A factor analysis model represents linear relationships between latent variables and observed variables. Although this is widely used for analysis of psychological tests, nonlinear relationships often need to be analysed. Here, a nonlinear factor analysis model that uses spline transformation of latent variables is proposed. The conditional distribution of observed variables given by the latent variables is assumed to have means (or location parameters) that are expressed in nonlinear transformations of the latent variables. For binary valued observed variables, logits of the binomial mean parameters are expressed as piecewise polynomials of the latent variables. Linear factor analysis and two-parameter IRT (item response theory) models are special cases of this model. Discrete approximation of the latent variables enables easy adaptation for the missing values of a MAR (missing at random) condition. Properties of the model are examined by artificial data and test scores from other sources.
The dimension for rating the similarity of objects is different from that for rating the degree of liking for the same objects. Using Abelson's contour mapping model, this study expressed the degree of liking for objects on configurations obtained by multidimensional scaling (MDS). Thirty participants evaluated similarity (measured on an 11-point scale) and the degree of liking (evaluated on a 5-point scale) for six professional baseball teams in the Central League of Japan. Configurations of the objects were obtained by MDS using the similarity data. Valences were computed based on the degree of liking obtained by a contour mapping model. Compared with other techniques such as PREFMAP, a contour mapping model has three advantages. First, a contour mapping model has a better fit with data. Second, mapping facilitates the visual comprehension of attitudes. Finally, a contour mapping model may integrate two types of attitude theories in social psychology. This model serves to express emotional components in the force field and offers a basis to develop a dynamic model of attitude expressed by a vector field.
Equivalence of two methods for obtaining composite scores that maximize individual differences from incomplete test scores is formally proved. One method is based on the least squares criterion and can get composite scores in such a way as to maximize individual differences while allowing for differences between difficulties of tests. The other method is formulated from the viewpoint of ANOVA model and thus can be easily extended to multi-component case. The basic result of the equivalence is shown to be available for developing an effective algorithm of PCA for incomplete data matrix.
The purpose of this study is to find out the types of classroom structure in the elementary schools and its general characteristic of their composition according to teacher's cognition using SYMLOG. Data collection was conducted in Seoul Korea. Thirty-four teachers from the elementary schools participated in this study and rated each child in their classrooms with SYMLOG Adjective Rating Forms. Classroom group types were analyzed by the field diagram using the three-dimensional model of SYMLOG : instrumentally controlled vs. emotionally expressive, dominant vs. submissive, and positive vs. negative. The major findings of this study were as follows. First, three main group types (Unified, Polarized, and Fragmented) and four intermediate types (Unified with Non-attracting Outlyer, Tending to Polarized, Scapegoated, and Tending to Fragmented) were classified and the proportion of Polarized Groups (41%) was remarkably high. Second, Korean teachers laid stress on the sociometric (positive vs. negative) dimension. The results of this study indicate that SYMLOG could provide us with an instrument for systematic perception of problematic classroom group structure and classroom members.
In behavioral sciences, it is often difficult to execute an experimental study with random assignment. Therefore researchers usually do a quasi-experiment or a survey study without random assignment. However, under these studies the distributions of the covariates that would affect dependent variables usually differ with the values of the independent variables. To eliminate the influence of the covariates, various adjustment methods such as analysis of covariance have been applied to these data. Recently new adjustment methods using the propensity score proposed by Rosenbaum & Rubin (1983) have been applied to many researches especially in the areas of medicine or economics, and these methods also attract attention in behavioral sciences. The propensity score methods are also used for adjustment of survey data. In this paper, we give a detailed explanation of several estimation methods of causal effect using the propensity scores and related topics. We also review adjustment methods of biased survey data using the propensity scores.