Recently several graphs for analysis of ranked observation have been proposed. Among them there exists rank graph proposed by Baba et al.. In this paper a graphical rank test method by using the rank graph is proposed and some merits of the rank graph are mainly discussed. Suppose that k items are ordered by n judges. The rank graph was proposed originally as a descriptive one in which the average rank and the degree of concordance of ranks assigned to each item are represented by the vector called item vector. It is shown that under the assumption of random rankings, the distribution of the final point of an item vector can be asymtotically approximated by a 2-dimensional normal distribution. This is applied to graphical test of null hypothesis that ranks are given at random to each item. It is shown that in the case of large sample, the null hypothesis for each item can be tested visually by the rank graph with a critical ellipse without the bother of using a table.
We consider in this paper a model of asymmetric power-transformation of response probability explained by linear function of some covariates. This model includes logistic and complementary log-log transformation models as its specific case, so we can use the model to evaluate the appropriateness or the goodness of fit of these models. Then the performances of the asymmetric power-transformation model are evaluated and examined, based on data used in published literatures. And we discuss various issues of diagnoses which may occur in the process of applying the model. Further we consider alternative transformations, and then in comparison with them, we point out the advantages of the asymmetric power-transformation.
Multidimensional scaling technique was applied to the Brazilian migration matrix in order to identify the functional regions of the nation, using the 1970 census data for males. The results obtained from three types of proximity matrices confirmed the key roles of Minas Gerais and Mato Grosso as the core states in addition to Rio de Janeiro and Sao Paulo. Substantial circulation of migrants among the core states runs counter to the popular notion about the Northeastern states as the major source of labor in Rio de Janeiro and Sao Paulo. The Northeast were found to consist of three groups of states: Maranhao, Piaui and Ceará showed a stable clustering, but peripherally located, in all configurations; and, the other two groups failed to form persistent regions across configurations. Though limited in scope, the observed attraction of Espirito Santo and Goiás violated the widely held negative effect of distance and deserves further investigation.
The purpose of this paper is to propose a method for identification of handwriting. From sample characters we obtained the “thresholding”, and then the “thinning” using an image recorder system. Individual parts of the characters were measured, and many variables were defined for each character. Since variables important in the discriminant analysis varied among subjects, the stepwise discriminant analysis turned on to be useful.
This paper introduces a probabilistic model that is capable of diagnosing and classifying cognitive errors in a general problem-solving domain. The model is different from the usual deterministic strategies common in the area of artificial intelligence because item response theory is utilized to handle the variability of response errors. As for illustrating the model, the dataset obtained from a 38-item fraction addition test is used, and the students' responses are classified into 34 groups of misconceptions. These groups are predetermined by the result of an error analysis previously done, and validated with the error diagnostic program written by a typical formal logic approach.
An extension of a bivariate probit model is presented for bivariate polychotomous ordered categorical responses. A linear model is considered on the assumption that the observed categorical variables are manifestations of the latent continuous variables having bivariate normal distributions. Method of inference and analytical procedures are given on the basis of the maximum likelihood procedure. Various applications are discussed and illustrated with examples. The model can be applied to analysis of association, paired comparison, matched pair experiments, testing homogeneity of marginal distributions and symmetry of a square table, factorial analysis with bivariate ordered categorical responses, and so on.
For the multiple linear regression problem, a number of alternative estimators to ordinary least squares (OLS) have been proposed for situations in which multicollinearity is present among the explanatory variables. Multicollinearity may have several adverse effects on estimated coefficients in a multiple regression analysis. This paper investigates the relative efficiency of these 12 alternative estimators from the point of view of mean squared error (MSE) by the Monte Carlo simulation, and discusses the practical implication of the use of such estimators. The results of this study are that OLS, Ridges, BYS and ITR estimators are more efficient than the others, when multicollinearity is not present. However, when multicollinearity is present, Ridges, GRB, BYS, ITR and PCA estimators are more efficient than OLS for almost all values of σ. Ridges have uniformly smaller MSEs than OLS. Relative efficiencies of these estimators vary with the value of σ. In the interval of small σ, Ridges are more efficient than the others, but, for large σ, each of GRB, BYS, ITR, PCA and LAT is more efficient. From our experiment in which these 12 estimators are applied to the economic data of France, we find that, while OLS has the negative coefficient, some of these alternative have positive appropriate values, where regression coefficient must have the positive sign from the point of view of Economics. Therefore, we can conclude that these alternative estimators are effective for the practical regression problem with multicollinearity.