In this paper, we consider methods to analyse longitudinal ordered categorical data. Several methods for analysing such data have been proposed, but they are often limited in their ranges of application. We propose to treat the ordered categorical data as if they are continuous ones by scoring ordered categories, and to apply randomization test to them. In addition, we recommend joint use of time-continuous type method (Zerbe, 1979) and time-discrete type method (Raz, 1989) when both treatment main effect and treatment-by-time interaction are to he tested by the randomization test. By a simulation study, we evaluated performances of our recommending approach for the tests of treatment main effect and treatment-by-time interaction based on longitudinal ordered categorical data. We defined effects of these two factors on an underlying continuous scale in the simulation study. As a result, it was found that the performances of these two tests are satisfactory with respect to type I error rate and power. However, in the case where extremely large (or small) score was given to the maximum (or the minimum) category, the powers of these two tests were slightly low.
A rank association coefficient t for measuring the nonmonotone association is defined. The mean and variance, some tables for the distribution are calculated. A new association analysis based on t is proposed and applied to some numerical examples.
Geometrical structures of some non-distance models for asymmetric MDS are examined in error-free data measured at a ratio level and a unified geometrical interpretation of these models is provided. These include CASK (Canonical Analysis of SKew symmetry), DEDICOM, GIPSCAL, and HCM (Hermitian Canonical Model). It is shown that these models except for CASK as well as other possible models for square asymmetric proximity data matrix are expressible in terms of finite-dimensional complex Hilbert space under some general condition, and that differences in form of these models depend only on the bases chosen. It is also shown that the Hilbert space structure has an interesting property which traditional distance model does not. Finally it is shown that the general condition relates to an extension of the famous Young-Householder theorem to complex Hilbert space.
The problem under consideration is to fit a straight line between true scores where, given n pairs of observed test scores, each observed score is assumed to be the sum of a true score and an error score. This problem may typically occur in the situation of pretest and posttest analysis. In order to facilitate the analysis, the split-halves technique is employed. Linearity between the split true scores is assumed as well as linearity between the true scores of the two tests. Based on these and other familiar assumptions, Bayesian estimates of the parameters, true scores, and reliability coefficients are derived.
Identifying the elements that make up an author's characteristic writing style is one of the keys to determining the authorship or authenticity of a literary composition. The present study, which constitutes a preliminary attempt to uncover such a key, focuses on the placement of commas in sentences, a matter that has hitherto been neglected, analysing the characters that commas follow in works by four authors. It is concluded that the placement of commas differs from writer to writer and may therefore be considered one of the features that makes up an individual literary style, thus providing valuable information for verifying authenticity and speculating on questions of authorship.
This paper discusses macro analysis of social change by means of cohort analysis. The material is based on over thirty-five years of experience with Chikio Hayashi, conducting statistical analyses of the Japanese National Character studies (Hayashi, 1987; Hayashi and Suzuki, 1984; Suzuki, 1970). In the mid 1980s, a new Bayesian approach to cohort analysis was introduced (Nakamura, 1982, 1986). The details of this method are discussed elsewhere (see Sasaki and Suzuki, 1987; Glenn, 1989; Sasaki and Suzuki, 1989). We have used this new methodology, which can automatically partition age effects, period effects, and cohort effects, and here we will present some of our results using Bayesian cohort analysis (Suzuki, 1986).
This paper reports a case study in the use of eleven methods of discrimination procedures applicable to binary data for the purpose of classifying survivors among 952 patients (test sample) who were treated for burn injuries between May 1976 to October 1977 in different hospitals in India. These techniques were initially used for predicting survival rates on the basis of information of involvement of six major body parts obtained from 582 cases admitted to a hospital in Lucknow city (training sample) during April 1970 to April 1976. The goal of this study was to compare the performances of discrete classification rules with that of commonly used Fisher's Linear discriminant function and Logistic discrimination procedures in the presence of sparse data. The results of this study indicated that LDF performed as good as any discrete procedures and also logistic discrimination rule for the purpose of minimising the overall misclassification rates. However, in the context of burn injuries problem where the aim is to identify highest proportion of survivals correctly, Logistic discrimination rule emerged as the single best rule.