On http://en.wikipedia.org/wiki/Multino...n#Introduction is written, that the estimation errors of separate binomial logit models (instead of one simultanous multinomial logit regression model) would accumulate as follows:
This provides a principled way of incorporating the prediction of a particular multinomial logit model into a larger procedure that may involve multiple such predictions, each with a possibility of error. Without such means of combining predictions, errors tend to multiply. For example, imagine a large predictive model that is broken down into a series of submodels where the prediction of a given submodel is used as the input of another submodel, and that prediction is in turn used as the input into a third submodel, etc. If each submodel has 90% accuracy in its predictions, and there are five submodels in series, then the overall model has only .95 = 59% accuracy. If each submodel has 80% accuracy, then overall accuracy drops to .85 = 33% accuracy. This issue is known as error propagation and is a serious problem in real-world predictive models, which are usually composed of numerous parts. Predicting probabilities of each possible outcome, rather than simply making a single optimal prediction, is one means of alleviating this issue.
I do not believe that. Do you?