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含固定与非正态潜变量的相关样本分析AI 解读

A general structural equation model is fitted on a panel data set that consists of I correlated samples. The correlated samples could be data from correlated populations or correlated observations from occasions of panel data. We consider cases in which the full pseudo-normal likelihood cannot be used, for example, in highly unbalanced data where the participating individuals do not appear in consecutive years. The model is estimated by a partial likelihood that would be the…

多元空间数据的潜变量分析AI 解读

Multivariate spatial or geo-referenced data arise naturally in such disciplines as ecology, agriculture, geology, and atmospheric sciences. In practice, interest often lies in modeling underlying structure and representing interrelationships in terms of a smaller number of variables. For such situations, statistical analysis using a latent variable model is proposed. We present a general model that incorporates spatial correlation and potential lagged or shifted dependencies…

多项式结构方程模型的估计AI 解读

Structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing. Subject matter needs for considering nonlinear structural models have been well documented. But current fitting procedures are available only for a limited class of models. In this article a systematic statistical approach is developed for the general polynomial structural equation model. The new procedure…

广泛因子分析模型的渐近卡方检验AI 解读

Three types of asymptotic $\chi^2$ goodness-of-fit tests derived under the normal assumption have been used widely in factor analysis. Asymptotic behavior of the test statistics is investigated here for the factor analysis model with linearly or nonlinearly restricted factor loadings under weak assumptions on the factor vector and the error vector. In particular the limiting $\chi^2$ result for the three tests is shown to hold for the factor vector, either fixed or random…

多元方差分量秩检验的分位点AI 解读

In the balanced one-way multivariate analysis of variance with random effects the likelihood ratio criterion for testing that the rank of the covariance matrix of the effect vector is not greater than a specified number is considered. The limiting distribution of −2 times the logarithm of the criterion is the distribution of the sum of squares of the positive characteristic roots of a certain random symmetric matrix. This paper presents exact and simulated quantiles of this…

摘要暂缺

多元方差分量秩检验的分位点AI 解读

In the balanced one-way multivariate analysis of variance with random effects the likelihood ratio criterion for testing that the rank of the covariance matrix of the effect vector is not greater than a specified number is considered. The limiting distribution of −2 times the logarithm of the criterion is the distribution of the sum of squares of the positive characteristic roots of a certain random symmetric matrix. This paper presents exact and simulated quantiles of this…

一般条件下因子分析估计量的渐近正态分布AI 解读

Asymptotic properties of estimators for the confirmatory factor analysis model are discussed. The model is identified by restrictions on the elements of the factor loading matrix; the number of restrictions may exceed that required for identification. It is shown that a particular centering of the maximum likelihood estimator derived under assumed normality of observations yields an asymptotic normal distribution that is common to a wide class of distributions of the factor…

非线性函数关系的估计AI 解读

Estimation of the parameters of the nonlinear functional model with known error covariance matrix is discussed. Asymptotic properties of the maximum likelihood estimator for the implicit functional model are presented. The approximate bias in the maximum likelihood estimator due to the nonlinearity of the relationship is given and a bias-adjusted estimator is suggested. Numerical and theoretical results support the superiority of the bias-adjusted estimator relative to the…

函数关系、随机系数与非线性回归：动力学数据应用AI 解读

List of Contents.- 1. An example from physiology.- 1.1 The experiment and the data.- 1.2 The model.- 2. The general linear model.- 2.1 Independent observations with the same variance.- 2.2 Correlated observations with known covariance matrix.- 2.3 Correlated observations with unknown covariance matrix.- 2.4 The general linear model with estimated weights.- 3. The linear functional relation.- 3.1 Introduction.- 3.2 The model and the estimates.- 3.3 Comments on the model.- 3.4…

摘要暂缺

测量误差协方差矩阵由估计获得时的多元变量误差模型估计AI 解读

The errors-in-variables model in which the unobserved true values satisfy multiple linear restrictions is considered. Under the assumptions that the unobservable true values are normally distributed and that an estimator of the covariance matrix of the measurement error is available, the maximum likelihood estimators are derived. The limiting properties of the estimators are obtained for a wide range of assumptions, including the assumption of fixed true values.