The missing response problem is one of the serious problems in Dual Scaling, s well as other methods of multivariate analysis. There are several approaches to handle missing responses in Dual Scaling, but the method of ignoring missing responses, among them, is regarded as more appropriate especially for a data set with many missing responses. The method is proceeded by inserting value os to all categories of missing response. In this paper, we show that the procedure can't give proper solutions, and propose a new kind of algorithm for ignoring missing responses.Furthermore we show the efficiency of the new algorithm, referring to the simulations based on artificial data and also present the application of it to actual data.
In practical sample surveys, stratified sampling is widely used to estimate population parameters with high precision. Although point estimation for a population mean was investigated from all viewpoints, interval estimation has not been sufficiently studied. This paper is concerned with several kinds of confidence intervals based on stratified random samples. Firstly we propose a confidence interval procedure for the population mean that uses Student's t-distribution, and also show that t-statistic can be constructed from stratified random sample when the objective variable is normal distributed in each stratum and the sample is drawn with Neyman allocation(the optimum allocation). If this sample allocation method is not used, the confidence interval is improved using Satterthwaite approximation for the distribution of the statistic unless the strata are terribly skew. In the difficult situation, we obtain the aid of the nonparametric bootstrap method. The coverage probabilities and some other properties for all methods considered in this paper are investigated through the simulation study for some theoritical distributions and actualdata.
The varimax rotation, a special case of the orthomax method, usually contains the process of normalization by the communalities of manifest variables. After rotation, factor loadings are re-scaled so that the communalities have original values. Although the standard errors of rotated factor-loadings have been discussed from the general view point of estimation of parameters with restrictions, the actual standard errors for normalized rotation have not been provided. In this paper a method of estimating the asymptotic standard errors in the normalized orthomax rotation is given. Two artificial examples are provided in which standard errors become extremely large with or without normalization.
Asymmetric multidimensional scaling(MDS)is reviewed which embeds objects in a certain distance space, given a square asymmetric data matrix whose elements denote(dis-)similarities between them, along with techniques related to MDS. A body of extant asymmetric MDS's are contrasted; these have been proposed in order to overcome difficulties encountered in traditional (symmetric)MDS's. They are(1)augmented distance models, (2)non-distance models, and(3)extended distance models. The augmented distance models are those which append some quantity to some traditional distance measure or square one. The non-distance models are those which approximate some quantity such as inner product to(dis-)similarity data. The extended distance models are those which generalize traditional distance measures in a certain manner. Next, a technique closely related to asymmetric MDS, namely, asymmetric cluster analysis, is reviewed. Finally, problems which still remain to be solved and possible future developments in asymmetric MDS and related techniques are discussed.