A new seven-parameter nonlinear growth model has been introduced and applied to the longitudinal growth data of height. This newly proposed growth model is compared with the modified Count-Gompertz growth model and the Jolicoeur et al. growth model based upon the longitudinal data of height of 365 Japanese females. The proposed growth model is better than these two growth models from viewpoints of residuals and AIC. The growth analysis system GAS is used which contains the estimation of the growth parameters of nonlinear growth models and the standard analysis of growth parameters.
Key words: GAS, Growth model, Height, Nonlinear regression, Velocity curveThe analysis of repeated measurements is studied on the situation where there are some outliers which deviate so much from the other data as to arouse suspicions that they were generated by different mechanisms. In these case, if we use distributions which are heavy-tailed relative to the normal distribution as the assumed error distributions, the estimates might be less affected by outliers. From this point of view, we assume scale mixtures of multivariate normal distributions as the error distributions. Also, we consider the case with missing observation and propose a method to obtain the maximum likelihood estimates by applying the EM algorithm. Model selection by AIC and detection of outliers are also discussed with the aid of real data.
Key words: Analysis of repeated measurements, EM algorithm, Outlier, Scale mixtures of normal distributionsEfficient and manipulative data analysis systems that can be utilized by non-statisticians, have begun to arouse considerable attention with the popularization of the computer and/or data analysis. Today, those systems are usually manipulated by utilizing command or menu on the display. Such useful methods have been developed with the advance of the study on user interface. One of the most attractive methods utilizes the graphics. Further, visual languages have been studied in the field of the information engineering. The concept of the visual languages is applied to the field of the data analysis and we get a view of visual data analysis. We have developed a data analysis system on a micro, equiped facilities that make possible the visual manipulations. This system deals with various matters arisen in the process of data analysis by independent programs. We introduce the system itself and its interface with the process.
Key words: Data analysis system, Visual languages, User interface, GraphicsProcedures to determine the type of the extreme value distribution that attracts the population distribution from a random sample are considered. Simple test procedures based on the Weissman's theorem (1978) are proposed. The mis-decision rates of the proposed procedures are examined by means of Monte Carlo simulation and performances of the procedures are evaluated by applying them to practical data and then campared to those of an ordinary method by Castillo et al.(1989). As a result, it is found that performances of the proposed procedures are as good as those of the ordinary method.
Key words: Extreme value distribution, Domain of attraction, Test of hypothesisWe demonstrate delicate but important differences between two types of transformation. The first transformation is by a link function which transforms expectations of observations to their linear predictors in context of the generalized linear model. The second is common transformation of observations themselves, such as Box-Cox's one. We can combine these two types of transformation into a double transformation model. Through the extended model we check which type of transformation is appropriate to several sets of practical data.
Key words: Transformation, Generalized linear model, Box-Cox transformation, Statistical diagnosisThe generalized linear models (in short GLM) proposed by Nelder and Wedderburn (1972) are generalization of classical linear model and include logistic linear model for proportions and log linear model for counts as typical examples. It seems that the success of GLM depends greatly on the fact that the theoretical and computational difficulties they caused are trivial relative to the generosity they gained. The notion of the quasi-likelihood proposed by Wedderburn(1974) has enlarged the applicability of GLM, thus, they have been extended in an analogous way as classical linear model and many techniques which are usefull in classical linear model have been adapted. In GLM, however, the results are less rigorous and less explicit. We can explain this problem as one of residual; there is no quantity which is comparable to the residual in classical linear model. In this paper, we intend to clarify the issues comparing Pearson chi-squared statistic with deviance.
Key words: Generalized linear models, Quasi-likelihood, Extended quasilikelihood, Diagnostics, Pearson chi-squared statistic, Deviance