Ordered probit marginal effects

[giulia leila]

hello,

I am doing an ordered probit with 3 outcomes (Help the economy, make no difference, hurt the economy). I need marginal effects after it. But as far as I have three outcomes if I use margins I obtain 3 different coefficients (one for help, one for make no difference, one for hurt). Is there a way to obtian a single coefficient for all the 3 outcomes? any idea?

thank you in advance

[John Mullahy]

Giulia: It seems that this depends on the particular parameter you want to understand. Using the xb option with margins would give you "a single coefficient" but you would need to be the one to decide if this (i.e. the margin related to the linear predictor) is the parameter of interest to you.

[Richard Williams]

This handout describes ways that may make interpretation easier with ordinal models.

https://www3.nd.edu/~rwilliam/stats3/Margins05.pdf

[Weiwen Ng]

hello,

I am doing an ordered probit with 3 outcomes (Help the economy, make no difference, hurt the economy). I need marginal effects after it. But as far as I have three outcomes if I use margins I obtain 3 different coefficients (one for help, one for make no difference, one for hurt). Is there a way to obtian a single coefficient for all the 3 outcomes? any idea?

thank you in advance

It may be worth clarifying that in an ordered probit or logit model, you get one set of coefficients that represent the odds of a higher response to the question. However, when it comes to margins, you are inherently predicting the average probability of responding in each of the response categories (and you have 3 of them). Now, for margins, you could just pick a single outcome; for example, assuming that "hurt the economy" is coded as 3:

margins, dydx(*) predict(outcome(3))

(Note: insert whatever variables of interest into the margins statement)

Alternatively, as John said, you could simply decide that the linear predictor is what you want, in which case I think you don't even need margins. However, there's no way around the fact that you have 3 total outcomes.

[giulia leila]

Thak you all very much. The point behind all of this is that i need a coefficient that can say something about the effect of my x on my y. As far as i understood the coefficient of the ordered probit can tell me the sign of the effect but the magnitude should have no meaning (?) and for this reason i do marginal effects. But i have been asked to have an individual value as marginal effect. Is ther any other specification for which i can get an individual coefficient for all outcomes whcih magnitude can be used for interpretation?


oprobit Help_Hurt Democrat Age Age2 Female i.Education i.income Rural City Unemployed i.state [pweight=weight] , nolog robust
margins, dydx(Left)

[CODE]
* Example generated by -dataex-. To install: ssc install dataex
clear
input float(Help_Hurt Republican Democrat)
1 0 0
2 0 0
3 0 0
2 0 1
1 1 0
1 0 1
1 . .
. 0 1
3 0 0
1 0 1
2 0 1
3 0 1
3 1 0
1 0 0
1 0 1
1 0 0
1 0 1
1 0 1
2 0 1
1 . .
1 0 0
2 1 0
1 1 0
. 0 0
3 1 0
1 0 1
. 1 0
. 0 0
2 1 0
2 0 0
. 1 0
2 0 0
2 0 0
3 0 0
1 0 1
1 0 1

[Weiwen Ng]

Thak you all very much. The point behind all of this is that i need a coefficient that can say something about the effect of my x on my y. As far as i understood the coefficient of the ordered probit can tell me the sign of the effect but the magnitude should have no meaning (?) and for this reason i do marginal effects. But i have been asked to have an individual value as marginal effect. Is ther any other specification for which i can get an individual coefficient for all outcomes whcih magnitude can be used for interpretation?

...

Perhaps we are losing something in translation.

I guess it is hard to interpret the raw coefficients from ordered probit. If you must present just one statistic, do ordered logit and exponentiate the coefficients. You will then have odds ratios. Is that what you were asking?

If your correspondent asked you to present just one value as marginal effects, then I guess you could just choose the highest response category to illustrate. I worry that this person doesn't understand what ordered response models are.

[Richard Williams]

I agree with Weiwen that the request is odd. If you want a single number then use the coefficient. Using margins, you could ask for the marginal effect using xb, but (at least in simple models) that is the same as the coefficient, e.g.

. webuse nhanes2f, clear

. oprobit health weight, nolog

Ordered probit regression                       Number of obs     =     10,335
                                                LR chi2(1)        =      17.82
                                                Prob > chi2       =     0.0000
Log likelihood = -15755.488                     Pseudo R2         =     0.0006

------------------------------------------------------------------------------
      health |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0028386   .0006725    -4.22   0.000    -.0041567   -.0015206
-------------+----------------------------------------------------------------
       /cut1 |  -1.677412   .0521723                     -1.779668   -1.575156
       /cut2 |  -.9366749   .0503992                     -1.035456   -.8378943
       /cut3 |  -.1628707   .0498771                     -.2606279   -.0651135
       /cut4 |   .5259313   .0500706                      .4277946     .624068
------------------------------------------------------------------------------

. margins, dydx(*) predict(xb)

Average marginal effects                        Number of obs     =     10,335
Model VCE    : OIM

Expression   : Linear prediction (cutpoints excluded), predict(xb)
dy/dx w.r.t. : weight

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0028386   .0006725    -4.22   0.000    -.0041567   -.0015206
------------------------------------------------------------------------------

If you want something more intuitively meaningful than the coefficient, I suggest you look at the handout I mentioned above. I don't see any way you can get a single number that is any more intuitive than the coeffient itself.