• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.339-345
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• 2004

This paper deals with a mixed logit model for ordered polytomous data. There are two types of factors affecting the response varable in this paper. One is a fixed factor with finite quantitative levels and the other is a random factor coming from an experimental structure such as a randomized complete block design. It is discussed how to set up the model for analyzing ordered polytomous data and illustrated how to estimate the paramers in the given model.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.467-477
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• 2006

A multidimensionality detecting procedure DETECT, based on conditional covariances between items, is extended and refined to deal with polytomous item data as well as binary one. A large body of simulation study shows extraordinary performance of DETECT in both enumerating degrees of multidimensionality in a test and discovering dimensionally distinctive item clusters. Real data study also provides very meaningful results, making DETECT a strong dimensionality assessment tool for the test data analysis.

• Journal of the Korean Data and Information Science Society
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• v.19 no.2
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• pp.577-585
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• 2008

This paper suggests a marginal probability model for analyzing repeated polytomous response data when some factors are nested in others in treatment structures on a larger experimental unit. As a repeated measures factor, time is considered on a smaller experimental unit. So, two different experiment sizes are considered. Each size of experimental unit has its own design structure and treatment structure, and the marginal probability model can be constructed from the structures for each size of experimental unit. Weighted least squares(WLS) methods are used for estimating fixed effects in the suggested model.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.34 no.1
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• pp.42-51
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• 2011

Poisson model and Gamma-Poisson model are popularly used to analyze statistical behavior from defective data. The methods are based on binary criteria, that is, good or failure. However, manufacturing industries prefer polytomous criteria for classifying manufactured products due to flexibility of marketing. In this paper, I introduce two multivariate Gamma-Poisson(MGP) models and estimation methods of the parameters in the models, which are able to handle polytomous data. The models and estimators are verified on defective pixels of LCD manufacturing. Experimental results show that both the independent MGP model and the multinomial MGP model have excellent performance in terms of mean absolute deviation and the choice of method depends on the purpose of use.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.187-193
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• 2006

This paper shows how to use continuation-ratio logits for the analysis of structured polytomous data. Here, response categories are considered to have a nested binary structure. Thus, conditionally nested binary random variables can be defined in each step. Two types of factors are considered as independent variables affecting response probabilities. For the purpose of analyzing categorical data with binary nested strutures a continuation-ratio mixed model is suggested. Estimation procedure for the unknown parameters in a suggested model is also discussed in detail by an example.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.597-603
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• 2000

A versatile dimensionality assessment index DETECT has been developed for binary item response data by Kim (1994). The present paper extends the use of DETECT to the polytomously scored item data. A simulation study shows DETECT performs well in differentiating multidimensional data from unidimensional one by yielding a greater value of DETECT in the case of multidimensionality. An additional investigation is necessary for the dimensionally meaningful clustering methods, such as HAC for binary data, particularly sensitive to the polytomous data.

• Journal of the Korean Data and Information Science Society
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• v.19 no.3
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• pp.735-749
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• 2008

This article suggests application of logit model for analysis of multicategory responses. Referring to the reference category, characteristic of each category is obtained from analysis of polytomous logit model. With National Pension data it is illustrated that application of logit model helps it possible to find significant factors which may not be found only with polytomous logit model. Application of the logit model is done by reducing the number of categories. Categories are grouped into the former and the latter group according to reference category. Extra finding of significant factor was possible from logistic regression analysis for the two groups after removing the reference category. It is expected that this application would be helpful for finding information and characteristics on ordered multicategory responses where the proportional odds model does not fit.

• The Korean Journal of Applied Statistics
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• v.21 no.4
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• pp.621-630
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• 2008

This paper discusses how to construct a generalized marginal logit model for analyzing repeated polytomous response data when some factors are applied to larger experimental units as treatments and time to a smaller experimental unit as a repeated measures factor. So, two different experimental sizes are considered. Weighted least squares(WLS) methods are used for estimating fixed effects in the suggested model.

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.33-44
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• 2016

There are many situations that the outcome for clinical decision and credit assessment should be predicted more than two categories. Five kinds of statistics which are used the concordance are proposed and used for these polytomous problems. However, these statistics are defined without exact distinction of categories, so that we have difficulty to use both the pair and set approaches and it is hard to understand the meanings of these statistics. Hence, it is not possible to compare and analyze them. In this paper, the polytomous confusion matrix is standardized and the concordance statistic can be represented based on the confusion matrix. The five kinds of statistics by using the concordance are defined. With the methods proposed in this paper, we could not only explain their meanings but also compare and analyze these statistics. Based on various data sets, properties of these five statistics are explored and explained.

• The Korean Journal of Applied Statistics
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• v.9 no.1
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• pp.1-15
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• 1996

This paper discusses the effectiveness of an infection rate under a certain disease on an immunity rate by a protective inoculation. A sequence of dependense models concerning the infection rate is derived by defining conditionally nested binary random variables for the analysis of polytomous data with hierarchical response scale. Maximum likelihood estimates based on the marginal log-likelihood functin are obtained numerically in the Nelder and Mead's(1965) simplex method.