- Simon HsiehLv 71 0 年前最佳解答
這種迴歸模型可稱為對數線性模型(Loglinear Model), 這種廣義的線性模型使用對數連結函數(Log Link Function)。主要使用於反應變數為間斷型資料。卜瓦松迴歸主要的應用是根據在某一段時間內已發生的次數，而以此資訊來推估未來的時間發生的行為。以銀行的信用卡客戶為例，我們可以根據某位顧客在過去一段時間內所刷卡的比例和消費金額，用來推算該顧客未來的消費行為和信用卡的使用機率，如此便可預估該顧客對其刷卡銀行的價值。
In statistics, the Poisson regression model attributes to a response variable Y a Poisson distribution whose expected value depends on a predictor variable x (written in lower case because the model treats x as non-random, typically in the following way:
(where "log" means natural logarithm). Poisson regression models are generalized linear models with the logarithm as the (canonical) link function, and the Poisson distribution function.
If Yi are independent observations with corresponding values xi of the predictor variable, then a and b can be estimated by maximu likelihood if the number of distinct x values is at least 2. The maximum-likelihood estimates lack a closed-form expression and must be found by numerical methods.
3.Poisson regression in practice
Poisson regression is appropriate when the dependent variable is a count, for instance of events such as the arrival of a telephone call at a call centre. The events must be independent in the sense that the arrival of one call will not make another more or less likely, but the probability per unit time of events is understood to be related to covariates such as time of day.