In the analysis of free-answer responses to a social survey questionnaire, some words similar in their dictionary definitions may sometimes need to be distinguished as responses of distinct (sub)cultural groups. A psychometric model called the bicultural generalized high threshold (BIGHT) model is presented to give a criterion to distinguish such words, based on a pattern analysis of responses to some multiple choice questions. This model includes parameters to characterize the respondents by their degrees of conformity to their cultural groups. The degrees are used in a maximum likelihood method to investigate the distinction of two groups corresponding to two similar words used as free-answer responses. This investigation can lead to the distinction of the words as responses of distinct groups. Three illustrative examples on the study of Japanese national characters are also given.
The aim of the present paper is to discuss a hierarchical assessment of continuous latent traits by use of latent Guttman's scales. The latent space under consideration is expressed as x a compact space ?? [0, 1], and is partitioned into several domains which imply the levels of K latent traits. The amount of information about the latent space, which the present latent class analysis includes, is considered, and the latent class analysis is evaluated through the amount of information about the latent space. Concerning the correlation of latent traits, an indicator of the correlation is derived, and in addition a method for testing the correlation of latent traits is proposed. A numerical example is also presented to demonstrate the present analysis.
The purpose of the present study is to propose a procedure for correlation analysis of several (especially two) sets of variables, which includes canonical correlation analysis, principal component analysis, and multiple regression analysis as a special case. The proposed method derives components from each set of variables which maximize the weighted geometric mean of two types of indicators: one is the contribution rate of the components for their original variables, the other is the squared correlation between the components. In terms of the test theory, the former are indicators of reliability and the latter are indicators of concurrent validity. Through the numerical examples applying this method to the data of two Japanese language personality inventory, the method is shown to be particularly useful when determining the weights for test items.