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# l92 - Multinomial Logit Models Overview This is adapted...

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Multinomial Logit Models Page 1 Multinomial Logit Models - Overview This is adapted heavily from Menard’s Applied Logistic Regression analysis ; also, Borooah’s Logit and Probit: Ordered and Multinomial Models ; Also, Hamilton’s Statistics with Stata, Updated for Version 7. When categories are unordered, Multinomial Logistic regression is one often-used strategy. Mlogit models are a straightforward extension of logistic models. Suppose a DV has M categories. One value (typically the first, the last, or the value with the highest frequency) of the DV is designated as the reference category. The probability of membership in other categories is compared to the probability of membership in the reference category. For a DV with M categories, this requires the calculation of M-1 equations, one for each category relative to the reference category, to describe the relationship between the DV and the IVs. Hence, if the first category is the reference, then, for m = 2, …, M, mi K k ik mk m Z X Yi P m Yi P 1 ) 1 ( ) ( ln Hence, for each case, there will be M-1 predicted log odds, one for each category relative to the reference category. (Note that when m = 1 you get ln(1) = 0 = Z 11 , and exp(0) = 1.) When there are more than 2 groups, computing probabilities is a little more complicated than it was in logistic regression. For m = 2, …, M, M h hi mi i Z Z m Y P 2 ) exp( 1 ) exp( ) ( For the reference category, M h hi i Z Y P 2 ) exp( 1 1 ) 1 ( In other words, you take each of the M-1 log odds you computed and exponentiate it. Once you have done that the calculation of the probabilities is straightforward. Note that, when M = 2, the mlogit and logistic regression models (and for that matter the ordered logit model) become one and the same.

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Multinomial Logit Models Page 2 We’ll redo our Challenger example, this time using Stata’s mlogit routine. In Stata, the most frequent category is the default reference group, but we can change that with the basecategory option, abbreviated b: . mlogit distress date temp, b(1) Iteration 0: log likelihood = -24.955257
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