A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

Covariance structure analysis of ordinal ipsative data

Data are ipsative if they are subject to a constant-sum constraint for each individual. In the present study, ordinal ipsative data (OID) are defined as the ordinal rankings across a vector of variables. It is assumed that OID are the manifestations of their underlying nonipsative vector y, which are difficult to observe directly. A two-stage estimation procedure is suggested for the analysis of structural equation models with OID. In the first stage, the partition maximum likelihood (PML) method and the generalized least squares (GLS) method are proposed for estimating the means and the covariance matrix of A_cy, where A_c is a known contrast matrix. Based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, the generalized least squares method is used to estimate the structural parameters in the second stage. A goodness-of-fit statistic is given for testing the hypothesized covariance structure. Simulation results show that the proposed method works properly when a sufficiently large sample is available.This research was supported by National Institute on Drug Abuse Grants DA01070 and DA10017. The authors are indebted to Dr. Lee Cooper, Dr. Eric Holman, Dr. Thomas Wickens for their valuable suggestions on this study, and Dr. Fanny Cheung for allowing us to use her CPAI data set in this article. The authors would also like to acknowledge the helpful comments from the editor and the two anonymous reviewers.     

A short note on the estimation of the asymptotic covariance matrix for polychoric correlations

By using a Taylor expansion of the equations that define the two step estimator for polychoric correlations, the asymptotic covariance matrix for the estimated correlations can be derived in a simple and straightforward way.     

When can we trust theF-approximation of the box-test?

Consider a multivariate context withp variates andk independent samples, each of sizen. To test equality of thek population covariance matrices, the likelihood ratio test is commonly employed. Box'sF-approximation to the null distribution of the test statistic can be used to computep-values, if sample sizes are not too small. It is suggested to regard theF-approximation as accurate if the sample sizesn are greater than or equal to 1+0.0613p ²+2.7265p-1.4182p ^0.5+0.235p ^1.4* In (k), for 5p30,k20.This research was supported by the Deutsche Forschungsgemeinschaft through Ste 405/2-1.     

A scale-invariant treatment for recursive path models

A reparameterization is formulated that yields estimates of scale-invariant parameters in recursive path models with latent variables, and (asymptotically) correct standard errors, without the use of constrained optimization. The method is based on the logical structure of the reticular action model.     

Alternative test criteria in covariance structure analysis: A unified approach

In the context of covariance structure analysis, a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided. The discussion develops within a general framework that distinguishes whether or not the fitting function is asymptotically optimal, and allows the null and alternative hypothesis to be only approximations of the true model. Also, the equivalent of the information matrix, and the asymptotic covariance matrix of the vector of summary statistics, are allowed to be singular. When the fitting function is not asymptotically optimal, test statistics which have asymptotically a chi-square distribution are developed as a natural generalization of more classical ones. Issues relevant for power analysis, and the asymptotic theory of a testing related statistic, are also investigated.This research has been supported by the U.S.-Spanish Joint Committee for Cultural and Educational Cooperation, grant number V-B.854020. The author wishes to express his gratitude to P. M. Bentler who provided very helpful suggestions and research facilities—with an stimulating working environment—at the University of California, Los Angeles, where this work was undertaken. Thanks are also due to W. E. Saris who provided very valuable comments to earlier versions of this paper. Finally, it has also to be acknowledged the editor's and reviewers suggestions which led to substantial improvements of this article.     

The Latin American contribution to the psychoanalytic concept of phantasy

The author argues that the ubiquity of phantasies at various levels of mental functioning is undisputed in the current schools of psychoanalytic thought; however, she demonstrates some variations in their understanding of how the psychotherapeutic access to different configurations occurs. In the process of examining and acknowledging the central role played by unconscious phantasies in his patients’ symptoms, Freud gradually broadened the vernacular meaning of the German word ‘Phantasie’ that refers to imagination and the world of imagination, conferring on it the specific features that came to characterize its use in the psychoanalytic vocabulary. Later, the expansion of the concept derived from Melanie Klein’s clinical material obtained from child analyses gave rise to important debates. The author discusses the main points of disagreement that led to these debates, as well as their various theoretical and technical implications. Psychoanalytic associations in Latin America were strongly influenced by Klein and her followers. Thus, most of their scientific writings use the concept of unconscious phantasy put forward by the Kleinian school. Taking Kleinian principles as their starting point, Baranger and Baranger made the most original Latin American contribution to the concept of unconscious phantasy with their works on the unconscious phantasies generated by the analytic pair.     

汉语儿童词语结构意识在阅读理解中的预测作用

以382名小学一、三、五年级学生为被试,进行为期一年的追踪研究,通过分层回归,探索了词语结构意识在儿童阅读理解中作用的发展性变化。结果发现：（1）在控制了性别、瑞文推理、汉字识别、口语词汇以及快速命名和语音意识之后,在三年级T2、五年级和五年级T2发现了词语结构意识对同期阅读理解有独特解释作用,而在一年级、一年级T2和三年级均未发现词语结构意识对同期阅读理解的独特贡献;（2）在控制了性别、瑞文推理、自回归效应以及其他相关变量的作用后,三年级和五年级时的词语结构意识分别对一年后的阅读理解具有独特的预测作用。结果表明,在小学低年级阶段,词语结构意识在阅读理解中的作用还未显现,在小学中高年级阶段,词语结构意识对儿童阅读理解有显著的预测作用。     

Nature's Longing for Beauty: Elegance as an Evolutionary Attractor,with Implications for Human Systems

This article suggests that the tendency of living systems to move toward more practical and more aesthetically fitting states be hypothesized as an evolutionary principle. The viewpoints of scientists and systems thinkers on the place of elegance in nature are considered, along with a discussion of issues related to perception of beauty. Implications for human systems and for meeting the challenges we presently face are considered.     

Characterization of Al/n-ZnO/p-Si/Al structure with low-cost solution-grown ZnO layer

We report the fabrication of Al/n-ZnO/p-Si/Al diode structures with a flower-like ZnO layer. The average grain size, microstrain and dislocation density in the ZnO layer were determined as 25?nm, 1.55?×?10^?3 and 3.23?×?10¹³?cm^?2, respectively. From absorption spectra, the optical band gap was found to be ～3.17?eV. A red shift was attributed to non-stoichiometry arising from Zn⁺² ions substituting for oxygen vacancies. The ideality factor was determined as 1.55. The barrier height was calculated as 0.71?eV from I–V characteristics and 0.73?eV using the Norde plots.