Logistic regression - Wikipedia, the free encyclopedia



Logistic regression - Wikipedia, the free encyclopedia
In statistics, logistic regression, or logit regression,or logit model,[1] is a type of probabilistic statistical classification model.[2] It is also used to predict a binary response from a binary predictor, used for predicting the outcome of a categorical dependent variable (i.e., a class label) based on one or more predictor variables (features). That is, it is used in estimating the parameters of a qualitative response model. The probabilities describing the possible outcomes of a single trial are modeled, as a function of the explanatory (predictor) variables, using a logistic function. Frequently (and subsequently in this article) "logistic regression" is used to refer specifically to the problem in which the dependent variable is binary—that is, the number of available categories is two—while problems with more than two categories are referred to as multinomial logistic regression or, if the multiple categories are ordered, as ordered logistic regression.


逻辑回归罗吉斯回归英语Logistic regression 或logit regression),即逻辑模型(英语Logit model,也译作“评定模型”、“分类评定模型”)是离散选择法模型之一,属于多重变量分析范畴,
IIA假设
Independent and irrelevant alternatives”假设,也称作“IIA效应”,指Logit模型中的各个可选项是独立的不相关的。
市场上有A,B,C三个商品相互竞争,分别占有市场份额:60%,30%和10%,三者比例为:6:3:1
一个新产品D引入市场,有能力占有20%的市场——
如果满足IIA假设,各个产品独立作用,互不关联:新产品D占有20%的市场份额,剩下的80%在A、B、C之间按照6:3:1的比例瓜分,分别占有48%,24%和8%。
如果不满足IIA假设,比如新产品D跟产品B几乎相同,则新产品D跟产品B严重相关:新产品D夺去产品B的部分市场,占有总份额的20%,产品B占有剩余的10%,而产品A和C的市场份额保持60%和10%不变。

满足IIA假设的优点[编辑]

  • 可以获得每个个性化的选择集合的一致的参数估计
  • 各个类别的子集的一般化的估计
  • 大大节省时间
  • 可选项数目很多的时候尤其如此

IIA假设的检验[编辑]


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