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分类变量随机有序分布的贝叶斯分析AI 解读

This article considers a finite set of discrete distributions all having the same finite support. The problem of interest is to assess the strength of evidence produced by sampled data for a hypothesis of a specified stochastic ordering among the underlying distributions and to estimate these distributions subject to the ordering. We present a Bayesian approach that is an alternative to using the posterior probability of the hypothesis and the Bayes factor in favor of the…

分类变量的离散程度与惩罚函数：推导、估计及可比性AI 解读

Measures of dispersion for categorical random variables based on penalty functions play a central role in establishing relevant measures of association between such variables. The literature concerning these measures provides little systematic treatment of such aspects of these measures as comparability, efficient estimation, and large-sample properties. This article provides a systematic and rigorous construction of dispersion measures based on penalty functions. Efficient…

分类面板数据的预测函数AI 解读

Prediction of categorical responses in panel studies is considered. Prediction functions based on general conditional $\log$-linear models are investigated for statistical properties both from a population perspective and a sampling perspective. Problems such as existence and uniqueness of optimal prediction functions are addressed, and basic properties of measures of prediction quality are examined. Estimation, consistency and asymptotic normality are studied for the…

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分析分类面板数据的条件对数线性模型AI 解读

Conditional log-linear models are developed for panel data and used to predict sequences of categorical responses. The class of models considered includes conventional Markov models and independence models as well as distance models in which all previous responses and present and past values of covariates are used to predict the current response. The approach taken in this article has some advantages over the marginal modeling approach that has become popular for…

用于分类面板数据分析的条件对数线性模型AI 解读

Conditional log-linear models are developed for panel data and used to predict sequences of categorical responses. The class of models considered includes conventional Markov models and independence models as well as distance models in which all previous responses and present and past values of covariates are used to predict the current response. The approach taken in this article has some advantages over the marginal modeling approach that has become popular for…

有序列联表的序约束 RC 模型：估计与拟合检验AI 解读

The RC model has been proposed as a model for ordered contingency tables. It involves parametric scores that are assigned to the rows and columns of the table so that these scores reflect the ordinality of the row and column categories. Efficient estimation of these parameters subject to order constraints remained an open problem mainly due to severe difficulties in computing these estimates and difficulties in deriving an appropriate asymptotic goodness-of-fit test. A…

二维列联表潜类别分析的贝叶斯方法AI 解读

Latent class analysis in two-way contingency tables usually suffers from unidentifiability problems. These an be overcome by using Bayesian techniques in which prior distributions are assumed on the latent parameters. Application of these techniques, however, involves some unusual computational difficulties. Bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper.

二维列联表合并与卡方缩减原则AI 解读

SUMMARY The value of the chi-square statistic for homogeneity of rows and columns in a contingency table remains unchanged if the table is collapsed (grouped) over homogeneous rows and columns. The difference between the chi-square values pertaining to the original table and to the collapsed table (the ‘chi-square reduction‘) is shown to have a meaningful canonical decomposition which can guide the researcher in detecting homogeneous rows and columns. The methodology…

二维列联表潜类别分析的贝叶斯方法AI 解读

Latent class analysis in two-way contingency tables usually suffers from unidentifiability problems. These an be overcome by using Bayesian techniques in which prior distributions are assumed on the latent parameters. Application of these techniques, however, involves some unusual computational difficulties. Bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper.

列联表典型分析的最大似然方法AI 解读

Canonical analysis has often been employed instead of log-linear models to analyze the relationship of two polytomous random variables; however, until the last few years, analysis has been informal. In this article, models are examined that place nontrivial restrictions on the values of the canonical parameters so that a parsimonious description of association is obtained. Maximum likelihood is used to obtain parameter estimates for these restricted models. Approximate…

列联表的分组与关联：探索性典型相关方法AI 解读

The criteria of homogeneity and structure were proposed by Goodman (1981a) for determining whether certain rows or columns of a contingency table should be grouped. A data-based procedure (using the canonical form of bivariate distributions) is presented in this article to guide exploratory analysis to determine which rows or columns of a table may be grouped. This procedure facilitates the application of the homogeneity criterion. Relationships between the proposed method…

总体间异质性的分析AI 解读

SUMMARY A set of populations, each of which is characterized by a distribution, is said to be “overall homogeneous” if the underlying distributions are identical. Assuming that the underlying distributions are normal or multinomial, this paper provides a theory of establishing test statistics for testing hypotheses of homogeneity within subsets of populations and of homogeneity between subsets of populations. The desired test statistics are derived by a decomposition of the…

双向列联表中典型相关模型与潜在类别模型的联系AI 解读

Relationships between parameters of canonical correlations models and latent class models for two-way contingency tables are explored. It is found that under certain conditions, canonical models and latent models are equivalent. As a result, a new interpretation of canonical variables in contingency tables is proposed.

二维列联表中典型相关模型与潜在类别模型的联系AI 解读

Relationships between parameters of canonical correlations models and latent class models for two-way contingency tables are explored. It is found that under certain conditions, canonical models and latent models are equivalent. As a result, a new interpretation of canonical variables in contingency tables is proposed.

合并列联表中 Pearson 卡方统计量的可分解性、单调性及应用AI 解读

The Pearson chi-square statistic for a contingency table is decomposed into a sum of components. Each component involves the Pearson chi-square statistic for tables that are formed by collapsing (i.e., combining) rows and/or columns of the original table. Since the terms in the decomposition are necessarily nonnegative, this leads to a monotonicity in the statistic; the Pearson chi-square value for any table N is never smaller than the corresponding values for tables formed…

合并列联表中 Pearson 卡方统计量的可分解性、单调性及应用AI 解读

The Pearson chi-square statistic for a contingency table is decomposed into a sum of components. Each component involves the Pearson chi-square statistic for tables that are formed by collapsing (i.e., combining) rows and/or columns of the original table. Since the terms in the decomposition are necessarily nonnegative, this leads to a monotonicity in the statistic; the Pearson chi-square value for any table N is never smaller than the corresponding values for tables formed…

概率矩阵的奇异值分解：二值潜变量的概率性质AI 解读

This paper gives a matrix approach to determine when a statistical dependence between two manifest categorical random variables can be viewed as generated by some unobserved latent variables, in the sense that the manifest variables are conditionally independent with respect to the latent variables. By the singular value decomposition of the matrix representing deviations from statistical independence of the two manifest variables, we give a necessary and sufficient…

概率矩阵的奇异值分解：二值潜变量的概率性质AI 解读

This paper gives a matrix approach to determine when a statistical dependence between two manifest categorical random variables can be viewed as generated by some unobserved latent variables, in the sense that the manifest variables are conditionally independent with respect to the latent variables. By the singular value decomposition of the matrix representing deviations from statistical independence of the two manifest variables, we give a necessary and sufficient…