Factor analysis as a tool for data analysis

The use of factor analysis in analyzing real data is influenced not only by mathematical models but also by the objectives of the research at hand, the amount of data to be analyzed and the departures of the data from the model. Factor analysis is a process performed in several steps, including data screening and assessment of assumptions necessary for the model as well as the actual computations—the new analyst may need assistance in deter-mining the initial method of extraction, how many factors to request, the method of rotation and how to interpret the factors— these steps are discussed with reference to figures containing computer output for a real problem. The importance of auxiliary information and graphical displays to aid the statistician during the factor analysis process is stressed.     

On a measure of dependence based on fisher's information matrix

A class of measures of dependence between two random vectors is defined, in terms of the canonical correlations obtained from Fisher's information matrix. Some basic properties are proved for this class of measures. Examples are given to illustrate that the class gives good measures, under normal models. Interesting measures are also arise for bivariate models where the correlation coefficient does not exist for some values of the parameters of the model.     

Extended Analysis of At Least Partially Ordered Multi‐factor ANOVA

For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to construct components that provide a deep nonparametric scrutiny of the data. The components assess generalised correlations and the resulting tests include and extend the Page and umbrella tests. Application of the tests described is straightforward. Orthonormal polynomials on the ANOVA responses and the factors are required and the formulae needed are given subsequently. These depend on the moments of the responses and of each factor and are easily calculated. Products of at least two of these orthonormal polynomials are then used as inputs into standard ANOVA routines. For example, using the first order orthonormal polynomial on factor A and the second order orthonormal polynomial on the ANOVA response will assess if, with increasing levels of factor A there is an umbrella response with either an increase and then a decrease or a decrease and then an increase.     

On the heterogeneity of fecundability

We propose to use a general mixing distribution in modeling the heterogeneity of the fecundability of couples. We introduce a sequence of parameters called canonical moments, which is in one to one correspondence with the moments, to characterize the mixing distribution. By using the bootstrap method, we can estimate the standard errors of our estimates. Our method modifies the usual moment estimates so that the resulting mixing distribution is always supported on [0, 1]. Moreover, the downward bias of the moment estimate of the number of support points would be reduced. Our approach can be used for censored data. The application of our technique in finding the sterile subpopulation is also discussed. The theory is illustrated with several data examples and simulations.     

矩阵方程X~2 AX XB C=0的解的讨论

讨论了一元二次矩阵方程X2 AX XB C=0的解,分别得出可对角化解及一般解的构造性结果.     

An assessment of the construct validity of Ryff’s Scales of Psychological Well-Being: Method, mode, and measurement effects

This study assesses the measurement properties of Ryff’s Scales of Psychological Well-Being (RPWB)—a widely used instrument designed to measure six dimensions of psychological well-being. Analyses of self-administered RPWB data from three major surveys—Midlife in the United States (MIDUS), National Survey of Families and Households II, and the Wisconsin Longitudinal Study (WLS)—yielded very high overlap among the dimensions. These large correlations persisted even after eliminating several methodological sources of confounding, including question wording, question order, and negative item-wording. However, in MIDUS pretest and WLS telephone administrations, correlations among the dimensions were much lower. Past research demonstrates that self-administered instruments provide more valid psychological measurements than telephone surveys, and we therefore place more weight on the consistent results from the self-administered items. In sum, there is strong evidence that RPWB does not have as many as six distinct dimensions, and researchers should be cautious in interpreting its subscales.     

矩阵方程AX-XB=C

本文利用矩阵的 Frobenius 标准形讨论了矩阵方程 AX-XB=C 的解的情况,特别给出了该方程有解时的递推解法,同时给出了该方程有唯一解的充要条件的另一个证明,且证明过程不用克罗内克尔乘法     

非英语专业大学生词汇学习策略的研究

词汇学习是英语学习的重要内容之一。近年来,有关词汇学习策略的研究在二语习得领域中受到广泛重视。在前人研究的基础上,笔者策划了对大学非英语专业二年级326名文理科及艺术类学生词汇学习策略的实证研究。本文运用定量分析的方法,对非英语专业学生所使用的词汇学习策略以及它们和词汇测试成绩之间的关系进行了讨论和分析,并对大学英语的词汇教学提出几点建议。     

Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form

In this article we study two methodologies which identify and specify canonical form VARMA models. The two methodologies are: (1) an extension of the scalar component methodology which specifies canonical VARMA models by identifying scalar components through canonical correlations analysis; and (2) the Echelon form methodology, which specifies canonical VARMA models through the estimation of Kronecker indices. We compare the actual forms and the methodologies on three levels. Firstly, we present a theoretical comparison. Secondly, we present a Monte Carlo simulation study that compares the performances of the two methodologies in identifying some pre-specified data generating processes. Lastly, we compare the out-of-sample forecast performance of the two forms when models are fitted to real macroeconomic data.     

Multivariate Stochastic Volatility: A Review

The literature on multivariate stochastic volatility (MSV) models has developed significantly over the last few years. This paper reviews the substantial literature on specification, estimation, and evaluation of MSV models. A wide range of MSV models is presented according to various categories, namely, (i) asymmetric models, (ii) factor models, (iii) time-varying correlation models, and (iv) alternative MSV specifications, including models based on the matrix exponential transformation, the Cholesky decomposition, and the Wishart autoregressive process. Alternative methods of estimation, including quasi-maximum likelihood, simulated maximum likelihood, and Markov chain Monte Carlo methods, are discussed and compared. Various methods of diagnostic checking and model comparison are also reviewed.