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列联表中的拟独立与拟依赖：兼论有序三角列联表AI 解读

In the usual statistical analysis of the entries (frequencies) in a contingency table having I rows and J columns (I ≥ 2, J ≥ 2), an important role is often played by the usual null hypothesis of independence (i.e., the hypothesis that the row variable and the column variable are statistically independent of each other). In the situation considered in this article, the entries in some of the I × J cells of the contingency table are omitted from the analysis (because these…

列联表的拟独立与拟依赖：特别关注有序三角列联表AI 解读

In the usual statistical analysis of the entries (frequencies) in a contingency table having I rows and J columns (I ≥ 2, J ≥ 2), an important role is often played by the usual null hypothesis of independence (i.e., the hypothesis that the row variable and the column variable are statistically independent of each other). In the situation considered in this article, the entries in some of the I × J cells of the contingency table are omitted from the analysis (because these…

多组多维列联表的潜在结构分析AI 解读

Statistical methods are introduced for latent structure analysis of a set of two or more multidimensional contingency tables. Three basic classes of models are considered: (a) models that assume complete homogeneity across tables, (b) models that allow partial homogeneity across tables, and (c) models that allow complete heterogeneity. Methods are presented for testing whether these models are congruent with the data in the tables and for assessing the significance of…

有序类别交叉分类分析中的关联模型与典型相关AI 解读

The association models considered in Goodman (1979a) for the analysis of cross-classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach. Both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories, and these scores can…

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使用可识别与不可识别模型的探索性潜在结构分析AI 解读

This paper considers a wide class of latent structure models. These models can serve as possible explanations of the observed relationships among a set of m manifest polytomous variables. The class of models considered here includes both models in which the parameters are identifiable and also models in which the parameters are not. For each of the models considered here, a relatively simple method is presented for calculating the maximum likelihood estimate of the…

有先后顺序变量的多维列联表分析：修正路径分析方法AI 解读

Models and methods for analyzing the relations among a set of polytomous variables, when some of the variables are posterior to others, are presented. The techniques proposed here yield ‘path diagrams’ that are somewhat analogous to those used in path analysis. Earlier path analysis models are not suited to the case where the variables are polytomous, or dichotomous, but the models proposed herein are. For each of our models, methods are presented for (a) testing whether the…

具有先后关系的多维列联表分析：修正路径分析方法AI 解读

Models and methods for analyzing the relations among a set of polytomous variables, when some of the variables are posterior to others, are presented. The techniques proposed here yield ‘path diagrams’ that are somewhat analogous to those used in path analysis. Earlier path analysis models are not suited to the case where the variables are polytomous, or dichotomous, but the models proposed herein are. For each of our models, methods are presented for (a) testing whether the…

交叉分类的关联度量（四）：渐近方差的简化AI 解读

The asymptotic sampling theory discussed in our 1963 article [3] for measures of association presented in earlier articles [1, 2] turns on the derivation of asymptotic variances that may be complex and tedious in specific cases. In the present article, we simplify and unify these derivations by exploiting the expression of measures of association as ratios. Comments on the use of asymptotic variances, and on a trap in their calculation, are also given.

卡方分解、边际列联表分析与多维列联表期望频数估计AI 解读

A step-by-step method is presented herein for partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobability in the m-way table. This step-by-step method facilitates both the testing of H and the calculation of , the estimated expected…

定性数据的多元分析：多重分类中的交互作用AI 解读

For the m-way contingency table, we discuss both the direct estimation of the multiplicative interactions among the m variables, and the indirect testing of hypotheses pertaining to these interactions. We consider, among other things, hierarchical hypotheses pertaining to the interactions among the m variables, including hypotheses that can be expressed in terms of one or more of the following kinds of concepts: (a) the usual concepts of independence and equiprobability; (b)…

三维列联表中的卡方分解与偏关联检测AI 解读

Summary This paper presents a method of partitioning a χ2 statistic for the I × J × K contingency table (viz. the χ2 statistic that is based upon the likelihood-ratio criterion for testing the null hypothesis that the three variables pertaining to the three-way table are mutually independent) into additive components that can be used to test (1) the null hypothesis of zero three-factor interaction, (2) the null hypothesis that the partial association between two of the…

双性别人口增长的随机模型AI 解读

SUMMARY In this paper we present stochastic models to describe the changes that take place with time in the numbers of females and males in the various age-intervals in the population. We first consider the case where females, or males, are marriage dominant, i.e. where the joint distribution of the numbers of boys and girls born at time t depends upon the numbers of females, or males, in the various age-intervals in the immediately preceding time-period. We then consider…

列联表三因素交互作用的简便分析方法AI 解读

The earlier literature on three-factor interactions in a three-way contingency table was concerned mainly with the null hypothesis H 0 that these interactions are all nil. In the present article, we present methods for testing H 0 which are easier to apply than those suggested by earlier writers on this subject, and in addition we develop methods for obtaining simultaneous confidence intervals for estimating the magnitudes of the three-factor interactions in the three-way…

列联表交叉乘积比的同时置信限AI 解读

Summary Fisher (1962) has proposed a method for obtaining confidence limits for the cross-product ratio in a 2 × 2 table which requires that the user solve a quartic equation. Based on a different mathematical derivation, Cornfield (1956) had proposed a similar method. In the present article, we shall present simpler methods for obtaining confidence limits for the cross-product ratio in a 2 × 2 table, and we shall extend these methods to obtain simultaneous confidence…

多事件链中持续性的分析AI 解读

This paper presents new methods for (i) estimating the magnitude of the persistence of events in a chain of multiple events, and (ii) testing hypotheses about this persistence, when the observed chain is of long duration and is of the kind considered earlier by Barton, David & Fix (1962). It also compares these methods with those suggested in the earlier literature. We find, for example, that the estimator of persistence suggested earlier by Barton, David & Fix is less…

交叉分类关联度量（三）：近似抽样理论AI 解读

The population measures of association for cross classifications, discussed in the authors' prior publications, have sample analogues that are approximately normally distributed for large samples. (Some qualifications and restrictions are necessary.) These large sample normal distributions with their associated standard errors, are derived for various measures of association and various methods of sampling. It is explained how the large sample normality may be used to test…

关于列联表交互作用的 Plackett 检验AI 解读

SUMMARY Based on a transformation matrix the rows of which are orthogonal to each other, a matrix that comes naturally to analysis of variance users, Plackett (1962) has proposed a test for zero second-order interaction in an r × s × t contingency table which requires that the user invert t +1 matrices, each having (r − 1) (s − 1) rows and (r −1) (s −1) columns. Based on a transformation matrix the rows of which are not orthogonal to each other, we present herein a…

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K 个随机变量乘积的方差AI 解读

An exact formula for the variance of the product of K random variables, x 1, x 2, ···, x K , is given as a function of the means and the central product-moments of the xi . The usual approximate variance formula for is compared with the exact formula; e.g., we note, in the case where the x i are mutually independent, that the approximate variance is too small, and that the relative accuracy of the approximation depends on the magnitude of the coefficients of variations of…

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迁移者—留守者模型的统计方法AI 解读

The mover-stayer model, a generalization of the Markov chain model, assumes that there are two types of individuals in the population under consideration: (a) the “stayer,” who with probability one remains in the same category during the entire period of study; (b) the “mover,” whose changes in category over time can be described by a Markov chain with constant transition probability matrix. The transition probability matrix for movers, and the proportion of stayers among…

时间序列共同变动的若干非参数检验AI 解读

The test, proposed by Moore and Wallis [23], of the existence of correlation between the movements in two time series (eliminating at least the primary effects of trends) was justified by them in “the special case of randomly arranged [signs of the] first differences” in both series. Moore and Wallis also noted that the signs of the first differences in a time series will have a negative serial correlation if the time series is a purely random process (or if it is a…