• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.471-479
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• 2007

This paper discusses about how to build up mixed-effects model for analysing ordinal response data by using cumulative logits. Random factors are assumed to be coming from the designed sampling scheme for choosing observational units. Since the observed responses of individuals are ordinal, a proportional odds model with two random effects is suggested. Estimation procedure for the unknown parameters in a suggested model is also discussed by an illustrated example.

• East Asian mathematical journal
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• v.23 no.1
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• pp.111-122
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• 2007

In this paper, we will show some relations between decomposition series {${\nu}^{\alpha}\;:\;{\alpha}$ is an ordinal } and supratopological series {${\sigma}_{\alpha}{\nu}\;:\;{\alpha}$ is an ordinal} for a neighborhood structure $\nu$ and the formular ${\sigma}_{\alpha}{\nu}\;=\;{\nu}^{({\omega}^{\alpha})}$, where $\omega$ is the first limit ordinal.

• Journal of the Korean Data and Information Science Society
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• v.23 no.1
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• pp.209-218
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• 2012

The method of generalized estimating equations (GEEs) provides consistent esti- mates of the regression parameters in a marginal regression model for longitudinal data, even when the working correlation model is misspecified (Liang and Zeger, 1986). In this paper we compare the estimators of parameters in GEE approach. We consider two aspects: coverage probabilites and efficiency. We adopted to ordinal responses th results derived from binary outcomes.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.61 no.2
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• pp.67-73
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• 2012

This paper proposes optimal maintenance strategies for power distribution systems that involve the use of the reliability-centered maintenance (RCM) method. We developed an improved decision model based on the Markov process. This model can obtain the optimal inspection interval and maintenance method based on the total expected cost. We used ordinal optimization for solving the optimal problem. Optimal maintenance strategies were presented by applying the developed method to the RBTS model. A B/C analysis proved that these strategies offer maximum benefit-to-cost.

• ETRI Journal
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• v.32 no.3
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• pp.490-492
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• 2010

This letter proposes a robust feature extraction method using a spatially normalized mean for temporal ordinal measurement. Before computing a rank matrix from the mean values of non-overlapped blocks, each block mean is normalized so that it obeys the invariance property against linear additive and subtractive noise effects and is insensitive against multiplied and divided noise effects. Then, the temporal ordinal measures of spatially normalized mean values are computed for the feature matching. The performance of the proposed method showed about 95% accuracy in both precision and recall rates on various distortion environments, which represents the 2.7% higher performance on average compared to the temporal ordinal measurement.

• The Mathematical Education
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• v.20 no.1
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• pp.47-49
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• 1981

In this paper, we give several properties of ordinal spaces [0, $\Omega$] and [0, $\Omega$].

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.149-161
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• 2006

The most important component in decision tree algorithm is the rule for split variable selection. Many earlier algorithms such as CART and C4.5 use greedy search algorithm for variable selection. Recently, many methods were developed to cope with the weakness of greedy search algorithm. Most algorithms have different selection criteria depending on the type of variables: continuous or nominal. However, ordinal type variables are usually treated as continuous ones. This approach did not cause any trouble for the methods using greedy search algorithm. However, it may cause problems for the newer algorithms because they use statistical methods valid for continuous or nominal types only. In this paper, we propose a ordinal variable selection method that uses Cramer-von Mises testing procedure. We performed comparisons among CART, C4.5, QUEST, CRUISE, and the new method. It was shown that the new method has a good variable selection power for ordinal type variables.

• The Korean Journal of Applied Statistics
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• v.33 no.1
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• pp.25-46
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• 2020

This paper presents ordinal probit semiparametric regression models using Bayesian Spectral Analysis Regression (BSAR) method. Ordinal probit regression is a way of modeling ordinal responses - usually more than two categories - by connecting the probability of falling into each category explained by a combination of available covariates using a probit (an inverse function of normal cumulative distribution function) link. The Bayesian probit model facilitates posterior sampling by bringing a latent variable following normal distribution, therefore, the responses are categorized by the cut-off points according to values of latent variables. In this paper, we extend the latent variable approach to a semiparametric model for the Bayesian ordinal probit regression with nonparametric functions using a spectral representation of Gaussian processes based BSAR method. The latent variable is decomposed into a parametric component and a nonparametric component with or without a shape constraint for modeling ordinal responses and predicting outcomes more flexibly. We illustrate the proposed methods with simulation studies in comparison with existing methods and real data analysis applied to a Korean National Health and Nutrition Examination Survey (KNHANES) 2016 for investigating nonparametric relationship between smoking behavior and coffee intake.

• Journal of Korean Institute of Industrial Engineers
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• v.32 no.1
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• pp.18-28
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• 2006

Some issues which should be considered in an R&D project selection problem are as follows: First, quantitative analysis on the efficiencies of R&D projects is required to guarantee objective validity in the evaluation of the projects. For this reason, the methodology for selecting R&D projects should be based on mathematical models that perform quantitative analysis. Second, in general there are ordinal factors like Likert-scale in the data for evaluating R&D projects. Previous researches, however, couldn't suggest explicit methods incorporating these ordinal factors into models. Third, for the R&D project selection problems with limited resources like budget, it is necessary to decide the perfect ranking of the all projects. This paper develops a mathematical model that can be applicable to the problems of selecting R&D projects with the previous features. In this paper, we improve the original DEA model for evaluating efficiency to incorporate ordinal factors and suggest a new model which can decide the perfect ranking of all projects by merging the improved DEA model and AHP method. Furthermore a web-based R&D project selection system using the DEA/AHP model suggested in this paper is developed and illustrated.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.297-310
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• 2002

Liang and Zeger proposed generalized estimating equations(GEE) for analyzing repeated data which is discrete or continuous. GEE model can be extended to model for repeated categorical data and its estimator has asymptotic multivariate normal distribution in large sample sizes. But GEE is based on large sample asymptotic theory. In this paper, we study the properties of GEE estimators for repeated ordinal data in small sample sizes. We generate ordinal repeated measurements for two groups using two methods. Through Monte Carlo simulation studies we investigate the empirical type 1 error rates, powers, relative efficiencies of the GEE estimators, the effect of unequal sample size of two groups, and the performance of variance estimators for polytomous ordinal response variables, especially in small sample sizes.