13).

As the help for mtable says, "atmeans option -- All regressors not specified with at() are held at their means. If if or in are used to specify the sample, the means are computed for the selected observations. If atmeans is not specified, marginal effects are averaged across observations."

So yes, mtable is giving you average adjusted predictions. If it isn't clear what that means, see http://www3.nd.edu/~rwilliam/stats/Margins01.pdf.

[Miguel A. Duran]

Thank you very much, Richard. Your comment and the linked pdf have been very helpful. If you do not mind, I would like to make you another question. After a probit regression, I want to calculate the marginal effect of each continuous variable (e.g., X) as the difference in predicted probabilities when moving from the 25th to the 75th percentile of the variables distribution, holding the rest of variables (K and H) constant at their median values. Can this be done in the following way: (i) margins, at(X = value at 25th percentile K = Median H = Median), (ii) margins, at(X = value at 75th percentile K = Median H = Median), and (iii) value in (i) - value in (ii)? Another option is to calculate the marginal effect at the median of X, K and H, and then, compute the difference between the percentiles of X distribution using the marginal effect obtained. But this second method assumes that the marginal effect is constant between the percentiles. Thanks in advance for your help.

[Richard Williams]

Look at

help margins##atspec

to see the many options available to you. Also see the help for mlincom, which is part of spost13. I think you can do what you want to do but you'll have to play around with the syntax to get it just right.

[Miguel A. Duran]

Thanks, Richard. As far as I understand what mlincom does, it is the same, if I am not mistaken, as what I had described in my previous post; i.e., (i) margins, at(X = value at 25th percentile K = Median H = Median), (ii) margins, at(X = value at 75th percentile K = Median H = Median), and (iii) value in (i) - value in (ii).
However, the p-values obtained when "margins" is used depend on the values at which marginal effects are computed. If I analyze X, I assume that the rest of variables are at their median values. Accordingly, although the marginal effect of X that I will report is this 25th-75th percentile effect, I thought of reporting p-values and standard errors based on the marginal effects at the medians of X and the rest of variables. Does it sound accurate?