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政大機構典藏 > 商學院 > 統計學系 > 學位論文 > Item 140.119/84410

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/84410

Title:	具有額外或不足變異的群集類別資料之研究 A Study of Modelling Categorical Data with Overdispersion or Underdispersion
Authors:	蘇聖珠 Su, Sheng-Chu
Contributors:	陳麗霞蘇聖珠 Su, Sheng-Chu
Keywords:	群集類別資料群內相關性額外變異不足變異 Dirichlet-Multinomial模式最大概似估計式廣義最小平方估計式 categorical data intra-cluster correlation overdispersion underdispersion Dirichlet-Multinomial model maximum-likelihood estimation generalized least squares estimation
Date:	2000
Issue Date:	2016-04-14 13:57:32 (UTC+8)
Abstract:	進行調查時，最後的抽樣單位常是從不同的群集取得的，而同一群集內的樣本對象，因背景類似而對於某些問題常會傾向相同或類似的反應，研究者若忽略這種群內相關性，仍以獨立性樣本進行分析時，因其共變異數矩陣通常會與多項模式的共變異數矩陣相差懸殊，而造成所謂的額外變異或不足變異的現象。本文在不同的情況下，提出了Dirichlet-Multinomial模式(簡稱DM模式)、擴展的DM模式、以及兩種平均數-共變異數矩陣模式，以適當的彙整所有的群集資料。並討論DM與EDM模式中相關之參數及格機率之最大概似估計法，且分別對此兩種平均數-共變異數矩陣模式，提出求導廣義最小平方估計的程序。此外，也針對幾種特殊的二維表及三維表結構，探討對應的參數及格機率之估計方法。並提出計算簡易的Score統計檢定量以判斷群內相關(intra-cluster correlation)之存在性，及判斷資料集具有額外或不足變異，而對於不同母體的群內相關同質性檢定亦提出討論。 This paper presents a modelling method of analyzing categorical data with overdispersion or underdispersion.　In many studies, data are collected from differ clusters, and members within the same cluster behave similary.　Thus, the responses of members within the same cluster are not independent and the multinomial distribution is not the correct distribution for the observed counts.　Therefore, the covariance matrix of the sample proportion vector tends to be much different from that of the multinomial model.　We discuss four different models to fit counts data with overdispersion or underdispersion feature, witch include Dirichlet-Multinomial model (DM model), extended DM model (EDM model), and two mean-covariance models.　Method of maximum-likelihood estimation is discussed for DM and EDM models.　Procedures to derive generalized least squares estimates are proposed for the two mean-covariance models respectively. As to the cell probabilities, we also discuss how to estimate them under several special structures of　two-way and three-way tables.　More easily evaluated Score test statistics are derived for the DM and EDM models to test the existence of　the intra-cluster correlation.　And the test of homogeneity of intra-cluster correlation among several populations is also derived.
Description:	博士國立政治大學統計學系
Source URI:	http://thesis.lib.nccu.edu.tw/record/#A2002000642
Data Type:	thesis
Appears in Collections:	[統計學系] 學位論文

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