To evaluate relationship between response observed on some ordered categories and associated explanatory variables, we consider log-gamma regression model. First, we provide inference under the log-gamma regression model and selection of special nested models included in the model. Next, we evaluate some relative performance of the log-gamma regression model to asymmetric power transformation models and examine usefulness of this model using several examples cited from some literatures.
In this paper Fisher's linear discriminant function is investigated in which some data move from one to the other of two populations in the process of time. Utilizing the model for such kind of data, the mean vectors, common covariance matrix, discriminant coefficient vector, and cutting point are derived for each time. Two theorems for the coefficient vector and cutting point are obtained and certain numerical results for them are presented. From these theorems and numerical results, it is shown that if the data which change populations are close to the boundary of the end population, they do not greatly affect the coefficient vector and cutting point. Lastly, we show the example of prevention of geriatric diseases and discuss the coefficient vector and cutting point.
Two types of measures(direct and indirect measures)are defined to assess the closeness between a given vector and an eigenvector of a certain positive definite matrix. By using some results of multivariate distribution theory it is shown that the indirect measure is the reasonable one. From the viewpoint of the closeness of eigenvectors we deal with the following two problems in principal component analysis: Does a given vector approximate the coefficient vector of some principal component?; How many principal components should be taken into account?
Six topics are discussed in this paper concerning to selection as a process of decisionmaking.(1)How can the ability dimension underlying selection be defined?(2)How can institutions adapt their treatments to their accepted applicants?(3)Is it fair to selet applicants without any consideration to length of study after highschool graduation?(4)What is the best strategy for competitve selection?(5)How can institutions develop their own selection scales which measure abilities indepen dent to each other?(6)What is the task and role of common scale of achievement measurement?
Some problems in mathematical formulation of university entrance examinations are discussed. An entrance examination can be regarded as an measurement of student's intelligence or “ability” and an error involved in it is treated. Various proposals to improve the accuracy of examination are discussed.
The entrance examinations of national and local public universities have been conducted as pair of the Joint Achievement Test(JAT)and respective test of each university since 1979. An example of statistical analysis aiming to assist the improvement of these tests is given for each constituent test of the pair. In the first place an estimation of differences in difficulties of JAT between alternative subjects by a generalized two-factorial linear model is discussed. Secondly, a linear discrimination of the admitted against the rejected is introduced. Some results of these analyses along with their evaluation are also shown.
“To hire or not to hire” To answer this question depends on the applicants' aptitude, or the quality as a member of a Japanese family-like business corporation. In the employee selection, psychological tests help for the understanding of the applicants' personalities. Psychological tests are not expected to be the tools for estimation of the aptitude for a specific job, such as clerical work, sales engineering, etc. Rather, they are used for better understanding of the applicants'total quality as a business person or an engineer. As a selection tool, psychological tests should be well constructed so as to make applicants feel that they are fairly treated. Psychological tests have been considered as more fair and efficient than other methods like oral examination or interview. And thus, they have taken a dominant role in the employee selection in Japanese business industry.
This paper is a report on the history of entrance examinations for national public service, from 1949 to the present. Examinations for public service in Japan are aimed at appointing new graduates in the given year. An examination consists of a written test and an oral interview which is designed to evaluate whether applicants have the appropriate quality. The competency of the applicants are also evaluated in terms of the potentiality of their career promotion.The method of the written examinations is considered to be adequate, although the method for administering the oral interview needs some inprovement.