Interpretation Probit Model and Marginal Effects

[Maastricht2006]

Hello,

I use a probit model, with takeover likelihood being 0 or 1 as dep.variables and with profitability numbers being the indep.variables.
I generated the following output in Stata below to get the idea of a likelihood ratio test and the probit model.

The null hypothesis Ho for the LR test means that 2 different models perform approximately the same. Thus, the LR test compares the fit of 2 models.

I am not sure about the conclusion after seeing the test results. I read that the Wald test and the LR test normally give the same conclusion. In this case I have a low test stat and high p-value from the Wald test (meaning: do not reject Ho). However, looking at the LR test provides me with a very high test stat and a low p-value (meaning: Rej Ho). That is why I am a bit confused now...

The marginal effects further below transform the probit coeff into the marginal effect of the indep.variables. However, they do not change at all. This seems to be surprising for me as well.



xtprobit takeovercompleted ebit ebitda netincome

Fitting comparison model:

Iteration 0: log likelihood = -2497.4917
Iteration 1: log likelihood = -2496.9941
Iteration 2: log likelihood = -2496.994

Fitting full model:

rho = 0.0 log likelihood = -2496.994
rho = 0.1 log likelihood = -2467.1486
rho = 0.2 log likelihood = -2463.3351
rho = 0.3 log likelihood = -2475.256

Iteration 0: log likelihood = -2463.335
Iteration 1: log likelihood = -2462.1183
Iteration 2: log likelihood = -2462.1117
Iteration 3: log likelihood = -2462.1117

Random-effects probit regression Number of obs = 3606
Group variable: gvkey Number of groups = 942

Random effects u_i ~ Gaussian Obs per group: min = 1
avg = 3.8
max = 11

Wald chi2(3) = 0.77
Log likelihood = -2462.1117 Prob > chi2 = 0.8574

------------------------------------------------------------------------------
takeoverco~d | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ebit | -.0000245 .0000353 -0.69 0.488 -.0000937 .0000447
ebitda | .0000138 .0000288 0.48 0.632 -.0000427 .0000703
netincome | 9.75e-06 .0000208 0.47 0.638 -.0000309 .0000504
_cons | .0269388 .0283924 0.95 0.343 -.0287092 .0825868
-------------+----------------------------------------------------------------
/lnsig2u | -1.57399 .1713363 -1.909803 -1.238177
-------------+----------------------------------------------------------------
sigma_u | .4552106 .038997 .38485 .5384349
rho | .1716483 .0243615 .129003 .2247534
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 69.76 Prob >= chibar2 = 0.000

. mfx

Marginal effects after xtprobit
y = Linear prediction (predict)
= .02524041
------------------------------------------------------------------------------
variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X
---------+--------------------------------------------------------------------
ebit | -.0000245 .00004 -0.69 0.488 -.000094 .000045 980.659
ebitda | .0000138 .00003 0.48 0.632 -.000043 .00007 1284.84
netinc~e | 9.75e-06 .00002 0.47 0.638 -.000031 .00005 467.826
------------------------------------------------------------------------------

I would interpret the number above as a takeover likelihood or probability of 0.02524041. Is that right?



. margins
Predictive margins Number of obs = 3606
Model VCE : OIM

Expression : Linear prediction, predict()

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .0252404 .0272188 0.93 0.354 -.0281074 .0785882
------------------------------------------------------------------------------

[bukharin]

Wald chi2(3) = 0.77
Log likelihood = -2462.1117 Prob > chi2 = 0.8574

This is the overall significance of the model - it compares your model with the null model.

Likelihood-ratio test of rho=0: chibar2(01) = 69.76 Prob >= chibar2 = 0.000

This is a test of the significance of the random effect term compared with a model fitted without the random effect.

. mfx

This command is outdated as of Stata 11; you should use -margins- as you did below. Since you didn't run it with any options it just gave you the average probability and the coefficients from the regression.

. margins
Predictive margins Number of obs = 3606
Model VCE : OIM

Expression : Linear prediction, predict()

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .0252404 .0272188 0.93 0.354 -.0281074 .0785882
------------------------------------------------------------------------------

This tells you that the mean predicted probability of a positive outcome is 0.0252404 (ie around 2.5%). This should be quite similar to the mean of -takeovercompleted-. It doesn't mean very much though - what are you actually trying to achieve with this command? You may want to have a look at the PDF documentation for -margins-; it starts with some good examples of using -margins- for increasingly sophisticated post-estimation questions.

[Maastricht2006]

I just selected some variables, the variables are not yet specified..