[R] probit regression marginal effects

[Quark at gmx.at]

Dear R-community,

I am currently replicating a study and obtain mostly the same results as the author. At one point, however, I calculate marginal effects that seem to be unrealistically small. I would greatly appreciate if you could have a look at my reasoning and the code below and see if I am mistaken at one point or another.

My sample contains 24535 observations, the dependent variable "x028bin" is a binary variable taking on the values 0 and 1, and there are furthermore 10 explaining variables. Nine of those independent variables have numeric levels, the independent variable "f025grouped" is a factor consisting of country names.

I would like to run a probit regression including country dummies and then compute marginal effects. In order to do so, I first eliminate missing values and use cross-tabs between the dependent and independent variables to verify that there are no small or 0 cells. Then I run the probit model which works fine and I obtain reasonable results:

> probit4AKIE <- glm(x028bin ~ x003 + x003squ + x025secv2 + x025terv2 + x007bin + x04chief + x011rec + a009bin + x045mod + c001bin + f025grouped, family=binomial(link="probit"), data=wvshm5red2delna, na.action=na.pass) 

> summary(probit4AKIE)


However, when calculating marginal effects with all variables at their means from the probit coefficients and a scale factor, the marginal effects I obtain are much too small (e.g. 2.6042e-78). My code looks like this:

> ttt <- cbind(wvshm5red2delna$x003,
wvshm5red2delna$x003squ,
wvshm5red2delna$x025secv2,
wvshm5red2delna$x025terv2,
wvshm5red2delna$x007bin,
wvshm5red2delna$x04chief,
wvshm5red2delna$x011rec,
wvshm5red2delna$a009bin,
wvshm5red2delna$x045mod,
wvshm5red2delna$c001bin,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped,
wvshm5red2delna$f025grouped) #I put variable "f025grouped" 9 times because this variable consists of 9 levels

> ttt <- as.data.frame(ttt)

> xbar <- as.matrix(mean(cbind(1,ttt[1:19]))) #1:19 position of variables in dataframe ttt

> betaprobit4AKIE <- probit4AKIE$coefficients

> zxbar <- t(xbar) %*% betaprobit4AKIE

> scalefactor <- dnorm(zxbar)

> marginprobit4AKIE <- scalefactor * betaprobit4AKIE[2:20] #2:20 are the positions of variables in the output of the probit model 'probit4AKIE' (variables need to be in the same ordering as in data.frame ttt), the constant in the model occupies the first position

> marginprobit4AKIE #in this step I obtain values that are much too small


I apologize that I can not provide you with a working example as my dataset is much too large. Any comment would be greatly appreciated. Thanks a lot.

Best,

Tobias
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