降低列聯表維數之可行性探討

• Main Author: 賴芬秀
• Language: 中文
• Published: 國立政治大學
• Subjects: 簡易合併; 嚴格合併; 強固合併; Collapsibility; Strict collapsibility; Strong collapsibility; Sum-to-zero constraints; Set-to-zero constraints
• Online Access: http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22B2002002097%22.

大體上來說，高維列聯表通常比較不容易分析，因此我們考慮將某柴暫不列入探討之因子的次數相加，以便降低列聯表的維數。但是降低列聯表維數的過程必需相當慎重，以確保合併的過程不致影響到所欲探討之因子間的相關性。本文就 "sun-to-zero" 及 "set-to-zero" 兩種不同的對數線性模式參數之限制式，分別探討簡易合併(collapsibility)、嚴格合併(strict collapsibility)及強固合併(strong collapsibility)之充要條件，並舉例說明及印證這些條件。 === A lower-dimensional contingency is usually easier to understand than a higher-dimensional one. Collapsing a larger table into a smaller one so that the associations among a set of factors can be easier to explain, however, should be exercised with care. In this study, definitions of collapsibility, strict collapsibility, and strong collapsibility are viewed. Distinctions among the three are compared. Necessary and sufficient condittions for these three types of collapsibility under conventional "set-to-zero" and "sum-to-zero" constraints are discussed and proved.