• 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.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1073-1084
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• 2009

For ordinal categorical $R{\times}R$ tables, a weighted measure of association, $H_{\omega}$, was proposed and its maximum likelihood estimator and asymptotic variance were drived. We redefined the last paradox of ${\kappa}$ and proved its relation to marginal distributions. We also introduced the new paradox of ${\kappa}$ and summaried the general relationships between ${\kappa}$ and marginal distributions.

• 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.

• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.363-376
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• 2012

Excessive zeroes are often observed in ordinal categorical response variables. An ordinary ordered Probit model is not appropriate for zero-inflated data especially when there are many different sources of generating 0 observations. In this paper, we apply a two-stage zero-inflated ordered Probit (ZIOP) model which incorporate the zero-flated nature of data, propose a Bayesian analysis of a ZIOP model, and apply the method to alcohol consumption data collected by the National Bureau of Statistics, Korea. In the first stage of a ZIOP model, a Probit model is introduced to divide the non-drinkers into genuine non-drinkers who do not participate in drinking due to personal beliefs or permanent health problems and potential drinkers who did not drink at the time of the survey but have the potential to become drinkers. In the second stage, an ordered probit model is applied to drinkers that consists of zero-consumption potential drinkers and positive consumption drinkers. The analysis results show that about 30% of non-drinkers are genuine non-drinkers and hence the Korean alcohol consumption data has the feature of zero-inflated data. A study on the marginal effect of each explanatory variable shows that certain explanatory variables have effects on the genuine non-drinkers and potential drinkers in opposite directions, which may not be detected by an ordered Probit model.