• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.1-14
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• 2020

Investigations of biosimilarity between reference drugs and test drugs required statistical tests; in addition, statistical tests to evaluate biosimilarity have been recently proposed. Ordinal outcome data has been observed in research; however, appropriate statistical tests to deal with ordinal endpoints for biosimilar have not yet been proposed. This paper extends existing design for ordinal endpoints. Using measure of nominal-ordinal association and relative distances between drugs are defined so that testing procedures are developed. Through simulation studies, we investigate type I error rate and power to show the performance of our suggested method. Furthermore, a comparison between the statistical tests and other designs is proviede to show significance of ordinal endpoints.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.330-333
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• 2006

Many practical problems of quality control in service management are derived from the use of ordinal variables. Ordered linguistic variables differ from measurement variables. This paper presents a new control chart of a production process based on ordinal variables.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.675-686
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• 2011

The aim of this paper is two fold: One of them is to introduce a formal definition of ordinals which is equivalent to Neumann's definition without assuming the axiom of regularity. The other is to introduce the weak transfinite set and show that the weak transfinite set is a transfinite limit ordinal.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.697-705
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• 2009

The Pearson chi-squared statistic or the deviance statistic is widely used in assessing the goodness-of-fit of the generalized linear models. But these statistics are not proper in the situation of continuous explanatory variables which results in the sparseness of cell frequencies. We propose a goodness-of-fit test statistic for the cumulative logit models with ordinal responses. We consider the grouping of a dataset based on the ordinal scores obtained by fitting the assumed model. We propose the Pearson chi-squared type test statistic, which is obtained from the cross-classified table formed by the subgroups of ordinal scores and the response categories. Because the limiting distribution of the chi-squared type statistic is intractable we suggest the parametric bootstrap testing procedure to approximate the distribution of the proposed test statistic.

• Asia pacific journal of information systems
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• v.20 no.2
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• pp.23-37
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• 2010

Conventional Support Vector Machines (SVMs) have been utilized as classifiers for binary classification problems. However, certain real world problems, including corporate bond rating, cannot be addressed by binary classifiers because these are multi-class problems. For this reason, numerous studies have attempted to transform the original SVM into a multiclass classifier. These studies, however, have only considered nominal classification problems. Thus, these approaches have been limited by the existence of multiclass classification problems where classes are not nominal but ordinal in real world, such as corporate bond rating and multiclass customer classification. In this study, we adopt a novel multiclass SVM which can address ordinal classification problems using ordinal pairwise partitioning (OPP). The proposed model in our study may use fewer classifiers, but it classifies more accurately because it considers the characteristics of the order of the classes. Although it can be applied to all kinds of ordinal multiclass classification problems, most prior studies have applied it to finance area like bond rating. Thus, this study applies it to a real world customer level classification case for implementing customer relationship management. The result shows that the ordinal multiclass SVM model may also be effective for customer level classification.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.711-720
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• 2000

A case study of modeling ordinal categorical response data with the MARS method is done. The study is to analyze the effect of some personal characteristics and socioeconomic status on the teenage marijuana use. The MARS method gave a new insight into the data set.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.49-63
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• 2023

A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-R², a better option than many other measures. We propose a simple modification of the LRI that adjusts for the effect of the number of response categories on the measure and that also rescales its values, mimicking an underlying latent measure. The modified measure is applicable to both binary and ordinal response models fitted by maximum likelihood. Results from simulation studies and a real data example on the olfactory perception of boar taint show that the proposed measure outperforms most of the widely used goodness-of-fit measures for binary and ordinal models. The proposed R² interestingly proves quite invariant to an increasing number of response categories of an ordinal model.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1057-1065
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• 2010

In this paper we discuss some cautionary notes in using the Pearson chi-squared test statistic for the goodness-of-fit of the ordinal response model. If a model includes continuous type explanatory variables, the resulting table from the t of a model is not a regular one in the sense that the cell boundaries are not fixed but randomly determined by some other criteria. The chi-squared statistic from this kind of table does not have a limiting chi-square distribution in general and we need to be very cautious of the use of a chi-squared type goodness-of-t test. We also study the limiting distribution of the chi-squared type statistic for testing the goodness-of-t of cumulative logit models with ordinal responses. The regularity conditions necessary to the limiting distribution will be reformulated in the framework of the cumulative logit model by modifying those of Moore and Spruill (1975). Due to the complex limiting distribution, a parametric bootstrap testing procedure is a good alternative and we explained the suggested method through a practical example of an ordinal response dataset.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1465-1475
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• 2013

The chi-square type test statistic is the most commonly used test in terms of measuring testing goodness-of-fit for multinomial logistic regression model, which has its grouped data (binomial data) and ungrouped (binary) data classified by a covariate pattern. Chi-square type statistic is not a satisfactory gauge, however, because the ungrouped Pearson chi-square statistic does not adhere well to the chi-square statistic and the ungrouped Pearson chi-square statistic is also not a satisfactory form of measurement in itself. Currently, goodness-of-fit in the ordinal setting is often assessed using the Pearson chi-square statistic and deviance tests. These tests involve creating a contingency table in which rows consist of all possible cross-classifications of the model covariates, and columns consist of the levels of the ordinal response. I examined goodness-of-fit tests for a proportional odds logistic regression model-the most commonly used regression model for an ordinal response variable. Using a simulation study, I investigated the distribution and power properties of this test and compared these with those of three other goodness-of-fit tests. The new test had lower power than the existing tests; however, it was able to detect a greater number of the different types of lack of fit considered in this study. I illustrated the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents.

• East Asian mathematical journal
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• v.22 no.1
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• pp.79-91
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• 2006

In this paper, we will show some relations between decomposition series {$\pi^{\alpha}q\;:\;{\alpha}$ is an ordinal} and topological series {$\tau_{\alpha}q\;:\;{\alpha}$ is an ordinal} for a convergence structure q and the formular ${\pi}^{\beta}(\tau_{\alpha}q)={\pi}^{{\omega^{\alpha}\beta}}q$, where $\omega$ is the first limit ordinal and $\alpha$ and $\beta({\geq}1)$ are ordinals.