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一般列联表模型的广义残差及其项目反应理论应用AI 解读

Generalized residuals are a tool employed in the analysis of contingency tables to examine possible sources of model error. They have typically been applied to log-linear models and to latent-class models. A general approach to generalized residuals is developed for a very general class of models for contingency tables. To illustrate their use, generalized residuals are applied to models based on item response theory (IRT) models. Such models are commonly applied to analysis…

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…

关联模型中最大似然估计的计算AI 解读

In association models for cross-classified data, computation of maximum likelihood estimates (MLE's) is relatively difficult due to the nonlinear constraints on the parameters. Currently available procedures based on the scoring algorithm for constrained maximum likelihood are relatively unreliable, and other cyclic procedures are relatively slow and do not provide estimated asymptotic standard deviations as by-products of calculations. To facilitate computations, it is…

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…

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…

凹性与估计AI 解读

Simplified conditions are given for consistency and asymptotic normality of $M$-estimates derived by maximization of averages of independent identically distributed random concave functions. Applications are made to maximum likelihood estimation.

小期望格频数频数表使用卡方统计量的警示AI 解读

When applied to frequency tables with small expected cell counts, Pearson chi-squared test statistics may be asymptotically inconsistent even in cases in which a satisfactory chi-squared approximation exists for the distribution under the null hypothesis. This problem is particularly important in cases in which the number of cells is large and the expected cell counts are quite variable. To illustrate this bias of the chi-squared test, this article considers the Pearson…

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…

最小判别信息调整AI 解读

Minimum discriminant information adjustment has primarily been used in the analysis of multinomial data; however, no such restriction is necessary. Let $P$ be a distribution on $R^a$, and let $\mathscr{C}$ be a convex set of distributions on $R^a$. Let $\mathbf{X}_i, 1 \leq i \leq n$, be independent and identically distributed observations with common distribution $P$. The minimum discriminant information adjustment (MDIA) of $P$ relative to $\mathscr{C}$ is the element $Q$ o…

基于典型相关与线性乘线性交互的双向列联表独立性检验AI 解读

Tests for independence of rows and columns in an $r \times s$ contingency table are developed from canonical correlation analysis and from models of linear-by-linear interaction. The resulting test statistics are asymptotically equivalent under the null hypothesis. They are consistent and asymptotically unbiased. Approximate critical values are available from existing tables. The proposed tests are most appropriate when the matrix of joint probabilities is well approximated…

对数线性模型与期望格频数较小的频数表AI 解读

In the case of frequency data, traditional discussions such as Rao (1973, pages 355-363, 391-412) consider asymptotic properties of maximum likelihood estimates and chi-square statistics under the assumption that all expected cell frequencies become large. If log-linear models are applied, these asymptotic properties may remain applicable if the sample size is large and the number of cells in the table is large, even if individual expected cell frequencies are small.…

指数响应模型中的极大似然估计AI 解读

Exponential response models are a generalization of logit models for quantal responses and of regression models for normal data. In an exponential response model, $\{F(\theta): \theta \in \Theta\}$ is an exponential family of distributions with natural parameter $\theta$ and natural parameter space $\Theta \subset V$, where $V$ is a finite-dimensional vector space. A finite number of independent observations $S_i, i \in I$, are given, where for $i \in I, S_i$ has…

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Gauss–Markov 与最小二乘估计相差多少？无坐标方法AI 解读

A simple expression is developed for the difference between the least squares and minimum variance linear unbiased estimators obtained in linear models in which the covariance operator of the observation vector is nonsingular. Bounds and series expansion for this difference are obtained, and bounds for the efficiency of least squares estimates are also obtained.

间接观测频数表的对数线性模型：最大似然方程AI 解读

Frequency tables are examined in which some cells are not distinguishable. Log-linear models are proposed for these tables which lead to likelihood equations closely related to those associated with log-linear models for conventional frequency tables. Just as in conventional tables, the maximum likelihood equations are shown to be the same under Poisson or multinomial sampling. Applications are made to the problem of estimation of gene frequencies from observed phenotype…

频数数据的对数线性模型：充分统计量与似然方程AI 解读

A general model is proposed for analysis of frequency tables. This model includes conventional log-linear models for complete and incomplete factorial tables and logit models for quantal response analysis. By use of coordinate-free methods of linear algebra and differential calculus, complete minimal sufficient statistics and likelihood equations for the maximum likelihood estimate are derived. The maximum likelihood estimate is shown to be unique if it exists, and necessary…