We propose a new response model for multiple choice items, which is an extension of the three-parameter logistic model. This model enables us to make use of the information provided by distractors as well as correct item alternatives. The essential idea of this model is the further partition of the incorrect response curves in terms of the weighted average of the“ideal”correct curve and incorrect curve. By using artificial data, we showed that this model can produce better estimates of the ability parameters than the usulal three parameter logistic model.
A Γ-shaped scatter diagram of factor scores has been reported previously in common with the data relating to cerebral and neural diseases; language tests of aphasia, finger function tests of hemiplegia, and symptoms in mild disturbance of consciousness. The factors were inter pretable as situated successively on severity continuum of the diseases. Scale analysis suggested a data structure based on Guttman perfect scale. Then Guttman perfect scale and quasi-scale models were investigated in respect to attributes of correlation matrices of dichotomous scale variables. Eigenvalues and eigenvectors were obtained in case of the perfect scale that subjects had a uniform distribution on the continuum. According to the number of eigenvalues greater than 1, the number of factors is expected as √t-½in the perfect scale, where t is the number of variables. The score of the 2-nd factor before factor rotation is represented by a parabola of the 1-st factor. The oscillation law of eigenvectors has a characteristic manifestation on the factor loadings after rotation, and on the Γ-shaped distribution of factor scores. Successive factors have high loadings on successive groups of variables located in the order determined by Guttman scale. In quasi-scale models, these properties undergo certain changes, so that the Γ-shape becomes ambiguous depending on the size of deviation from the perfect scale.
This paper is concerned with a problem of constrained clustering for qualitative data. Combinatorial problem of scheduling meetings is a typical example. The desired schedule of meetings is such one that minimizes the total number of man-days. In those clustering problems, the computational time to find the optimal solution increases exponentially as the number of meetings grows. In order to find a near optimal solution efficiently, we discuss some methods; 1)methods based on quantification methods(Quantification Theory3, Karhunen-Loeve Expansion)and2)a Bottom-up Merging(Hierarchical Clustering)method which is derived from the inherent criterion of the problem. In method 2), particularly, the representative vector of each cluster and the metric for merging clusters are logically and uniquely determined by the criterion. It is shown by experiments that schedules obtained by these methods are better than those obtained in trial and error.
In this paper, we study the change of the influence of the factors affecting individuals' occupations from 1955 to 1975 with SSM data, using regression and logit models. The following findings have been obtained from regression model analysis. The influence of father's occupation hadn't changed during 20 years. That of education had weakened gradually. That of first job had become stronger from 1955 to 1965, but hadn't changed from 1965 to 1975. The following findings have been obtained from logit model analysis. The influence of father's occupation had changed differently according to occupational categories. That of education had been strong at 1955 and 1965, but weakened from 1965 to 1975. That of first job had become stronger. The difference between the findings from regression and logit model analyses means that these models shed light on the different aspects of the real world.
In the first half of this paper, we examined psychological validity of two measures derived from singular value decomposition of‘0-1’matrix in which a Kata-Kana letter was quantitized. Variance of extracted eigenvalues reasonably predicted recognition accuracy of a letter, and variance of contributions of principal components correlated with complexity and regularity ratings of a letter. In the last half, we constructed the pattern recognition model implementing pre-process by singular value decomposition and also feature-sampling-process by Walsh-Hadamard transformation. Similarity structure output through the model was quite similar to the one obtained from the psychological experiment.
Statistical Data Analysis(SDA)is considered to be aprocess which extracts some“productive”findings from data through certain filter of thoughts or statistical viewpoints. The substantial SDA has provided heartwarming stories based on the data. However, it seems to us that recent drastic progress of computer, including desktop computer, promotes having made the SDA into instant and tasteless process. In order to cope with these tendencies, we at first appeal the inherent attractions of the SDA, considering it as unified process. The SDA consists of three elements, namely, data, methodology and analyst including statistician. In practice of the SDA, these three elements get interwined, and can not be treated independently. Thus, it is important that implication of the SDA be flexible and adaptive. Consequently, the second purpose is to introduce the principles and procedures of data investigation, and data-adaptive methods that can Hexibly take into account some diagnoses in each stage of the SDA process. It gose without saying that skills of the analyst, or in other words, technical aspects play important roles in the SDA. Finally, we pigeonhole remarks or rules of thumb that are required in applying statistical methods to each stage of the SDA, and consider qualification of appropriate analyst.
In this paper, fuzzy set theory which provides a methodology of treating human subjectivity, linguistic meanings, etc. is reviewed and its novel applications to some actual problems are introduced to show the efficiency of the theory. First, fundamental concept of fuzzy set theory is explained to point out the differences with probability theory, and then follows the descriptions on fuzzy operations, fuzzy relations, fuzzy reasonings, etc. with their mathematical aspects. Next, the application studies on three fields such as fuzzy control, fuzzy decision making and fuzzy mathematical programming which are considered as the most appropriate examples in showing the efficiency of fuzzy set theory are presented. Finally, the future research topics on fuzzy set theory are briefly discussed.