I'm having a little bit of difficulty interpreting the marginal effects results I obtained since I am quite new to this sort of stuff. For my model I'm running an ordered probit regression where there are 6 different levels to measure customer satisfaction, where 1 is very high and 6 is very low. The Conditions A, B, C, and D are all different things which can affect Customer Satisfaction levels, and I have the marginal effects results given below:

                                   Customer Satisfaction Level
                      1   |    2    |    3    |    4    |    5    |    6    
Condition   A     0.0003    0.0007    0.0055    0.0013    -0.0020   -0.0059
            B    -0.0016   -0.0024   -0.0327   -0.0020    -0.0066    0.0455
            C    -0.0357   -0.0487   -0.3493   -0.0334    -0.0561    0.5234
            D     0.0940    0.1320    1.3187    0.1834     0.4578   -2.1861

Basically, I'm having a bit of difficult interpreting what these results actually mean. I was reading through this question (Average Marginal Effects interpretation) and I was trying to apply it to my results but I'm not sure how to. Like, what does the 0.0055 mean in row "Condition A" column "Customer Satisfaction Level 3", and what does the -2.1851 mean in row "Condition D" column "Customer Satisfaction Level 6"?

If anyone could help me with this then I'd appreciate it, thanks!

EDIT: I've been reading more about marginal effects in ordered probit regressions and by the look of it marginal effects appear to show the percentage point changes of variables when it comes to probit regressions. If that's the case then isn't it possible for variables to change by over 100 percentage points? I'm just a bit confused about it, as a (really bad) example of my problem I've included a bit of code here which should generate the marginal effects of a data set in R using the oglmx package:

n = 1000
x = rnorm(n, mean = 0, sd = 0.002)
y = ifelse(pnorm(1 + 0.5*x + rnorm(n))>0.5, 1, 0)
data = data.frame(y,x)
margins.oglmx(oglmx(y~x, data=data, link="probit",constantMEAN=FALSE, constantSD=FALSE,delta=0,threshparam=NULL), AME=TRUE)

This code outputs the following marginal effects table:

Marginal Effects on Pr(Outcome==0)
  Marg. Eff   Std. error  t value Pr(>|t|)  
x -11.95828594   5.88897011 -2.03062 0.042293 *
Marginal Effects on Pr(Outcome==1)
  Marg. Eff  Std. error t value Pr(>|t|)  
x 11.95828594  5.88897011 2.03062 0.042293 *
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Now, if we look at the x variable we see that it varies quite a lot - the minimum value is -0.0060243275671 while the maximum value is 0.0070822805553 so is this why the marginal effects coefficients are so large? There are also values such as 0.0003295985976000 inbetween the minimum and maximum values so the values also do get quite small. This does seem to me that marginal effects are showing percentage point changes rather than marginal probabilities, but can anyone explain to me if I'm right or wrong? Thanks!

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    $\begingroup$ I think you should show your code (or even carry out a similar exercise on a publicly available dataset). Without this, it would be impossible to answer what these numbers mean. I doubt these are average marginal effects of any sort, since those should be bounded between 0 and 1 in an ordered probit. $\endgroup$ – Dimitriy V. Masterov Jun 26 '18 at 22:32
  • $\begingroup$ Ah okay sure, I'll try and check around for data which looks similar to mine then. I'm using the package oglmx in R, and for my code in order to obtain average marginal effects I'm using the line margins.oglmx(Regression, AME = TRUE) $\endgroup$ – ThePlowKing Jun 26 '18 at 23:02
  • $\begingroup$ @DimitriyV.Masterov Sorry I just have a quick question, according to this site: cran.r-project.org/web/packages/margins/vignettes/… , average marginal effects can have values not bounded by 0 and 1. Is it only ordered probit which are bounded by 0 and 1? $\endgroup$ – ThePlowKing Jun 26 '18 at 23:38
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    $\begingroup$ This is because this model gives you in predicted probability of a given outcome. The most that can be is to go all the way from zero to one (or vice versa), so the change is bounded by -1 to 1. In models with continuous outcomes, you can get AMEs outside that bound since the outcome is unbounded. Note that I made an error in my first comment. $\endgroup$ – Dimitriy V. Masterov Jun 26 '18 at 23:47
  • $\begingroup$ @DimitriyV.Masterov I see, thanks, I think there might be an issue with my code then. So basically that means the regression is (for some reason) assuming that my data is continuous rather than being discrete... $\endgroup$ – ThePlowKing Jun 27 '18 at 1:50

There is no problem with the code, the marginal effect is not bounded between 0 and 1, or -1 and 1. The marginal effect measures the slope of the probability at a particular point. For an example that illustrates that the marginal effect is unbounded, suppose we have a continuous variable that perfectly predicts the outcome, so if x>0.5 then the outcome is 1, otherwise 0. In this case the slope of the probability function evaluated at 0.5 would be infinite.

In your example the estimated parameter associated with x is 47, this very imprecise estimate is the reason why the marginal effect is so large in this case.

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