• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.1-8
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• 2004

We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Robin (1974), is extended to a more general case of non-monotone missing data. The proposed method is algebraically equivalent to the Newton-Raphson method for the observed likelihood, but avoids the burden of computing the first and the second partial derivatives of the observed likelihood Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method. A numerical example is also presented to illustrate the method.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.1254-1259
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• 2009

과거 관측된 수문자료는 분석을 통해 다양한 수문모형의 평가 및 예측과 수자원 정책결정에서 활용된다. 하지만 관측장비의 오작동 및 관측범위의 한계에 의해 수집된 자료에는 결측이 존재한다. 단순히 결측이 존재하는 벡터를 제외하거나, 결측이 존재하는 자료 구간에 선형성이 존재한다는 가정 하에 평균을 활용하기도 했으나, 이로 인하여 자료의 통계특성에 왜곡이 야기될 수 있다. 본 연구는 결측의 보정으로 자료가 보유하는 정보의 손실 및 왜곡을 최소화 할 수 있는 방안을 연구하고자 한다. 자료의 결측은 크게 완벽한 무작위 결측(missing completely at random, MCAR), 무작위 결측(missing at random, MAR), 무작위성이 없는 결측(nonrandom missingness)으로 분류되며, 수문자료는 결측을 포함한 기간이 그 외 기간의 자료와 통계적으로 동일하지는 않지만 결측자료의 추정이 가능한 MAR에 속하는 것이 일반적이므로 이를 가정으로 결측을 보정하였다. Local Lest Squares Imputation(LLSimput)을 결측의 추정을 위해 사용하였으며, 기존에 쉽게 사용되던 선형보간법과 비교하였다. 적용성 평가를 위해 소양강댐 일 유입량 자료에 1 - 5 %의 결측자료를 임의로 생성하였다. 동일한 양의 결측자료에 대해 100개의 셋을 사용하여 보정의 불확실성 범위를 적용된 방법에 대해 비교..평가하였으며, 결측 증가에 따른 보정효과의 변화를 검토하였다. Normalized Root Mean Squared Error(NRMSE)를 사용하여 적용된 두 방법을 평가한 결과, (1) 결측자료의 비가 낮을수록 간단한 선형보간법을 사용한 보정이 효과적이었다. (2) 하지만 결측의 비가 증가할수록 선형보간법의 보정효과는 점차 큰 불확실성과 낮은 보정효과를 보인 반면, (3) LLSimpute는 결측의 증가에 관계없이 일정한 보정효과 및 불확실성 범위를 나타내는 것으로 드러났다.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.425-433
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• 2011

Reject inference in credit scoring is a statistical approach to adjust for nonrandom sample bias due to rejected applicants. Function estimation approaches are based on the assumption that rejected applicants are not necessary to be included in the estimation, when the missing data mechanism is missing at random. On the other hand, the density estimation approach by using mixture models indicates that reject inference should include rejected applicants in the model. When mixture models are chosen for reject inference, it is often assumed that data follow a normal distribution. If data include missing values, an application of the normal mixture model to fully observed cases may cause another sample bias due to missing values. We extend reject inference by a multivariate normal mixture model to handle incomplete characteristic variables. A simulation study shows that inclusion of incomplete characteristic variables outperforms the function estimation approaches.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.493-505
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• 1997

The analysis of binary data appears to many areas such as statistics, biometrics and econometrics. In many cases, data are often collected in which some observations are incomplete. Assume that the missing covariates are missing at random and the responses are completely observed. A method to Bayesian analysis of the binary regression model with incomplete data is presented. In particular, the desired marginal posterior moments of regression parameter are obtained using Meterpolis algorithm (Metropolis et al. 1953) within Gibbs sampler (Gelfand and Smith, 1990). Also, we compare logit model with probit model using Bayes factor which is approximated by importance sampling method. One example is presented.

• Communications for Statistical Applications and Methods
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• v.29 no.5
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• pp.561-589
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• 2022

When multiple classifications and regression trees are combined, tree-based ensemble models, such as random forest (RF) and Bayesian additive regression trees (BART), are produced. We compare the model structures and performances of various ensemble models for regression settings in this study. RF learns bootstrapped samples and selects a splitting variable from predictors gathered at each node. The BART model is specified as the sum of trees and is calculated using the Bayesian backfitting algorithm. Throughout the extensive simulation studies, the strengths and drawbacks of the two methods in the presence of missing data, high-dimensional data, or highly correlated data are investigated. In the presence of missing data, BART performs well in general, whereas RF provides adequate coverage. The BART outperforms in high dimensional, highly correlated data. However, in all of the scenarios considered, the RF has a shorter computation time. The performance of the two methods is also compared using two real data sets that represent the aforementioned situations, and the same conclusion is reached.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1211-1218
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• 2008

Maximum likelihood estimator (MLE) and restricted maximum likelihood estimator (REMLE) approaches are available in analyzing the linear mixed model (LMM) like bioequivalence trials. US FDA (2001) guides that REMLE may be useful to assess bioequivalence (BE) test. This paper studies the statistical behaviors of the methods in assessing BE tests when some of observations are missing at random. The simulation results show that the REMLE maintains the given nominal level well and the MLE gives a bit higher power. Considering the levels and the powers, the REMLE approach is recommended when the sample sizes are small to moderate and the MLE approach should be used when the sample size is greater than 30.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.355-368
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• 2023

This article introduces the R package ELCIC (https://cran.r-project.org/web/packages/ELCIC/index.html), which provides an empirical likelihood-based information criterion (ELCIC) for model selection that includes, but is not limited to, variable selection. The empirical likelihood is a semi-parametric approach to draw statistical inference that does not require distribution assumptions for data generation. Therefore, ELCIC is more robust and versatile in the context of model selection compared to the currently existing information criteria. This paper illustrates several applications of ELCIC, including its use in generalized linear models, generalized estimating equations (GEE) for longitudinal data, and weighted GEE (WGEE) for missing longitudinal data under the mechanisms of missing at random and dropout.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1439-1447
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• 2014

Most of literatures on Korean child aggression are based on using the cross-sectional data sets. Although there is a related study with a longitudinal data set, it is assumed that the data sets measured repeatedly in the longitudinal data are mutually independent. A longitudinal data analysis for Korean child aggression is then necessary. This study is to analyze the effect of child development outcomes including academic achievement, self-esteem, depression anxiety, delinquency, victimization by peers, abuse by parents and internet using time on child aggression with Korea Welfare Panel Study data observed three times between 2006 and 2012. Since Korea Welfare Panel Study data have missing values, the missing at random is assumed. The linear mixed effect model and the restricted maximum likelihood estimation are considered.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1347-1359
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• 2016

Finite mixtures of regression models provide an effective tool to explore a hidden functional relationship between a response variable and covariates. However, it is common in practice that data are not fully observed due to several reasons. In this paper, we derived an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimator when some covariates are missing at random in the finite mixture of regression models. We conduct some simulation studies and we also provide some real data examples to show the validity of the derived EM algorithm.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.1-10
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• 2017

Longitudinal data of Korean child academic achievement have been used to find the significant exploratory variables under the assumption of independent repeated measured data. Using the exploratory variables in previous research works, we analyze the linear mixed model incorporating the fixed and random effects for child academic achievement to detect the significant exploratory variables. Korea welfare panel study data observed three times between 2006 and 2012 by additional survey for children. The child academic achievement is evaluated by the sum of academic achievements of Korean, English and Mathematics. We also investigate the multicollinearity and the missing mechanism and select some popular correlation matrices to analyze the linear mixed model.