Bivariate ordered probit model: Average Marginal Effects

[Inna Petrunyk]

Dear Statalists,
1) Which Stata command yields average marginal effects?
2) Is there any command for bivariate ordered probit correspondent to biprobittreat, which calculates the ATE & ATT for all categories of the dependent variable?

Thanks in advance.

[Richard Williams]

With regards to 1,

margins, dydx(*)

gives you AMEs. Add -atmeans- if you want MEMs instead.

[Inna Petrunyk]

Dear Richard,
this is true for the univariate (ordered) probit model, but not for the bivariate (ordered) probit. In fact, Stata reports an error: "default prediction is a function of possibly stochastic quantities other than e(b)".

[Richard Williams]

If you have Stata 14, type

help biprobit_postestimation##margins

to see what your options are.

[Inna Petrunyk]

Unfortunately only Stata 13, it must be a bit cumbersome to calculate the AME for bivariate rather than univariate probit.

[Richard Williams]

Here is what it says in Stata 14.

        margins [marginlist] [, options]

        margins [marginlist] , predict(statistic ...) [predict(statistic ...) ...] [options]

    statistic          Description
    --------------------------------------------------------------------------------------------
    p11                Pr(depvar1=1, depvar2=1); the default
    p10                Pr(depvar1=1, depvar2=0)
    p01                Pr(depvar1=0, depvar2=1)
    p00                Pr(depvar1=0, depvar2=0)
    pmarg1             Pr(depvar1=1); marginal success probability for equation 1
    pmarg2             Pr(depvar2=1); marginal success probability for equation 2
    pcond1             Pr(depvar1=1 | depvar2=1)
    pcond2             Pr(depvar2=1 | depvar1=1)
    xb1                linear prediction for equation 1
    xb2                linear prediction for equation 2
    stdp1              not allowed with margins
    stdp2              not allowed with margins
    -------------------------------------------------------------------------------------------

    Statistics not allowed with margins are functions of stochastic quantities other than e(b).

If any of these appeal to you you can try them in Stata 13 and see if they work.

[Inna Petrunyk]

Probably, it is possible to calculate the AME for the Bivariate Ordered Probit manually. Any suggestion of those who have worked with the bivariate ordered probit model using the user-written command bioprobit would be appreciated. Does anyone know whether there is a counterpart to reoprobit (random effects ordered probit model) for the bivariate ordered probit model? Is there any possibility to estimate a panel (random effects) bivariate ordered probit model?

[Dimitriy V. Masterov]

Try adding

, force

at the end of margins.

[John Mullahy]

Inna: There quite well may be a more streamlined way to do this. But if you are interested in marginal effects of the x's on the joint probabilities p_jk here is one possibility.

1. Compute the linear predictions xb₁ and xb₂ from the bioprobit estimates.

2. Take the bioprobit estimates — xb₁, xb₂, and the correlation coefficient — and plug them into Mata's mvnormalderiv function to compute the derivatives w.r.t. xb₁ and xb₂. The particular joint probability of interest will determine specifically how xb₁ and xb₂ are entered.

3. Use the chain rule to get the derivative w.r.t. your covariate of interest, x_m (which would amount to multiplying by the relevant elements of the beta vector and summing).

4. Average these results over your sample to obtain the AMEs.

See

help mf_mvnormal

If you wanted to do inference about the AMEs, you might then consider bootstraping this process.

If the covariate of interest was discrete instead of continuous, you could just compute the mvnormal joint probability at two different values of the linear predictors and then compute the difference. Again, the particular joint probability of interest will determine specifically how xb₁ and xb₂ are entered.

You would, of course, have to determine which of the parameters Richard describes in #6 would be of interest; if it is a parameter other than a joint probability then the computations would be a bit more complicated.

Hopefully someone else offers a less complicated way to do this, but if not at least there is one way to proceed.

P.S. The above suggestion relates straightforwardly to bivariate probit, but for bivariate ordered probit essentially the same logic would apply once the relevant linear predictors are defined (they would involve the cut points, for instance).

P.P.S. I might just note that I have found the mvnormaland mvnormalderiv functions in Mata to be enormously useful and quite flexible when working with joint-normal distributions.

[chrispine cheelo]

Asking for an example of stata command for bivariate ordered probit regression

[John Mullahy]

ssc describe bioprobit