The asymptotic standard errors of the estimates of rotated factor loadings and factor correlations are derived for the cases with weights for observed variables such as those for Kaiser's normalization. The factor analysis models employed in this paper are the exploratory ones which have orthogonal or oblique common factors and unstandardized or standardized observed variables. The asymptotic standard errors are given from an augmented information matrix. As an application, the result for the direct oblique rotation by general quartic criteria with Kaiser's normalization is derived. The results of simulation show that the theoretical standard errors are close to simulated ones.
We propose an optimal scaling method to analyze the data describing the repeated choice responses of individuals among categories. In the method, each individual is represented as a polynomial growth curve, while each category is expressed as a point in a low-dimensional space. The solution which is explicitly obtained with eigenvalue decomposition provides the configuration representing the longitudinal changes of individuals with the growth curves. We further modify the method so that it performs the clustering of individual growth curves simultaneously with optimal scaling. The solution is obtained with the alternating least squares algorithm that iterates the scaling through eigenvalue decomposition and the clustering by a K-means method. The resulting configuration of clustered growth curves allows us to easily find some trends in individual changes.
Research in the behavioral sciences often leads to an analysis of ordered categorical data. Likewise the analysis of ordered categorical data is often an important activity in developing high quality products. Taguchi's Accumulation Analysis (AA) is one technique for exploring these data and essentially consists of using traditional analysis of variance methods on cumulative ordered categorical data. For AA in the multifactor setting, the ordered category data are generated using fractional factorial designs and the analysis proceeds by considering collapsed distributions under the design. To overcome some difficulties with AA Nair (1986) has suggested a modification to Taguchi's AA statistic. In addition Hamada and Wu (1990) have performed simulations to demonstrate some failings of AA and advocate alternative methods of analysis. In this paper we show that these deficiencies are not with the modified AA statistic but are due to the collapsed distributions under fractional designs. We also show that the use of fractional factorial designs with ordered categorical data can lead to one of five situations including the reversal of strong location effects. To counter the criticisms, alternative designs have been constructed which do not bias the modified AA statistic. These designs are not peculiar to the modified AA statistic but apply to other location and dispersion statistics such as those used in the Mann-Whitney-Wilcoxon test or Mood's dispersion test.
The Bayesian hierarchical model for polychotomous item responses and the Bayesian method for inferences of the parameters in this model were proposed using the Gibbs Sampler. The model is complex but reflects psychological reality. The method was applied to 40 sets of simulated data and its efficiency in estimation was compared to other established methods. The same method was also applied to the real data, and the individual differences of the estimated competence among the subjects of the same test score could be given good interpretation.
This article describes the results of a statistical survey for public-interest corporations in Japan today. First the brief introduction of position of public-interest corporations in non-profit organizations in Japan is given. Then, the probability sampling design and the methods to heighten the quality of data are shown with its evaluation. The multifarious features of public-interest corporations are depicted by various methods of data analysis. The characteristic features of public interest corporations, which are hidden in data, are revealed by a sophisticated method of data science. The Japanese characteristics of public-interest corporations are also elucidated.