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In Stata 11, the margins command replaced mfx.
| Title | Marginal effects and the travelvl option | |
| Author | May Boggess, StataCorp |
The tracelvl(1) option is very useful for watching mfx at work. Let’s look at an example:
. sysuse auto, clear
(1978 Automobile Data)
. mlogit rep78 length displacement turn gear_ratio, nolog
Multinomial logistic regression Number of obs = 69
LR chi2(16) = 50.40
Prob > chi2 = 0.0000
Log likelihood = -68.492767 Pseudo R2 = 0.2690
------------------------------------------------------------------------------
rep78 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1 |
length | -.0077791 .0857701 -0.09 0.928 -.1758855 .1603272
displacement | -.0203556 .0217033 -0.94 0.348 -.0628933 .0221822
turn | .2606348 .4279448 0.61 0.542 -.5781215 1.099391
gear_ratio | -1.84238 3.056085 -0.60 0.547 -7.832197 4.147436
_cons | -2.307812 16.15227 -0.14 0.886 -33.96567 29.35005
-------------+----------------------------------------------------------------
2 |
length | -.0257227 .0503671 -0.51 0.610 -.1244405 .0729951
displacement | -.0227271 .0139469 -1.63 0.103 -.0500626 .0046083
turn | .5413776 .2719147 1.99 0.046 .0084346 1.074321
gear_ratio | -3.959613 2.582289 -1.53 0.125 -9.020805 1.10158
_cons | -2.896173 9.00731 -0.32 0.748 -20.55018 14.75783
-------------+----------------------------------------------------------------
4 |
length | .0485892 .0351597 1.38 0.167 -.0203226 .117501
displacement | -.0006782 .009394 -0.07 0.942 -.0190901 .0177337
turn | -.2454005 .1682703 -1.46 0.145 -.5752041 .0844032
gear_ratio | 1.615741 1.430829 1.13 0.259 -1.188633 4.420116
_cons | -4.694191 7.392889 -0.63 0.525 -19.18399 9.795606
-------------+----------------------------------------------------------------
5 |
length | .2154726 .0826013 2.61 0.009 .053577 .3773682
displacement | -.1231205 .0456459 -2.70 0.007 -.2125848 -.0336562
turn | -.561081 .2635563 -2.13 0.033 -1.077642 -.0445202
gear_ratio | -4.795507 2.475835 -1.94 0.053 -9.648054 .0570406
_cons | 14.0879 11.59243 1.22 0.224 -8.632844 36.80864
------------------------------------------------------------------------------
(rep78==3 is the base outcome)
. mfx, predict(p outcome(2)) tracelvl(1)
calculating dydx (nonlinear method)
-------------------------
variable | dy/dx
---------+---------------
length | -.00184
displa~t | -.00094
turn | .02686
gear_r~o | -.19349
-------------------------
calculating standard errors (nonlinear method)
length ... continuous
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
length: Std. Err. = .00272748
displacement ... continuous
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
displacement: Std. Err. = .00066346
turn ... continuous
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
turn: Std. Err. = .01852245
gear_ratio ... continuous
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
gear_ratio: Std. Err. = .11812354
Marginal effects after mlogit
y = Pr(rep78==2) (predict, p outcome(2))
= .04557427
------------------------------------------------------------------------------
variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X
---------+--------------------------------------------------------------------
length | -.0018412 .00273 -0.68 0.500 -.007187 .003505 188.29
displa~t | -.0009443 .00066 -1.42 0.155 -.002245 .000356 198
turn | .0268613 .01852 1.45 0.147 -.009442 .063165 39.7971
gear_r~o | -.1934947 .11812 -1.64 0.101 -.425013 .038023 2.99928
------------------------------------------------------------------------------
I’ve chosen mlogit as an example because it is a multiple-equation estimation with many coefficients, so mfx can take quite some time to complete its calculations.
Let’s go through the extra output that tracelvl(1) has created and see what it means. The first part of the output is
calculating dydx (nonlinear method)
-------------------------
variable | dy/dx
---------+---------------
length | -.00184
displa~t | -.00094
turn | .02686
gear_r~o | -.19349
-------------------------
First mfx tells us that it is calculating the marginal effects and that it is using the nonlinear method (see the FAQ stata.com/support/faqs/statistics/marginal-effects-methods for an explanation of what nonlinear means). We see this output appear very quickly indeed. Let’s look at the next piece of output:
calculating standard errors (nonlinear method) length ... continuous 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 length: Std. Err. = .00272748
mfx begins by letting us know it is doing the standard errors, again using the nonlinear method. Then, for each independent variable in the estimation, we have numbers counting across the screen in front of us. It is comforting to see them because at least we know mfx is still at work, but what do they mean?
To compute the standard error of each marginal effect, we need to compute a number corresponding to each coefficient in the estimation (see the FAQ stata.com/support/faqs/statistics/marginal-effects-methods for a full description of exactly what they are). So, the list of numbers tells you which variable it is up to in the computation. We can use tracelvl(2) if we want to see each of those numbers as mfx computes it:
. webuse fish, clear
. zip count persons, inf(child camper) vuong nolog
Zero-inflated Poisson regression Number of obs = 250
Nonzero obs = 108
Zero obs = 142
Inflation model = logit LR chi2(1) = 417.56
Log likelihood = -895.1643 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
count |
persons | .8061845 .0460454 17.51 0.000 .7159371 .8964318
_cons | -.5040989 .1658804 -3.04 0.002 -.8292184 -.1789793
-------------+----------------------------------------------------------------
inflate |
child | 1.513283 .2652983 5.70 0.000 .9933076 2.033258
camper | -1.007936 .3499951 -2.88 0.004 -1.693914 -.3219581
_cons | -.3299887 .2913634 -1.13 0.257 -.9010505 .2410732
------------------------------------------------------------------------------
Vuong test of zip vs. standard Poisson: z = 3.94 Pr>z = 0.0000
. mfx, predict(n) nonlinear tracelvl(1)
calculating dydx (nonlinear method)
-------------------------
variable | dy/dx
---------+---------------
persons | 1.7639
child | -1.7485
camper | 1.1334
-------------------------
calculating standard errors (nonlinear method)
persons ... continuous
1 2 3 4 5
persons: Std. Err. = .17607926
child ... continuous
1 2 3 4 5
child: Std. Err. = .2973726
camper ... discrete
1 2 3 4 5
camper: Std. Err. = .37428072
Marginal effects after zip
y = predicted number of events (predict, n)
= 2.1880131
------------------------------------------------------------------------------
variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X
---------+--------------------------------------------------------------------
persons | 1.763942 .17608 10.02 0.000 1.41883 2.10905 2.528
child | -1.74851 .29737 -5.88 0.000 -2.33135 -1.16567 .684
camper*| 1.13338 .37428 3.03 0.002 .399803 1.86696 .588
------------------------------------------------------------------------------
(*) dy/dx is for discrete change of dummy variable from 0 to 1
. mfx, predict(n) nonlinear tracelvl(2)
calculating dydx (nonlinear method)
-------------------------
variable | dy/dx
---------+---------------
persons | 1.7639
child | -1.7485
camper | 1.1334
-------------------------
calculating standard errors (nonlinear method)
persons ... continuous
1 d^2f/dxdb = 6.6472574
2 d^2f/dxdb = 1.7639419
3 d^2f/dxdb = -.63714517
4 d^2f/dxdb = -.54772145
5 d^2f/dxdb = -.93149901
persons: Std. Err. = .17607926
child ... continuous
1 d^2f/dxdb = -4.4202341
2 d^2f/dxdb = -1.7485094
3 d^2f/dxdb = -1.0882794
4 d^2f/dxdb = .05773436
5 d^2f/dxdb = .09819149
child: Std. Err. = .2973726
camper ... discrete
1 d^2f/dxdb = 2.8651844
2 d^2f/dxdb = 1.1333799
3 d^2f/dxdb = -.0730116
4 d^2f/dxdb = -1.1329221
5 d^2f/dxdb = -.10674212
camper: Std. Err. = .37428072
Marginal effects after zip
y = predicted number of events (predict, n)
= 2.1880131
------------------------------------------------------------------------------
variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X
---------+--------------------------------------------------------------------
persons | 1.763942 .17608 10.02 0.000 1.41883 2.10905 2.528
child | -1.74851 .29737 -5.88 0.000 -2.33135 -1.16567 .684
camper*| 1.13338 .37428 3.03 0.002 .399803 1.86696 .588
------------------------------------------------------------------------------
(*) dy/dx is for discrete change of dummy variable from 0 to 1
