Haruo Yanai

RELATIONSHIPS AMONG SEVERAL METHODS OF LINEARLY CONSTRAINED CORRESPONDENCE ANALYSIS

This paper shows essential equivalences among several methods of linearly constrained correspondence analysis. They include Fishers method of additive scoring, Hayashis second type of quantification method, ter Braaks canonical correspondence analysis, Nishisatos type of quantification method, ter Braaks canonical correspondence analysis, Nishisatos ANOVA of categorical data, correspondence analysis of manipulated contingency tables, Böckenholt and Böckenholts least squares canonical analysis with linear constraints, and van der Heijden and Meijerinks zero average restrictions. These methods fall into one of two classes of methods corresponding to two alternative ways of imposing linear constraints, the reparametrization method and the null space method. A connection between the two is established through Khatris lemma.

Assessing Items on the SF-8 Japanese Version for Health-Related Quality of Life: A Psychometric Analysis Based on the Nominal Categories Model of Item Response Theory

OBJECTIVES The Short Form-8 (SF-8) questionnaire is a commonly used 8-item instrument of health-related quality of life (QOL) and provides a health profile of eight subdimensions. Our aim was to examine the psychometric properties of the Japanese version of the SF-8 instrument using methodology based on nominal categories model. METHODS Using data from an adjusted random sample from a nationally representative panel, the nominal categories modeling was applied to SF-8 items to characterize coverage of the latent trait (theta). Probabilities for response choices were described as functions on the latent trait. Information functions were generated based on the estimated item parameters. RESULTS A total of 3344 participants (53%, women; median age, 35 years) provided responses. One factor was retained (eigenvalue, 4.65; variance proportion of 0.58) and used as theta. All item response category characteristic curves satisfied the monotonicity assumption in accurate order with corresponding ordinal responses. Four items (general health, bodily pain, vitality, and mental health) cover most of the spectrum of theta, while the other four items (physical function, role physical [role limitations because of physical health], social functioning, and role emotional [role limitations because of emotional problems] ) cover most of the negative range of theta. Information function for all items combined peaked at -0.7 of theta (information = 18.5) and decreased with increasing theta. CONCLUSION The SF-8 instrument performs well among those with poor QOL across the continuum of the latent trait and thus can recognize more effectively persons with relatively poorer QOL than those with relatively better QOL.

Canonical correlation analysis with linear constraints

Abstract We develop canonical correlation analysis by imposing linear constraints upon parameters corresponding to two sets of variables. The results of our method, which we call canolc , are shown in terms of projection operators both orthogonal and oblique. Further, calc (correspondence analysis with linear constraints) turns out to be a special case of canolc .

Some generalized forms of least squares g -inverse, minimum norm g -inverse, and Moore—Penrose inverse matrices

Abstract For given matrices A , M and L of orders n × m , n × q and m × r respectively, we consider various types of g -inverses of A by imposing some rank conditions, i.e., rank( A ′ M ) = rank( AL ) = rank( A ), on these matrices. Further, we introduce two square matrices H = A ( M ′ A ) − and F = L ( AL ) − A , which turn out to be idempotent under the rank conditions. In the light of these properties, we develop some equivalent conditions on g -inverses of A . Based on these results, the L -inverse, M -inverse and LMN inverse (when N = 0) developed by Rao and Yanai (1985a) as generalized forms of least-squares g -inverse, minimum norm g -inverse and Moore—Penrose g -inverse matrices, respectively, are shown to be special cases of the g -inverse matrices which we introduce in section 3 without assuming the nonnegative definite condition.

Interpersonal Trust and Quality-of-Life: A Cross-Sectional Study in Japan

Background There is growing interest in psychosocial factors with positive attitudes, such as interpersonal trust, as determinants for Quality-of-life (QOL) or subjective well-being. Despite their longevity, Japanese people report a relatively poor subjective well-being, as well as lower interpersonal trust. Our aim in this study was to evaluate the possible association between interpersonal trust and QOL among Japanese people. Methodology and Principal Findings Based on the cross-sectional data for Japanese adults (2008), we analyzed the relationship between interpersonal trust and each of four domains of the WHOQOL-BREF. Interpersonal trust was assessed using three scales for trust in people, in human fairness and in human nature. In a total of 1000 participants (mean age: 45 years; 49% women), greater trust was recognized among women (vs. men), those aged 60–69 (vs. 20–29), or the high-income group (vs. low-income). Each of three trust scales was positively correlated with all domains of QOL. Multiple linear-regression models were constructed for each of QOL and the principal component score of the trust scales, adjusted for age, gender, area size of residence, income, education, and occupation. For all QOL domains, interpersonal trust was significantly and positively associated with better QOL with p<0.001 for all four domains including physical, psychological, social, and environmental QOL. Other factors associated with QOL included gender, age class, area size of residence, and income. Education and occupation were not associated with QOL. Conclusions and Significance Greater interpersonal trust is strongly associated with a better QOL among Japanese adults. If a causal relationship is demonstrated in a controlled interventional study, social and political measures should be advocated to increase interpersonal trust for achieving better QOL.

On oblique projectors

Abstract Oblique projectors are useful in many contexts, especially in the instrumental variable estimation in regression models in econometrics, where the disturbance term tends to be correlated with predictor variables. This paper addresses two important questions regarding oblique projectors: (1) products of two oblique projectors and (2) decompositions of oblique projectors. In (1), we investigate what determines the onto- and the along-spaces of an oblique projector defined as a product of two oblique projectors under a variety of conditions. In (2), we examine various decompositions of oblique projectors when both predictor variables and instrumental variables consist of two distinct sets of variables. These decompositions are analogous to those of orthogonal projectors.

An improved method for generalized constrained canonical correlation analysis

An improved method for generalized constrained canonical correlation analysis (GCCANO) is proposed. In the original GCCANO, data matrices were first decomposed into the sum of several matrices according to some external information on rows and columns of the data matrices. Decomposed matrices were then subjected to canonical correlation analysis (CANO). However, orthogonal decompositions of data matrices do not necessarily entail orthogonal decompositions of projectors defined by the data matrices. This latter property is crucial in additive partitionings of the total association between two sets of variables. Consequently, no additive partitionings of the total association was possible in the original GCCANO. In this paper two orthogonal decompositions of projectors were proposed that allow additive partitionings of the total association. Terms in the decompositions have straightforward interpretations. An improved method for GCCANO is developed based on the decompositions, while preserving the most important features of the original method. An example is given to illustrate the proposed method.

Relationships between working status and health or health-care utilization among Japanese elderly.

Background:  As we have previously proposed redefining elderly from “65 years and over” to “75 and over” in Japan, many elderly Japanese now keep working beyond the traditional retirement age, around 60–65 years of age, in this rapidly aging society. It is important to assess the influence of working status on health and health‐care utilization among elderly Japanese.

Singular Value Decomposition (SVD)

In the previous section, we utilized the orthogonal direct-sum decomposi- tions