Multinomial Logit - Introduction


Multinomial logit regression is used when the dependent variable in question is nominal (a set of categories which cannot be ordered in any meaningful way, also known as categorical) and consists of more than two categories. Some examples would be:

  • Which major will a college student choose, given their grades, stated likes and dislikes, etc.?
  • Which blood type does a person have, given the results of various diagnostic tests?
  • In a hands-free mobile phone dialing application, which person's name was spoken, given various properties of the speech signal?

These are all statistical classification problems. They all have in common a dependent variable to be predicted that comes from one of a limited set of items which cannot be meaningfully ordered, as well as a set of independent variables (aka observations, features, etc.), which are used to predict the dependent variable. Multinomial logit regression is a particular solution to the classification problem that assumes that a linear combination of the observed features and some problem-specific parameters can be used to determine the probability of each particular outcome of the dependent variable. The best values of the parameters for a given problem are usually determined from some training data (e.g. some people for whom both the diagnostic test results and blood types are known, or some examples of known words being spoken).

Multinomial logit regression is appropriate in cases where the response is not ordinal in nature as in ordered logit. Ordered logit regression is used in cases where the dependent variable in question consists of a set number (more than two) of categories which can be ordered in a meaningful way (for example, highest degree, social class) while multinomial logit is used when there is no apparent order (e.g. the choice of muffins, bagels or doughnuts for breakfast) .

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