How do I get the direct, indirect, and total marginal effects from a probit model with spatial lags?

[Lom Newton]

I have searched for Stata commands or routines for spatial probit regression but I could not find one. I read from page 79 of Spatial Autoregressive Models Reference Manual (http://www.stata.com/manuals/sp.pdf) that we can manually generate spatially-lagged variables and include them for example in a logistic model.

My question is how do I get (or compute) the direct, indirect and total marginal effects from such a model? Below is the model I estimate and for which I wanted calculate the marginal direct, indirect and total marginal effects. My data is a balanced panel data. The non-spatial version of my model is a fractional probit model. I added the spatially lagged counterparts of the variables as shown below:

spmatrix create idistance W1 if year == 2015, vtruncate(1) normalize(row)

* I manually generate the spatially lagged variables

spgenerate Wlnx1 = W1*lnx1 if year == 2015

* I run the following fractional probit model, with the spatial lags included

fracreg probit y Wy lnx1 Wlnx1 lnx2 Wlnx2 lnx3 Wlnx3 lnx4 Wlnx4 ///
lnx1bar Wlnx1bar lnx2rbar Wlnx2bar lnx3bar Wlnx3bar lnx4bar Wlnx4bar y2 y3 y4 y5, vce(cluster unit)

The results is:

Iteration 0:   log pseudolikelihood = -4073.5974  
Iteration 1:   log pseudolikelihood = -3581.4823  
Iteration 2:   log pseudolikelihood =  -3577.173  
Iteration 3:   log pseudolikelihood = -3577.1671  
Iteration 4:   log pseudolikelihood = -3577.1671  

Fractional probit regression                    Number of obs     =     10,525
                                                Wald chi2(21)     =    1472.25
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -3577.1671               Pseudo R2         =     0.1613

                                           (Std. Err. adjusted for 2,105 clusters in unit)
------------------------------------------------------------------------------------------
                         |               Robust
                       y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
                      Wy |   2.035385   .1083074    18.79   0.000     1.823106    2.247663
                    lnx1 |   .0527919   .0454799     1.16   0.246    -.0363472    .1419309
                   Wlnx1 |  -.0086928   .0464401    -0.19   0.852    -.0997138    .0823281
                    lnx2 |   .5919209   .1449197     4.08   0.000     .3078835    .8759583
                   Wlnx2 |  -.1015673   .0464814    -2.19   0.029    -.1926693   -.0104654
                    lnx3 |   .2130867   .0147082    14.49   0.000     .1842591    .2419143
                   Wlnx3 |  -.0638728   .0224947    -2.84   0.005    -.1079617    -.019784
                    lnx4 |   .0921782   .0184267     5.00   0.000     .0560625    .1282938
                   Wlnx4 |  -.1135582   .0226331    -5.02   0.000    -.1579184   -.0691981
                 lnx1bar |   .1436024   .1636457     0.88   0.380    -.1771372     .464342
                Wlnx1bar |  -.2615471    .166226    -1.57   0.116    -.5873441    .0642499
                 lnx2bar |   .0000472   .0004234     0.11   0.911    -.0007828    .0008771
                Wlnx2bar |  -.0007677   .0004669    -1.64   0.100    -.0016827    .0001474
                 lnx3bar |  -.0436437   .0452084    -0.97   0.334    -.1322504    .0449631
                Wlnx3bar |  -.0410011   .0614048    -0.67   0.504    -.1613523    .0793501
                 lnx4bar |  -.1223141   .0319689    -3.83   0.000    -.1849719   -.0596563
                Wlnx4bar |    .162088   .0374745     4.33   0.000     .0886393    .2355367
                      y2 |  -.0606188    .020703    -2.93   0.003    -.1011959   -.0200417
                      y3 |  -.3554308   .0423882    -8.39   0.000    -.4385101   -.2723515
                      y4 |  -.4245551   .0459211    -9.25   0.000    -.5145588   -.3345514
                      y5 |  -.4592257   .0464956    -9.88   0.000    -.5503554    -.368096
                   _cons |  -3.337843   .7537008    -4.43   0.000    -4.815069   -1.860616
------------------------------------------------------------------------------------------

Would the margins command -margins, dydx(*)- give me the direct and indirect effects? Or how may I get the marginal direct and indirect effects? Better still, is my model statistically sound and am I estimating what I want to estimate?

Any help or suggestion is highly appreciated.

[Phil Bromiley]

Margins works on the estimate you give it so it is dealing in direct effects. You can't have indirect effects as I understand them unless you have more than one equation. I suspect GSEM may be the easiest way to deal with your problem.

As for whether you're estimating a sound model and estimating what you want, that is not something we can answer for you.

[Jeff Wooldridge]

I actually had to teach some of this about 6 weeks ago. I believe I worked out that, if the spatial weighting matrix is row normalized, using the margins command for x gives the direct effect and using it for W_x gives the indirect effect. It’s a pity Stata does not support spatial HAC standard errors for OLS, probit, Poisson regression, and so on.

[Lom Newton]

Thank you very much Phil Bromiley and Jeff Wooldridge for your very very important feedback. My work on this model has stalled for a while because I could not find an "authoritative" material to cite in support of how the margins command would produce the direct effect and the indirect effect of x and W_x respectvely . Please Prof Jeff Wooldridge, do you have any publicly available material (or published work) on this that I can refer to and officially cite in my work?

[Maxence Morlet]

I found the responses on this thread very helpful. Lom Newton you may want to check these papers out if you're still interested: https://ij-healthgeographics.biomedc...72X-11-45#Sec2
https://journals.sagepub.com/doi/ful...UtFak2JQM2nbsA

[Maxence Morlet]

EDIT: The answer to the question I was about to ask can be found here: https://www.cambridge.org/core/servi...ction-data.pdf

[Maxence Morlet]

Hi again, apologies for reviving this thread, but just one quick question: can the coefficient on Wy in #1 be readily interpreted as rho, the coefficient measuring spatial clustering in y? Does Wy have to go through margins as well to yield rho?