• Communications for Statistical Applications and Methods
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• 제7권3호
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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.

• Journal of the Korean Data and Information Science Society
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• 제24권6호
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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.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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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.

• Communications for Statistical Applications and Methods
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• 제27권1호
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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.

• Journal of the Korean Data and Information Science Society
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• 제23권1호
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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.

• Communications for Statistical Applications and Methods
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• 제30권1호
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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.

• 응용통계연구
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• 제15권2호
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• pp.297-310
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• 2002

Liang과 Zeger는 이산형 혹은 연속형 반복측정자료를 분석하기 위한 일반화 추정방정식 (GEE)을 제안하였다 GEE모형은 범주형 반복측정자료의 모형으로 확장될 수 있으며, 이 GEE추정량은 대표본인 경우 다변량 정규분포를 따른다. 그러나 GEE는 대표본근사이론에 기초한다. 본 논문에서는 소표본인 경우 반복 측정된 순서자료에 대한 GEE추정량의 성질을 연구한다. 우리는 두가지 방법을 사용하여 두그룹의 반복 측정된 순서자료를 생성하며 모의실험을 통하여 소표본인 경우 여러 개 범주를 갖는 순서반응 자료에 대하여 GEE추정량의 1종 오류율, 검정력, 상대효율, 두 그룹의 표본크기가 다를 경우 효과, 그리고 분산 추정량의 성질등을 연구한다.

• 대한안전경영과학회지
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• 제9권2호
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• pp.161-169
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• 2007

This paper presents three methods for expression of reliability measures for large and small data. First method is to express parametric estimation of cardinal reliability measure data for large sample, which requires numerous sample. Second is to obtain nonparametric distribution classification of ordinal reliability measure data for small sample. However it is difficult for field user to understand this method. Last method is to acquire parametric estimation of ordinal reliability measure data for small data. Because this method requires small sample and is comprehensive, we recommend this one among the proposed methods. Various reliability rank measures are presented.

• 응용통계연구
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• 제23권6호
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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.

• 품질경영학회지
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• 제30권3호
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• pp.38-52
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• 2002

This paper is concerned with the analysis of structural equation model(SEM) with the ordinal data such as Likert scale. The SEM is misused when the arbitrary scores allocated to the Likert scale are treated as quantitative data. The underlying distribution approaches have been studied to solve this problem, and the partial least squares(PLS) Is also tried. In this paper the quantification methods for the Likert scale are proposed to analyze the SEM. We assume that the Likert scale is an observation of the interval of the continuous underlying distribution, and the respondents have their own patterns in the response of some questions. Normal and beta distributions as the response patterns are considered to quantify the Likert scale. To compare the efficiency of the proposed method the bootstrap simulations are tried.