tailieunhanh - Lecture Advanced Econometrics (Part II) - Chapter 4: Discrete choice analysis - Multinomial models

Lecture "Advanced Econometrics (Part II) - Chapter 4: Discrete choice analysis - Multinomial models" presentation of content: The multinomial logit model, conditional logit model, mixed logit mode, independence of irrelevant alternatives, nested logit model, multinomial probit model. | Advanced Econometrics - Part II Chapter 4 Discrete choice analysis Multinomial Models Chapter 4 DISCRETE CHOICE ANALYSIS MULTINOMIAL MODELS We look at settings with multiple unordered choices. A key notion here is the independence of irrelevant alternative property Models for discrete choice with more than two choices We assume for the ith consumer faced with i choices j 1 2 . J suppose that the utility of choice j is U1 XjP S1 If the consumer makes choice j in particular then we assume that Uij is the maximum among J alternatives. Prob Uiz. Uk for all k j This is a probability of individual I makes choice j. Y j if Uj Uk for all k j The model is made by a particular choice of distribution for the disturbances. Let Yi be a random variable that indicates the choice made McFadden 1974 has shown that if and only if the J disturbances are independent and identically distributed with type I extreme value distribution F Sj exp - exp -Sj e 11 Then exp XjF _ exp ZyF Pr ob Y 1 J J E exp Xij E exp Zjớ 1 1 1 1 Utility depends on Zij which includes aspects specific to the individual i as well as to choice j . Let Zj Xj wi e p a Xij varies across choices j and possibly across individual i as well . wi contains the characteristics of the individual i therefore the same for all choice. Nam T. Hoang UNE Business School 1 University of New England Advanced Econometrics - Part II Chapter 4 Discrete choice analysis Multinomial Models exp Xjp p ai Prob Y j exp Xjfi wa J E exp XjP wp j 1 J E exp XP . j 1 exp wia exp Xjp E exp X P j 1 For example a model of a shopping centre choices by individual Depends on number of stores Sij distance from the centre of the city Dij and income of the individual i i which varies across individuals but not across the choices. Zij S a I. THE MULTINOMIAL LOGIT MODEL Suppose we have only individual specifre characteristics i w which is the same for all choice. The model response probability as exp w .a Prob Y j w i Pj J X 1 E exp j 1 For all .