午餐講座系列
LUNCHEON SEMINAR
2024/2025
第一學期
講座信息
日期：10月9日（週三）
時間：13:00-14:00
地點：E21B-G002
語言：英文
講座
簡介
摘要：泊松模型自二十世紀初就成為分析頻次數據的常用工具。儘管備受歡迎，泊松模型均值與方差需相等的同質性假設限制了其應用範圍。通過在原始泊松分布基礎上添加參數以擴大其適用範圍的做法，可追溯至格林伍德和尤爾（1920年）。通過這種方式，誕生了一類叫做復合泊松的模型（或稱混合模型），其可以應對過渡離散或離散不足和截斷問題（左截、右截或雙向截斷）。處理非同質性還有另一種思路，就是從數據生成過程入手。比如說，研究的隨機變量可能來自一系列與其他隨機變量的組合，基於這些組合分布衍生出了新的模型（如零膨脹泊松模型和零一膨脹泊松模型）。此外，為應對潛在的聚類，帶隨機效應的混合模型也應運而生。本研究綜述了幾種常見的混合泊松模型，探討了它們在處理非同質性時的優缺點，並根據偏差、有效性、可用性和實現難度這四個標準，給出了模型選擇的建議。
Abstract
Poisson model has been the default tool for count data analysis since the early twentieth century. While its popularity grows, the restriction of homogeneity-quality of its mean and variance has limited its application. Adding one or more parameters in the original Poisson distribution to offer more flexibility is a common practice that can be traced back to Greenwood and Yule (1920), to handle potential violations of homogeneity. This kind of practice leads to a class of so-called Compound Poisson models (occasionally referred as mixture models) that can deal with non-equidispersion (over and under), and truncations (left, right and both). Besides that, an alternative way to theorize the non-homogeneity is from data-generating process. For instance, the random variable under investigation is derived from a collection of other random variables. New models (e.g., Zero-inflated Poisson and Zero-and-one inflated Poisson) are proposed based on the combined distributions. In addition, to cooperate potential clustering, compound and mixture models with random effects were also proposed.
This study surveys popular choices of compound and mixture Poisson models for handling the issue of non-homogeneity, and evaluates their strengths and limitations. Suggestions for the choice of models are given according to four criteria, such as the bias, the efficiency, the availability and the difficulty of implementation.
講者
信息
蔡天驥，澳門大學社會科學學院副院長、社會學系教授，於2010年獲得北卡羅來納大學教堂山分校社會學博士學位。他的研究興趣包括定量分析方法與應用、數據挖掘、基因與社會環境交互、社會網絡分析等。他的文章發表於American Sociological Review、American Journal of Sociology、Chinese Sociological Review等國際權威SSCI學術期刊。
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編輯｜由一凡
審核｜UMSociology
