• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.585-594
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• 2003

It has been generally recognized that conventional binomial or Poisson model provides poor fits to the actual correlated binary data due to the extra-binomial variation. A number of generalized statistical models have been proposed to account for this additional variation. Among them, beta-binomial, correlated-binomial, and modified-binomial models are binomial-related models which are frequently used in modeling the sum of n correlated binary data. In many situations, it is reasonable to assume that n correlated binary data are exchangeable, which is a special case of correlated binary data. The sum of n exchangeable correlated binary data is modeled relatively well when the above three binomial-related models are applied. But the estimation results of correlation coefficient turn to be quite different. Hence, it is important to identify which model provides better estimates of model parameters(success probability, correlation coefficient). For this purpose, a small-scale simulation study is performed to compare the behavior of above three models.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.46
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• pp.127-136
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• 1998

In many cases where the binomial distribution fails to apply to real world data it is because of more variability in the data than can be explained by that distribution. Several authers have proposed models that are useful in explaining extra-binomial variation. In this paper we point out a characterization of sequences of exchangeable Bernoulli variables which can be used to develop models which show more variability than the binomial. We give sufficient conditions which will yield such models and show how existing models can be continued to generate further models. A numerical example and simulation given.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.809-817
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• 2012

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

• Journal of the Korean Institute of Landscape Architecture
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• v.22 no.3
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• pp.1-12
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• 1994

This study was carried out to identify destination choice behavior for one-day use recreation areas. Previous positioning study was utilized to select 4 study areas, and the secondary data were used for logit analyses. The Hausamn-McFadden test for IIA was conducted to examine whether conditional logit models are valid methodology for this study. The results revealed that IIA assumption among the study areas was violated; therefore, generalized binomial and generalized multinomial logit models were used in this study. In the binomial logit analysis, 2 to 5 independent variables were included in the models: their $\rho$2 values were from 0.1to 0.323, and accuracy of predictions were from 65.38 to 79.86 percent. In the multinomial logit analysis, 4 independent variables were included in the model: its $\rho$2 value was 0.207, and accuracy of prediction was 45.82 percent. The results showed that the conditional logit should be used with caution because of the IIA assumption. Several suggestions were described, mainly due to utilization of the secondary data for this study.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.507-516
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• 2011

Comparative studies on generalized binomial models (Moon, 2003; Ng, 1989; Paul, 1985; Kupper and Haseman, 1978; Griffiths, 1973) are restrictive in that the models compared are rather limited and MSE of the estimates is the only measure considered for the model adequacy. This paper is aimed to report simulation results which provide possible guidelines for selecting a proper model. We examine Pearson type of goodness-of-fit statistic to its degrees of freedom and AIC for the overall model quality. MSE and Bias of the individual estimates are also considered as the component fit measures. Performance of some models varies widely for a certain range of the parameter space while most of the models are quite competent. Our evaluation shows that the Extended Beta-Binomial model (Prentice, 1986) turns out to be particularly favorable in the point that it provides consistently excellent fit almost all over the values of the intra-class correlation coefficient and the probability of success.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.271-280
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• 2009

For bivariate binomial data with both intra and inter-class correlation, Danaher and Hardie (2005) proposed a bivariate beta-binomial model. However, the model is limited to the situation where the intra-class correlation is strictly positive. Thus it might be seriously inadequate for data with a negative intra-class correlation. Several authors have considered generalized binomial distributions covering a wider range of intra-class correlation which could relax the possible model restrictions imposed. Among others there are the additive/multiplicative and the beta/extended beta binomial model. In this study, bivariate models of the Sarmanov (1966) type are formed by combining each of those univariate models to take care of the inter-class correlation, and are evaluated in terms of the goodness-of-fit. As a result, B-mB and B-ebB are fitted, successfully, to real data and that B-mB, which has a wider permissible range than B-ebB for the intra-class correlation is relatively preferred.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.761-770
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• 2012

We frequently encounter outcomes of count that have extra variation. This paper considers several alternative models for overdispersed count responses such as a quasi-Poisson model, zero-inflated Poisson model and a negative binomial model with a special focus on a generalized linear mixed model. We also explain various goodness-of-fit criteria by discussing their appropriateness of applicability and cautions on misuses according to the patterns of response categories. The overdispersion models for counts data have been explained through two examples with different response patterns.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.829-843
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• 2010

To test for the serial dependence in time series of counts data, Jung and Tremayne (2003) evaluated the size and power of several tests under the class of INARMA models based on binomial thinning operations for Poisson marginal distributions. The overdispersion phenomenon(i.e., a variance greater than the expectation) is common in the real world. Overdispersed count data can be modeled by using alternative thinning operations such as random coefficient thinning, iterated thinning, and quasi-binomial thinning. Such thinning operations can lead to time series models of counts with negative binomial or generalized Poisson marginal distributions. This paper examines whether the test statistics used by Jung and Tremayne (2003) on serial dependence in time series of counts data are affected by overdispersion.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.61-70
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• 2018

Modeling of the random effects covariance matrix in generalized linear mixed models (GLMMs) is an issue in analysis of longitudinal categorical data because the covariance matrix can be high-dimensional and its estimate must satisfy positive-definiteness. To satisfy these constraints, we consider the autoregressive and moving average Cholesky decomposition (ARMACD) to model the covariance matrix. The ARMACD creates a more flexible decomposition of the covariance matrix that provides generalized autoregressive parameters, generalized moving average parameters, and innovation variances. In this paper, we analyze longitudinal count data with overdispersion using GLMMs. We propose negative binomial loglinear mixed models to analyze longitudinal count data and we also present modeling of the random effects covariance matrix using the ARMACD. Epilepsy data are analyzed using our proposed model.

• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.13-18
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• 2005

We explore the structure and usefulness of the 3-D residual plot as a basic tool for dealing with interaction in generalized linear models. If predictors have an interaction effect, the shape obtained by rotating the 3-D residual plot will show its presence. To illustrate the use of this plot as an aid to exploring the interaction, we present an example of a binomial regression model using simulated data.