• Genomics & Informatics
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• v.20 no.4
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• pp.48.1-48.7
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• 2022

Penalized regression has been widely used in genome-wide association studies for joint analyses to find genetic associations. Among penalized regression models, the least absolute shrinkage and selection operator (Lasso) method effectively removes some coefficients from the model by shrinking them to zero. To handle group structures, such as genes and pathways, several modified Lasso penalties have been proposed, including group Lasso and sparse group Lasso. Group Lasso ensures sparsity at the level of pre-defined groups, eliminating unimportant groups. Sparse group Lasso performs group selection as in group Lasso, but also performs individual selection as in Lasso. While these sparse methods are useful in high-dimensional genetic studies, interpreting the results with many groups and coefficients is not straightforward. Lasso's results are often expressed as trace plots of regression coefficients. However, few studies have explored the systematic visualization of group information. In this study, we propose a multi-level polar Lasso (MP-Lasso) chart, which can effectively represent the results from group Lasso and sparse group Lasso analyses. An R package to draw MP-Lasso charts was developed. Through a real-world genetic data application, we demonstrated that our MP-Lasso chart package effectively visualizes the results of Lasso, group Lasso, and sparse group Lasso.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.965-976
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• 2015

Determining relevant variables for a regression model is important in regression analysis. Recently, a variable selection methods using a penalized likelihood with various penalty functions (e.g. LASSO and SCAD) have been widely studied in simple statistical models such as linear models and generalized linear models. The advantage of these methods is that they select important variables and estimate regression coefficients, simultaneously; therefore, they delete insignificant variables by estimating their coefficients as zero. We study how to select proper variables based on penalized hierarchical likelihood (HL) in semi-parametric frailty models that allow three penalty functions, LASSO, SCAD and HL. For the variable selection we develop a new function in the "frailtyHL" R package. Our methods are illustrated with breast cancer survival data from the Medical Center at Chonnam National University in Korea. We compare the results from three variable-selection methods and discuss advantages and disadvantages.

• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.125-133
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• 2013

In this paper, penalized binary logistic regression models are employed as statistical models for determining the discharge of 668 patients with a chief complaint of dyspnea based on 11 blood tests results. Specifically, the ridge model based on $L^2$ penalty and the Lasso model based on $L^1$ penalty are considered in this paper. In the comparison of prediction accuracy, our models are compared with the logistic regression models with all 11 explanatory variables and the selected variables by variable selection method. The results show that the prediction accuracy of the ridge logistic regression model is the best among 4 models based on 10-fold cross-validation.

• Genomics & Informatics
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• v.14 no.4
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• pp.138-148
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• 2016

The success of genome-wide association studies (GWASs) has enabled us to improve risk assessment and provide novel genetic variants for diagnosis, prevention, and treatment. However, most variants discovered by GWASs have been reported to have very small effect sizes on complex human diseases, which has been a big hurdle in building risk prediction models. Recently, many statistical approaches based on penalized regression have been developed to solve the "large p and small n" problem. In this report, we evaluated the performance of several statistical methods for predicting a binary trait: stepwise logistic regression (SLR), least absolute shrinkage and selection operator (LASSO), and Elastic-Net (EN). We first built a prediction model by combining variable selection and prediction methods for type 2 diabetes using Affymetrix Genome-Wide Human SNP Array 5.0 from the Korean Association Resource project. We assessed the risk prediction performance using area under the receiver operating characteristic curve (AUC) for the internal and external validation datasets. In the internal validation, SLR-LASSO and SLR-EN tended to yield more accurate predictions than other combinations. During the external validation, the SLR-SLR and SLR-EN combinations achieved the highest AUC of 0.726. We propose these combinations as a potentially powerful risk prediction model for type 2 diabetes.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1213-1224
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• 2011

In high dimensionality where the number of variables are excessively larger than observations, it is required to remove the noninformative variables to cluster observations. Most model-based approaches for variable selection have been considered under the assumption of homoscedasticity and their models are mainly estimated by a penalized likelihood method. In this paper, a different approach is proposed to remove the noninformative variables effectively and to cluster based on the modified normal mixture model simultaneously. The validity of the model was provided and an EM algorithm was derived to estimate the parameters. Simulation studies and an experiment using real microarray dataset showed the effectiveness of the proposed method.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.1025-1036
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• 2003

Variable selection algorithm for principal component analysis using penalty function is proposed. We use the fact that usual principal component problem can be expressed as a maximization problem with appropriate constraints and we will add penalty function to this maximization problem. Simulated annealing algorithm is used in searching for optimal solutions with penalty functions. Comparisons between several well-known penalty functions through simulation reveals that the HARD penalty function should be suggested as the best one in several aspects. Illustrations with real and simulated examples are provided.

• Communications for Statistical Applications and Methods
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• v.22 no.2
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• pp.173-180
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• 2015

We propose a selection procedure of principal components in principal component regression. Our method selects principal components using variable selection procedures instead of a small subset of major principal components in principal component regression. Our procedure consists of two steps to improve estimation and prediction. First, we reduce the number of principal components using the conventional principal component regression to yield the set of candidate principal components and then select principal components among the candidate set using sparse regression techniques. The performance of our proposals is demonstrated numerically and compared with the typical dimension reduction approaches (including principal component regression and partial least square regression) using synthetic and real datasets.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.359-370
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• 2019

Grouping structures in covariates are often ignored in regression models. Recent statistical developments considering grouping structure shows clear advantages; however, reflecting the grouping structure on the quantile regression model has been relatively rare in the literature. Treating the grouping structure is usually conducted by employing a group penalty. In this work, we explore the idea of group penalty to the quantile regression models. The grouping structure is assumed to be known, which is commonly true for some cases. For example, group of dummy variables transformed from one categorical variable can be regarded as one group of covariates. We examine the group quantile regression models via two real data analyses and simulation studies that reveal the beneficial performance of group quantile regression models to the non-group version methods if there exists grouping structures among variables.

• The Korean Journal of Applied Statistics
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• v.37 no.1
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• pp.1-12
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• 2024

In many real-world data, multiple response variables are often dependent on the same set of explanatory variables. In particular, if several response variables are correlated with each other, simultaneous estimation considering the correlation between response variables might be more effective way than individual analysis by each response variable. In this multivariate regression analysis, least distance estimator (LDE) can estimate the regression coefficients simultaneously to minimize the distance between each training data and the estimates in a multidimensional Euclidean space. It provides a robustness for the outliers as well. In this paper, we examine the least distance estimation method in multivariate linear regression analysis, and furthermore, we present the penalized least distance estimator (PLDE) for efficient variable selection. The LDE technique applied with the adaptive group LASSO penalty term (AGLDE) is proposed in this study which can reflect the correlation between response variables in the model and can efficiently select variables according to the importance of explanatory variables. The validity of the proposed method was confirmed through simulations and real data analysis.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.771-783
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• 2018

The life insurance industry is interested in various factors that influence the long-term extensions of insurance contracts such as the necessity for the advisors' long-term management of consumers, product consulting, and improvement of the investment aspects. This paper investigates important factors leading to a long-term contract that forms an important part of the life insurance industry in Korea. For this purpose we used the data of contents (i.e., data from Jan 1, 2011 to Dec 31, 2016) of the contracts of xxx insurance company. In this paper, we present how to select important variables to influence the duration of the contract maintenance via a penalized Cox's proportional hazards (PH) modelling approach using insurance life data. As the result of analysis, we found that the selected important factors were the advisor's status, the reward type 2 (annuity insurance) and tendency 4 (safety-pursuing type).