Then run the -margins- command for each category. CategoryREP78 category == LowestPoor
CategoryREP78 category == LowerFair
CategoryREP78 category == MiddleAverage
CategoryREP78 category == HigherGood
CategoryREP78 category == HighestExcellent
Then run the -margins- command for each category. Category == Lowest
Category == Lower
Category == Middle
Category == Higher
Category == Highest
Then run the -margins- command for each category. REP78 category == Poor
REP78 category == Fair
REP78 category == Average
REP78 category == Good
REP78 category == Excellent
You only get one coefficient in an ordinal probit model because you are actually fitting the model for a latent continuous variable y* (rather than, say, the log-odds of each alternative relative to the base alternative in a multinomial logit model). Think about it this way: The ordinal variable categories are rankings, such that although your outcomes may have been coded as 0, 1, 2, 3, 4, etc., the "distance" between category 0 and category 1 may not be the same as the distance between category 1 and category 2, and so on. For example, if the ordinal variable was a patient's response to the question of how well he or she can perform a specific activity of daily living unassisted, and the categories are:
0 - Not well at all 1 - Somewhat not well 2 - Neutral 3 - Somewhat well 4 - Extremely wellThe distance between "Not well at all" and "Somewhat not well" may not be the same as the distance between "Somewhat not well" and "Neutral"
By definition, y* is unobservable, but we can model the thresholds (boundaries)for each category. In Stata, along with coefficients for your model covariates, you should have also got (k-1) intercepts, where k is the number of categories in your ordinal outcome variable. These intercepts are given as /cut1, /cut2, ... ,/cut(k-1).
You would compute the average marginal effects of a categorical predictor after running -oprobit- just as you would other models, and that is by using the -margins- command. Note that you need to specify which category you want the average marginal effects for, otherwise Stata will choose a category for you.
A trivial example:
First fit the model
. webuse fullauto,clear
(Automobile Models)
. xtile pricequint=price,n(5)
. label define pq 1"Lowest" 2"Lowest" 3"Middle" 4"Higher" 5"Highest",replace
. label value priceq pq
. oprobit rep78 i.pricequint
Iteration 0: log likelihood = -93.692061
Iteration 1: log likelihood = -92.643441
Iteration 2: log likelihood = -92.643323
Iteration 3: log likelihood = -92.643323
Ordered probit regression Number of obs = 69
LR chi2(4) = 2.10
Prob > chi2 = 0.7178
Log likelihood = -92.643323 Pseudo R2 = 0.0112
------------------------------------------------------------------------------
rep78 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pricequint |
Lowest | -.1271055 .4100538 -0.31 0.757 -.9307962 .6765851
Middle | -.0845474 .3940693 -0.21 0.830 -.856909 .6878142
Higher | .3882535 .4029081 0.96 0.335 -.4014319 1.177939
Highest | .1246315 .4102926 0.30 0.761 -.6795273 .9287903
-------------+----------------------------------------------------------------
/cut1 | -1.865516 .3978601 -2.645308 -1.085725
/cut2 | -1.013338 .3095532 -1.620051 -.406625
/cut3 | .2638664 .3002598 -.3246321 .8523649
/cut4 | 1.076626 .3157065 .4578531 1.6954
------------------------------------------------------------------------------
Then run the -margins- command for each category. Category == Lowest
. margins, dydx(*) predict(outcome(1))
Conditional marginal effects Number of obs = 69
Model VCE : OIM
Expression : Pr(rep78==1), predict(outcome(1))
dy/dx w.r.t. : 2.pricequint 3.pricequint 4.pricequint 5.pricequint
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pricequint |
Lowest | .0100147 .0330296 0.30 0.762 -.0547221 .0747515
Middle | .0064042 .0300529 0.21 0.831 -.0524983 .0653067
Higher | -.0189492 .02406 -0.79 0.431 -.0661059 .0282074
Highest | -.0077672 .0258943 -0.30 0.764 -.0585191 .0429847
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
Category == Lower
. margins, dydx(*) predict(outcome(2))
Conditional marginal effects Number of obs = 69
Model VCE : OIM
Expression : Pr(rep78==2), predict(outcome(2))
dy/dx w.r.t. : 2.pricequint 3.pricequint 4.pricequint 5.pricequint
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pricequint |
Lowest | .0222821 .0722996 0.31 0.758 -.1194225 .1639866
Middle | .0146452 .068373 0.21 0.830 -.1193634 .1486538
Higher | -.0559815 .059961 -0.93 0.350 -.1735029 .0615399
Highest | -.0201156 .0663317 -0.30 0.762 -.1501233 .1098922
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
Category == Middle
. margins, dydx(*) predict(outcome(3))
Conditional marginal effects Number of obs = 69
Model VCE : OIM
Expression : Pr(rep78==3), predict(outcome(3))
dy/dx w.r.t. : 2.pricequint 3.pricequint 4.pricequint 5.pricequint
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pricequint |
Lowest | .0157357 .0511898 0.31 0.759 -.0845945 .1160659
Middle | .0111273 .0523686 0.21 0.832 -.0915133 .1137679
Higher | -.0786234 .0835623 -0.94 0.347 -.2424024 .0851556
Highest | -.0208081 .0692807 -0.30 0.764 -.1565958 .1149797
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
Category == Higher
. margins, dydx(*) predict(outcome(4))
Conditional marginal effects Number of obs = 69
Model VCE : OIM
Expression : Pr(rep78==4), predict(outcome(4))
dy/dx w.r.t. : 2.pricequint 3.pricequint 4.pricequint 5.pricequint
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pricequint |
Lowest | -.0215554 .0697354 -0.31 0.757 -.1582343 .1151234
Middle | -.0141387 .0658856 -0.21 0.830 -.1432722 .1149947
Higher | .0487688 .0536304 0.91 0.363 -.0563448 .1538823
Highest | .0189647 .0623698 0.30 0.761 -.1032778 .1412071
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
Category == Highest
. margins, dydx(*) predict(outcome(5))
Conditional marginal effects Number of obs = 69
Model VCE : OIM
Expression : Pr(rep78==5), predict(outcome(5))
dy/dx w.r.t. : 2.pricequint 3.pricequint 4.pricequint 5.pricequint
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pricequint |
Lowest | -.026477 .0854652 -0.31 0.757 -.1939857 .1410317
Middle | -.018038 .0843658 -0.21 0.831 -.1833919 .1473159
Higher | .1047854 .1095801 0.96 0.339 -.1099878 .3195585
Highest | .0297262 .0983159 0.30 0.762 -.1629695 .2224219
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
What happens when we don't specify a category in our -margins- command?
. margins, dydx(*)
Conditional marginal effects Number of obs = 69
Model VCE : OIM
Expression : Pr(rep78==1), predict()
dy/dx w.r.t. : 2.pricequint 3.pricequint 4.pricequint 5.pricequint
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pricequint |
Lowest | .0100147 .0330296 0.30 0.762 -.0547221 .0747515
Middle | .0064042 .0300529 0.21 0.831 -.0524983 .0653067
Higher | -.0189492 .02406 -0.79 0.431 -.0661059 .0282074
Highest | -.0077672 .0258943 -0.30 0.764 -.0585191 .0429847
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
Stata chose a category for us for the marginal effects calculation, in this case, the category chosen was 1 (lowest)