Several methods of statistical inference in factor analysis are first reviewed under the normality assumption as well as the case in which no assumption about the population ditribution is made. Normal theory inference, whether it is asymptotically efficient, is shown to be robust against a wide class of distributions which may be encountered in many practical fields. For small or medium sample sizes, simple procedures of estimation, such as simple least-squares and noniterative methods, are recommended, whereas the method of maximum likelihood or other asymptotically efficient ways should be utilized for large samples.
This paper deals with models of covariance structures and methods for their analysis. First, we discuss the properties of latent variables and latent variable models using Bentler's definition. Second, the methods of estimating parameters in covariance structures are discussed based on various criteria from a general viewpoint. Third, the goodness-of-fit indices are evaluated and the method which use the basic models apart from the saturated model is explained. Finally, FAREG(combination of Factor Analysis and REGression)model which has been developed by the author is presented with an example.
This paper consider sexploratory methods for investigating the factor invariance or factor changes in multigroup, multiset, and three-mode data, orthogonal rotations achieving the congruence of loading matrices, canonical analysis of component scores, and simultaneous principal component analytical methods with various optimization criteria and constraints. Desirable properties which should be shared by exploratory factor analytical methods are discussed based on simple schematic models of differences of factor loadings and factor scores between two data matrices. The hierarchical principal component analysis method is derived as an extension of van de Geer's Maxbet method for multiset data. The method is equivalent to the slightly generalized Tuckals2 model(Kroonenberg and de Leeuw)for three-mode data, and can be modified to be applicable to multigroup data. It is demonstrated that these methods have the desirable properties as exploratory analysis.
In this article, the author discusses statistical problems associated with the factor analysis of categorical data in the general context of the latent variable model. Modelling process for categorical data and the estimation procedure for the parameters of the model are discussed. Also, it is argued that the usefulness of these models as item response models can be tested in the area of educational measurement. Finally, the problems which remain unsolved are discussed and the future directions of the latent variable model are suggested.
Multidimensional graphical method can be utilized on a multivariate data analysis through a procedure in which the multidimensional graphical method supports the statistical method with supplying deficiency of them.We present a procedure of combining both the face graph and Discriminant Function Method(DFM)to carry out exploratively discriminant analysis. However, in order to realize this procedure it needs to previously investigate differences of function between both methods.The results of the investigation showed that the face graph has two advantages over DFM that the discriminant analysis can be carried out when the training data are not sufficiently obtained and outliers in analysed data set can be easily found. Therefore, adopting the procedure of combining the face graph and DFM will make an efficient exploratory discriminant analysis.
An interactive method of multivariate data analysis is proposed. With this method we can use effectively our prior knowledge about the data to perform clustering. The knowledge about objects and variables is represented by frame structure. A simplified algorithm of conceptual clustering and an effective method of graphical representation are adopted to support analysis. Using these features, data analysts can find the intrinsic structure of data easily.
The politeness of honorific expressions is expressed not only through portions of the utterance such as honorific word forms, but also through structural elements of the complete utterance. In order to quantify the politeness of utterances, we must consider their complete structure and honorific functions irrespective of length, style, or number of sentences. In honorific expressions in current Japanese, if elements with a high level of politeness are used, other elements tend to be interpreted as plite forms for the conformity of the complete utterance. In the present research, a methodology combining the number of elements functioning as polite expressions with the total number of structural elements of the utterance was employed to quantify the politeness of an utterance. Also, categorical regression analyses of social factors(such as personal differences)related to politeness were performed.