interpretation margins

[Marzieh Goodarzi]

hi every body. i have a question from you:

I first run a probit regression. In this regression, all variables are dummy variables (binary) variables.
Then I get the margins of all variables when two explanatory variables are in the value of 1 (beside on the following code.)
These two explanatory variables are i.L2underline and i.Lunderline.
What is the interpretation of the i.L2underline coefficient?
In other words What is the interpretation of .3406954؟؟




code of stata:

. probit underline i.Lq i.Lunderline i.L2q i.L2underline [pw=Weight]

Iteration 0: log pseudolikelihood = -4148965.2
Iteration 1: log pseudolikelihood = -2930488
Iteration 2: log pseudolikelihood = -2919236.4
Iteration 3: log pseudolikelihood = -2919231
Iteration 4: log pseudolikelihood = -2919231

Probit regression Number of obs = 20,174
Wald chi2(4) = 2340.87
Prob > chi2 = 0.0000
Log pseudolikelihood = -2919231 Pseudo R2 = 0.2964

-------------------------------------------------------------------------------
| Robust
underline | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
1.Lq | .2236635 .0531638 4.21 0.000 .1194644 .3278627
1.Lunderline | 1.19886 .0436968 27.44 0.000 1.113215 1.284504
1.L2q | .1820238 .054248 3.36 0.001 .0756998 .2883479
1.L2underline | .890711 .0461142 19.32 0.000 .8003288 .9810932
_cons | -1.656304 .0233418 -70.96 0.000 -1.702053 -1.610555
-------------------------------------------------------------------------------

. margins, dydx(_all) at(L2underline=1 Lunderline=1)

Average marginal effects Number of obs = 20,174
Model VCE : Robust

Expression : Pr(underline), predict()
dy/dx w.r.t. : 1.Lq 1.Lunderline 1.L2q 1.L2underline
at : Lunderline = 1
L2underline = 1

-------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
1.Lq | .0753659 .0175447 4.30 0.000 .0409789 .1097529
1.Lunderline | .4457022 .0146431 30.44 0.000 .4170022 .4744022
1.L2q | .0618543 .0181925 3.40 0.001 .0261978 .0975109
1.L2underline | .3406954 .016691 20.41 0.000 .3079815 .3734092
-------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

[Clyde Schechter]

It means that when Lunderline and L2underline are both equal to 1, a unit increase in L2underline is associated with an increase of 0.34 (to 2 decimal places) in the adjusted probability of underline (adjusted to the observed distribution of all other model variables.)

However, looking at your outputs, I'm getting the strong impression that Lunderline and L2underline are both 0/1 variables. If that's true, then a unint increase in L2underline starting from L2underline = 1 is impossible, meaningless, or, at best, an extrapolation beyond your observed data. For that reason, I would be quite reluctant to take these results seriously. I'm not sure what your context and research questions are and what motivated you to compose your -margins- command in the particular way you did, so it is difficult for me to suggest an improvement with any confidence. But if you are interested in the marginal effect of L2underline, I would at least revise the command to have L2underline = 0 in the -at()- option.

[Justin Niakamal]

Check out Econometrics Academy, they walk through the interpretation here.

[David Benson]

Also see Richard Williams excellent tutorial on Stata's margins command (and how to interpret various interactions) here.

[Marzieh Goodarzi]

thank you very much Mr. Schechter and justin and Mr.benson

Mr. Schechter, The research question is about marginal effect of L2q. But I wanted to know what the .3406954 number shows?

When I got the marginal effect at(L2underline=1 Lunderline=1) , does it mean that these two variables (L2underline & Lunderline) have been entered into the regression constant ?

[Clyde Schechter]

The number .3406954 represents the expected difference in probability of outcome underline associated with a unit changeof L2 underline from while holding Lunderline at 1 and allowing other variables to take their observed values.

[quote]When I got the marginal effect at(L2underline=1 Lunderline=1) , does it mean that these two variables (L2underline & Lunderline) have been entered into the regression constant ?[/qutoe]
No, the regression is not rerun. Instead, the regression results are applied to the data to calculate the predicted probabilities. In doing that, the values of L2underline and Lunderline are replaced by 1's for the purpose of that calculation, while the other variables are left at their original values.

[Marzieh Goodarzi]

Thanks a lot for your answer