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.     

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.     

寂寞身后事,蓄势待来年——让·皮亚杰(J.Piaget)逝世30周年祭

皮亚杰逝世已30年,但皮亚杰所创立的发生认识论研究不应走向历史。皮亚杰的理论遭到许多人的误解。遗传论和生物学化是两项最为不恰当的帽子。皮亚杰不是传统意义上的心理学家,心理学只是其研究康德意义上的"先验范畴"之个体发生发展的"方法论插曲"。发生认识论具有鲜明的跨学科性质,应该进行"发生认识论"与当代"认知科学"的比较研究。应正确认识理论生物学、结构主义方法论、代数工具和逻辑学在发生认识论研究中的作用和地位,尤其应注重晚年皮亚杰运用新的意义逻辑(logic of meaning)和态射(morphisms)、范畴(categories)等新的代数概念作为形式化认知结构之工具的价值和意义。要深入研究发生认识论对以"具身化"和"回归大脑"为特色的第二代认知科学的启示,探讨它们之间的联系。至少在两个方面可以明显看到这种联系:一是发生认识论中的"动作协调"及对由协调而产生的逻辑—数学经验的"反省抽象"这两个概念,表明了皮亚杰对心智具身性的卓越洞见;二是在皮亚杰所主张的"表型复制"(phynocopy)观点中体现的衍生论(epigenesis)和建构论(constructionism)思想,它们与第二代认知科学的动力系统理论之基本思想——所涉因素或变量之间的关系是一种互为因果、相互塑造的对偶(coupling)关系而不是线性的单向因果关系——两者是完全一致的。皮亚杰及其发生认识论定会随着认知科学的未来发展而被"再发现"。     

Intact emotion–cognition interaction in schizophrenia patients and first-degree relatives: Evidence from an emotional antisaccade task

Schizophrenia patients have deficits in cognitive control as well as in a number of emotional domains. The antisaccade task is a measure of cognitive control that requires the inhibition of a reflex-like eye movement to a peripheral stimulus. Antisaccade performance has been shown to be modulated by the emotional content of the peripheral stimuli, with emotional stimuli leading to higher error rates than neutral stimuli, reflecting an implicit emotion processing effect. The aim of the present study was to investigate the impact on antisaccade performance of threat-related emotional facial stimuli in schizophrenia patients, first-degree relatives of schizophrenia patients and healthy controls. Fifteen patients, 22 relatives and 26 controls, matched for gender, age and verbal intelligence, carried out an antisaccade task with pictures of faces displaying disgusted, fearful and neutral expressions as peripheral stimuli. We observed higher antisaccade error rates in schizophrenia patients compared to first-degree relatives and controls. Relatives and controls did not differ significantly from each other. Antisaccade error rate was influenced by the emotional nature of the stimuli: participants had higher antisaccade error rates in response to fearful faces compared to neutral and disgusted faces. As this emotional influence on cognitive control did not differ between groups we conclude that implicit processing of emotional faces is intact in patients with schizophrenia and those at risk for the illness.     

Understanding responses to predictive genetic testing: A grounded theory approach

Abstract

In view of the absence of data concerning the understanding and experience of families in which one or more members have undergone predictive genetic testing, a pilot study using a qualitative methodology was conducted with members of families at risk for the late-onset genetic disease, familial adenomatous polyposis (FAP). Semistructured interviews were conducted to elicit illness representations, with responses tape-recorded and analysed using a grounded theory approach. Several themes emerged. The most striking was that when genetic testing indicated an extremely low risk of developing the disease, there was a desire to continue regular bowel screening, even though it was experienced as extremely aversive. Possible explanations draw upon both other themes of the interviews, and psychological models. The role of “functional pessimism” and “uncertain wellness” in maintaining a high threat from the disease, and the role of reinforcement and the nature of tests in providing bowel screening with a high value are discussed.     

A genetic variant (COMT) coding dopaminergic activity predicts personality traits in healthy elderly

Association studies between the NEO five factor personality inventory and COMT rs4680 have focused on young adults and the results have been inconsistent. However, personality and cortical changes with age may put older adults in a more sensitive range for detecting a relationship. The present study examined associations of COMT rs4680 and personality in older adults.Genetic association analyses were carried out between the NEO and the targeted COMT rs4680 in a large, well-characterized sample of healthy, cognitively normal older adults (N = 616, mean age = 69.26 years).Three significant associations were found: participants with GG genotype showed lower mean scores on Neuroticism (p = 0.039) and higher scores on Agreeableness (p = 0.020) and Conscientiousness (p = 0.006) than participants with AA or AG genotypes.These results suggest that older adults with higher COMT enzymatic activity (GG), therefore lower dopamine level, have lower Neuroticism scores, and higher Agreeableness and Conscientiousness scores. This is consistent with a recent model of phasic and tonic dopamine release suggesting that even though GG genotype is associated with lower tonic dopamine release, the phasic release of dopamine might be optimal for a more adaptive personality profile.     

Classification of dog barks: a machine learning approach

In this study we analyzed the possible context-specific and individual-specific features of dog barks using a new machine-learning algorithm. A pool containing more than 6,000 barks, which were recorded in six different communicative situations was used as the sound sample. The algorithm's task was to learn which acoustic features of the barks, which were recorded in different contexts and from different individuals, could be distinguished from another. The program conducted this task by analyzing barks emitted in previously identified contexts by identified dogs. After the best feature set had been obtained (with which the highest identification rate was achieved), the efficiency of the algorithm was tested in a classification task in which unknown barks were analyzed. The recognition rates we found were highly above chance level: the algorithm could categorize the barks according to their recorded situation with an efficiency of 43% and with an efficiency of 52% of the barking individuals. These findings suggest that dog barks have context-specific and individual-specific acoustic features. In our opinion, this machine learning method may provide an efficient tool for analyzing acoustic data in various behavioral studies.