Thank you Richard Williams. It's an interesting approach, however it is not clear that it would work with the multinomial case. Not only because the command may not be built for it, but also if you're trying to do the calculation yourself.
One thing is assuming that the 95% confidence interval of a nonlinear transformation of a linear prediction is given by the nonlinear transformation of the 95% confidence interval boundaries of the linear prediction, which is the logit case. Another is to get the 95% confidence interval of a nonlinear transformation of a nonlinear function of several linear predictions, which is the multinomial case. Notice that it is not even clear which should be the lower bound to transform, do we use the lower bounds of all linear predictions for all the alternatives? This does not seem right. I would personally bootstrap the marginal effects and use the estimated quantiles to do the confidence interval.
One thing is assuming that the 95% confidence interval of a nonlinear transformation of a linear prediction is given by the nonlinear transformation of the 95% confidence interval boundaries of the linear prediction, which is the logit case. Another is to get the 95% confidence interval of a nonlinear transformation of a nonlinear function of several linear predictions, which is the multinomial case. Notice that it is not even clear which should be the lower bound to transform, do we use the lower bounds of all linear predictions for all the alternatives? This does not seem right. I would personally bootstrap the marginal effects and use the estimated quantiles to do the confidence interval.
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