AN EMPIRICAL-INVESTIGATION OF SOME EFFECTS OF SPARSENESS IN CONTINGENCY-TABLES
AN EMPIRICAL-INVESTIGATION OF SOME EFFECTS OF SPARSENESS IN CONTINGENCY-TABLES
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DOI：
10.1016/0167-9473(87)90003-x
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发表时间：
1987-03-01
影响因子：
1.8
通讯作者：
YANG, MC
中科院分区：
文献类型：
--
作者：
AGRESTI, A;YANG, MC
一个模拟研究调查的一些影响，有“稀疏”的分类数据，其中的样本大小的细胞数的比例是相对较小的。在这项研究中，真正的细胞比例满足有序变量的均匀关联模型。结论如下：（1）对于模型的直接检验，Pearson拟合优度统计量的分布比似然比统计量的分布更接近渐近卡方分布。(2)为了比较两个非饱和对数线性模型（例如在假设特定模型成立的情况下检验独立性），通常比较似然比统计量而不是皮尔逊统计量。(3)稀疏性的一个有益方面是，对于固定的样本大小，某些单自由度检验统计量的功效往往随着表变得更稀疏而增加。(4)向空单元格添加常数的常见做法可能会对Pearson统计量的分布造成严重破坏。
A simulation study investigates some effects of having ‘sparse’ categorical data, for which the ratio of the sample size to the number of cells is relatively small. In this study, the true cell proportions satisfy the uniform association model for ordinal variables. Conclusions include the following: (1) For direct testing of the model, the distribution of the Pearson goodness-of-fit statistic is closer to the asymptotic chi-squared distribution than is the distribution of the likelihood-ratio statistic. (2) For comparing two unsaturated loglinear models (such as in testing independence under the assumption that a particular model holds), it is usually preferable to compare likelihood-ratio statistics rather than Pearson statistics. (3) A beneficial aspect of sparseness is that the power of certain single-degree-of-freedom test statistics tends to increase as the table becomes more sparse, for a fixed sample size. (4) The common practice of adding constants to empty cells can cause havoc with the distribution of the Pearson statistic.