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使用因子模型对二元响应进行量表评分AI 解读

SUMMARY A simple method for scaling a set of binary responses is proposed using the logit factor model of Bartholomew (1980). It is shown that individuals may be ranked on the basis of a linear combination, ∑αi x i of the responses (xi = 0 or 1) where the αi's are the appropriate factor loadings. This completely avoids the need to calculate the y-scores suggested in Bartholomew (1980) and hence the heavy numerical integration which that method involves.

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因子分析的基础AI 解读

A new approach to factor analysis and related latent variable methods is proposed which is based on data reduction using the idea of Bayesian sufficiency. Considerations of symmetry, invariance and independence are used to determine an appropriate family of models. The results are expressed in terms of linear functions of the manifest variables after the manner of principal components analysis. The approach justifies some of the practices based on the normal theory factor…

分类数据的因子分析AI 解读

Summary The method of factor analysis is widely used as an exploratory tool to reduce the dimensionality of multivariate data. The fact that the standard model is strictly applicable only when the manifest variables are scaled is a serious limitation in social science where the variables are often categorical. In this paper we aim to provide a theoretical framework within which methods for the factor analysis of categorical data can be devised and compared. Discussion is…

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将样本量视为随机变量时的假设检验AI 解读

Summary In the Neyman-Pearson theory of hypothesis testing it is customary to calculate significance levels and power functions on the assumption that the sample size is fixed. The main purpose of this paper is to propagate the view that the restriction of the theory to reference sets in which the sample size is constant is neither necessary nor desirable. The paper falls into two parts. In the first we consider the test of a simple null hypothesis versus a simple…

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若干贝叶斯与频率学派推断的比较AI 解读

Suppose that we have a sample of observations on a continuous random variable with a distribution depending on one unknown parameter θ. We consider the problem of making inferences about θ when there is no prior information about the value of the parameter. Some examples are discussed for which it is not possible to find Bayesian methods possessing the properties required by frequentist statisticians. The magnitude of the difference between comparable Bayesian and…

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受限备择下的均值齐性检验AI 解读

SUMMARY Suppose that observations x1, x2, …, xk have been obtained from normal populations with unknown means μ1, μ2, …, μk and known standard deviations σ1, σ2, …, σk. The paper discusses tests of the hypothesis μ 1, μ 2, … = μk when prior information is available about the μ‘s under the alternative hypothesis. A generalized form of the χ 2-test, denoted by x2¯, has been developed for use when this information takes the form of order restrictions between some or all of the…

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