A reformulation of the aggregate association index using the odds ratio

Abstract

a b s t r a c tSince its inception in the 1950s the odds ratio has become one of the most simple and popular measures available for analysing the association between two dichotomous variables. Since the direction and magnitude of the association can be captured in such a simple measure, its impact has been felt throughout much of scientific research, in particular in epidemiology and clinical trials. Despite this, its applicability for analysing aggregate data has rarely been considered. In this paper we shall express a new measure of association (the aggregate association index, or AAI), in terms of the classic odds ratio. The advantage of doing so is that we are able to explore the use of the odds ratio in a context for which it was not originally intended, and that is for the analysis of a 2 × 2 table where only the aggregate data is known.Crown

The aggregate association index and its links with common measurements of association in a 2x2 table: an analysis of early New Zealand gendered voting data

“…In addition, the effect of sample size to the result should be examined and it is useful to extend the connection of the traditional AAI with other well-known association measurements such as adjusted standardised residual, Pearson's ratio, contingency, and correlation. Further generalisations for non-linear transformations of p 11 , including the odds ratio (Beh, Tran & Hudson, 2013) can also be considered.…”

Can we use the approaches of ecological inference to learn about the potential for dependence bias in dual-system estimation? An application to cancer registration data.

“…Unlike the numerous EI techniques that are now available, the AAI is applicable to the analysis of a single (as well as multiple) table and has been studied further recently. For example, Beh, Cheema, Tran and Hudson (2014) examine the role of the sample size on the magnitude of the AAI and Beh, Tran and Hudson (2013) consider the derivation of the AAI in terms of the odds ratio of the two-by-two contingency table. Brown et al, Can we use the approaches of ecological inference to learn about the potential for dependence bias in dual-system estimation: application to cancer registration data?…”

“…Exploring the relationship between χ and γ for different values of the true under-lying association as captured by the OR Figure 2a shows the quadratic relationship between the chi-squared statistic and the log-odds ratio. Such a curve is akin to the AAI curves of Beh, Tran and Hudson (2013) that are used to graphically explore the association between the variables of a two-by-two contingency table using only the aggregate data. From the AAI curve, the AAI is quantified.…”

Model and measurement of payment for ecosystem services at small scale

“…1 引言 随着中国社会经济的高速发展以及城镇化进 程的不断推进， 区域间生态环境与经济发展失衡和 利益错配的问题日益严重 [1] 。区域之间发展的不平 衡、 不协调影响到社会福利在不同群体间的公平分 配 [2] ， 并且国土空间格局失衡带来的负外部性导致 人与自然之间的矛盾愈演愈烈 [3,4] 。探索区域间以 地方政府为主导的横向生态补偿机制是生态文明 建设的重要命题与区域协调发展的制度供给 [5,6] [10,11] [12] ； 而生态系统服务价值 法由于在区域层面核算较为简单方便被广泛地应 用于区域之间的横向生态补偿标准的设计 [13][14][15][16] 。从 生态补偿标准设计来看， 区域生态补偿以生态系统 服 务 价 值 减 去 治 理 污 染 投 入 的 实 际 成 本 的 差 额 法 [13,14] 和生态系统服务价值乘以生态盈余系数的分 摊法为主导 [15,16] [17] 。那么用经济数学的方式可以把社会经济因素 与自然因素对 LUCC 的作用方式表达为： [18] ， 表示一 个群体暴露在一定风险下某事件发生的概率与未 暴露在该风险下某事件发生概率的比值， 又称相对 风险 [19] 。因此， 本文利用土地利用转移几率比矩阵 衡量地类之间转移的可能性， 即： [20,21] ； 另外， 生态系统服务不仅受土 地利用变化的影响， 还与前期初始生态禀赋有着密 不可分的关系， 遗漏初始生态禀赋可能造成估计结 果存在偏差 [22] 。生态系统服务价值 (Ecosystem Ser- [23] 。环境正义理论认为个人、 群体、 以及区 (国) 际之间均拥有改造自然的平等权利， 同时也要 履行保护自然的平等义务 [10,11] [26] 。 自 1999 年 Constanza 等 [27] 比较全面地评估了全球生态 系统服务价值以来， 其核算理论与方法在全球范围 内不断发展与完善。本文以谢高地等 [28] 修订的比较 符合中国实际情况的 "中国生态系统单位面积生态 服务价值当量表" 为核算基础， 借鉴熊鹰等 [29] 对不同 地类的各种生态系统服务价值当量因子的确定， 其 中城乡建设用地的当量因子参考 Constanza 等 [27] 价精度达到 94.3%以上 [30] 。为了研究需要， 根据 《中 国 科 学 院 土 地 利 用/覆 盖 分 类 体 系 标 准》 [30] [24] 。江汉平原与汉江中游是重要农业耕作区， 承担 着较多的农业生产功能， 而武汉城市圈承载了较多 的非农生产功能和高强度的人类活动 [32] [19,22] [ 7 ] 李国平, 李潇. 国家重点生态功能区的生态补偿标准、 支付额度 与调整目标 [J].…”