Ordered Probit: Interpret, test and compare coefficients

[Mischa Kleis]

Dear colleagues,

I estimate the following model:
oprobit swb ib2.marital_status if syear==2005, vce(cluster pid)
Coding:
Dependent variable - swb: discrete values from 0 - 10.
Predictor - marital status: categorical variable 1 married, 2 single, 3 widowed, 4 divorced, 5 separated.

oprobit swb ib2.marital_status if    syear==2005, vce(cluster pid)

Iteration 0:   log pseudolikelihood    = -10375.864  
Iteration 1:   log pseudolikelihood    = -10347.239  
Iteration 2:   log pseudolikelihood    = -10347.239  

Ordered probit regression    Number of obs    =       5519
    Wald chi2(4)    =      51.92
    Prob > chi2    =     0.0000
Log pseudolikelihood = -10347.239    Pseudo R2    =     0.0028

    (Std. Err. adjusted for    5519 clusters in pid)
        
    Robust
swb       Coef.    Std. Err.      z    P>z    [95% Conf. Interval]
        
marital_status
[1] Married        1     .0758386    .0326055     2.33   0.020    .0119331    .1397441
[3] Widowed        3    -.0873954    .1555698    -0.56   0.574    -.3923067    .2175159
[4] Divorced       4     -.217214    .0585252    -3.71   0.000    -.3319213   -.1025066
[5] Separated      5    -.3878464    .0974401    -3.98   0.000    -.5788255   -.1968673

I would like to avoid evaluating (average) marginal effects (at means) for all 10 values of swb.

Question 1) Does the sign of the coefficients give the direction of the effects?
Is it possible to make a statement such as "compared to being single, being married increases the probability of scoring high in SWB" or "is associated with higher SWB scores than being single"?

Question 2) How can I test whether the effects on SWB are equal?
E.g., is the command "test _b[1.marital_status] = _b[5.marital_status]" valid to make statements?

Thank you very much in advance!

Kind regards,
Mischa

[Joseph Coveney]

Given assumptions for ordered probit regression, your proposed answers to your questions seem right. With 10 ordered categories, SWB might be close enough to an interval variable that you could handle the outcome as continuous.

What's pid? That is, why do you have 5519 clusters in 5519 total observations?

[Roman Mostazir]

Are you sure you have clustered data? Seems like you have a single year = 2005, which is likely to have all different individuals (pid?) in your dataset. In that case you don't have a clustered data.

[Carlo Lazzaro]

Mischa:
I agree with Roman.
Your -oprobit- outcome reports the same number of observations and clusters (5519): hence, clustered standard errors seem pointless.

[Mischa Kleis]

Thanks for the already given feedback!

PID: Person ID -> it's defining the individual.
And yes, I only have the survey year 2005 at this point.

I have to use a model for the ordinal, discrete structure here and am not allowed to apply a linear model.

"If you have aggregate variables (like class size), clustering at that level is required."
-> PID is no aggregate, so clustered SE on PID are pointless?
-> If I had two years of data, should I cluster then and how?

Can I answer my questions 1 (sign of the coefficients) and 2 (test whether the effects on SWB are equal) from above then in the way I proposed?

Thanks again.

Kind regards,
Mischa

[Maarten Buis]

The sign of the marginal effect of falling in the lowest category is the opposite of the sign of the coefficient (the coefficient tells you the effect on the odds of getting a higher value, so the effect will be opposite for the lowest value). The sign of the marginal effect of falling in the highest category will be the same as the sign of the coefficients. The sign of the marginal effect of falling in the intermediate categories depends, and may actually change. So if you want to avoid using marginal effects, your best bet will be interpret the results in terms of odds ratios.

[Joseph Coveney]

The answers to your two questions are shown in the user's manual entries for oprobit and test if you don't like what's in #2 above.

Whom are you quoting?

[Mischa Kleis]

Maarten Buis: Thanks. If I write it down like that, I am on the safe side. However, I was hoping to write less abstract.
I am pretty sure that they interpret coefficients of Ordered Probit in
Akay, Alpaslan, Olivier Bargain, and Klaus F. Zimmermann. "Relative concerns of rural-to-urban migrants in China." Journal of Economic Behavior & Organization 81.2 (2012): 421-441.
as "a positive relationship with SWB.. a strong impact".

Joseph Coveney: It's lecture slides. I saw your answer in #2. I am sorry and didn't want to be rude. I am just very cautious and was hoping for more opinions.