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Lecture 14 - Econ 513 USC Fall 2005 Lecture 14 Models...

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Econ 513, USC, Fall 2005 Lecture 14. Discrete Response Models: Ordered Multinomial Response Models Now we consider discrete response models with more than two possible responses. In this lecture we limit ourselves to the case where the outcomes are ordered. There are two important cases. In the first there is an underlying continuous variable but we only observe an indicator for a particular range. An example is earnings data that may come coded in intervals: 0, [0 , 10], [10 , 50], [50 , ). Another example is educational choices where outcomes may be coded as less than high school, high school, some college, more than college. Such data are referred to as interval-coded data. Typically we model the underlying continuous variable as linear and normal (or logistic) with a set of covariates: y * i = x i β + ε i , with the observed outcome an indicator for the interval for j = 0 , . . . , J : y i = j if α j y * < α j +1 , with α J +1 = , α 0 = -∞ , and α j - 1 < α j . In this case the key assumption is that the boundaries α j are known a priori. In this case we are typically interested in the conditional expectation of the latent outcome E [ y * | x ] , rather than in the distribution of the observed outcome, Pr( y = j | x ) .
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