• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.191-202
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• 2024

The goal of this paper is to show how multivariate regression analysis with high-dimensional responses is facilitated by the response dimension reduction. Multivariate regression, characterized by multi-dimensional response variables, is increasingly prevalent across diverse fields such as repeated measures, longitudinal studies, and functional data analysis. One of the key challenges in analyzing such data is managing the response dimensions, which can complicate the analysis due to an exponential increase in the number of parameters. Although response dimension reduction methods are developed, there is no practically useful illustration for various types of data such as so-called large p-small n data. This paper aims to fill this gap by showcasing how response dimension reduction can enhance the analysis of high-dimensional response data, thereby providing significant assistance to statistical practitioners and contributing to advancements in multiple scientific domains.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.205-215
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• 2021

Sufficient dimension reduction is useful dimension reduction tool in regression, and sliced inverse regression (Li, 1991) is one of the most popular sufficient dimension reduction methodologies. In spite of its popularity, it is known to be sensitive to the number of slices. To overcome this shortcoming, the so-called fused sliced inverse regression is proposed by Cook and Zhang (2014). Unfortunately, the two existing methods do not have the direction application to large p-small n regression, in which the dimension reduction is desperately needed. In this paper, we newly propose seeded sliced inverse regression and seeded fused sliced inverse regression to overcome this deficit by adopting iterative projection approach (Cook et al., 2007). Numerical studies are presented to study their asymptotic estimation behaviors, and real data analysis confirms their practical usefulness in high-dimensional data analysis.

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.537-546
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• 2012

In this paper, for analyzing binary data, Poisson regression with offset and logistic regression are compared with respect to the power via simulations. Poisson distribution can be used as an approximation of binomial distribution when n is large and p is small; however, we investigate if the same conditions can be held for the power of significant tests between logistic regression and offset poisson regression. The result is that when offset size is large for rare events offset poisson regression has a similar power to logistic regression, but it has an acceptable power even with a moderate prevalence rate. However, with a small offset size (< 10), offset poisson regression should be used with caution for rare events or common events. These results would be good guidelines for users who want to use offset poisson regression models for binary data.

• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.235-243
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• 2018

Many studies exist on the influence of one or few observations on estimators in a variety of statistical models under the "large n, small p" setup; however, diagnostic issues in the regression models have been rarely studied in a high dimensional setup. In the high dimensional data, the influence of observations is more serious because the sample size n is significantly less than the number variables p. Here, we investigate the influence of observations on the least absolute shrinkage and selection operator (LASSO) estimates, suggested by Tibshirani (Journal of the Royal Statistical Society, Series B, 73, 273-282, 1996), and the influence of observations on selected variables by the LASSO in the high dimensional setup. We also derived an analytic expression for the influence of the k observation on LASSO estimates in simple linear regression. Numerical studies based on artificial data and real data are done for illustration. Numerical results showed that the influence of observations on the LASSO estimates and the selected variables by the LASSO in the high dimensional setup is more severe than that in the usual "large n, small p" setup.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.553-562
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• 2021

Directional regression (DR; Li and Wang, 2007) is well-known as an exhaustive sufficient dimension reduction method, and performs well in complex regression models to have linear and nonlinear trends. However, the extension of DR is not well-done upto date, so we will extend DR to accommodate multivariate regression and large p-small n regression. We propose three versions of DR for multivariate regression and discuss how DR is applicable for the latter regression case. Numerical studies confirm that DR is robust to the number of clusters and the choice of hierarchical-clustering or pooled DR.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.835-842
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• 2018

The so-called sliced average variance estimation (SAVE) is a popular methodology in sufficient dimension reduction literature. SAVE is sensitive to the number of slices in practice. To overcome this, a fused SAVE (FSAVE) is recently proposed by combining the kernel matrices obtained from various numbers of slices. In the paper, we consider practical applications of FSAVE to large p-small n data. For this, near-infrared spectroscopy of biscuit dough data is analyzed. In this case study, the usefulness of FSAVE in high-dimensional data analysis is confirmed by showing that the result by FASVE is superior to existing analysis results.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.105-117
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• 2016

In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central $k^{th}$-moment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.

• Asian-Australasian Journal of Animal Sciences
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• v.22 no.5
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• pp.667-673
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• 2009

Ninety six intact male sheep (12 months old with mean live weight of about 35 kg) were used to assess the effects of restricted feeding on intake, digestion, nitrogen balance and metabolizable energy (ME). The animals were selected from two known Iranian small and large body size breeds: 48 Sangsari (S) and 48 Afshari (A), and were divided into two equal groups: restricted (R) and a control (C). Each group had 48 sheep (24 each breed). The experiment had a duration of 15 and 75 days adaptation and treatment periods, respectively. The animals were individually placed in metabolism cages and fed a diet based on pelleted concentrate mixture consisting of alfalfa, barley grain, cottonseed meal and barley straw. The animals in group C were fed ad libitum, while animals in group R were fed at maintenance level and maintained a relatively constant live weight. During the experiment, the average daily weight gain (ADG) of S and A animals in R group was 0.34 and -0.25 g/d (0.02 and -0.02 $g/kg^{0.75}/d$), respectively. While that of S and A animals in C group was 174.4 and 194.4 g/d (10.16 and 11.48 $g/kg^{0.75}/d$), respectively. Nitrogen (N) was determined by both measured and regression methods. Animals of R group stayed at about zero N balance (0.01 and -0.00 g $N/kg^{0.75}/d$ for S and A animals, respectively). The N retention of animals of both S and A breeds in C group were similar (0.45 and 0.46 g $N/kg^{0.75}/d$, respectively). Digestible organic matter intake (DOMI) and ME requirement for maintenance (MEm) were measured by both constant weight technique and regression method by regressing N balance on DOMI and ME intake on ADG. The measured DOMI during constant weight was 24.61 and 24.27 g $DOMI/kg^{0.75}/d$ and the calculated DOMI from regression equation was 24.24 and 24.22 g $DOMI/kg^{0.75}/d$, for S and A animals, respectively. The measured MEm was 402 and 401 kJ $ME/kg^{0.75}/d$ and the calculated MEm from regression analysis was 398 and 400 kJ $ME/kg^{0.75}/d$ for S and A breeds, respectively. There were no significant differences between both measured and regression techniques. There was no significant difference between S and A breeds for DOMI, N retention, MEm, digestibility and metabolizability values. Digestibility values for OM, GE and CP and metabolizability were significantly (p<0.05) higher in restricted feeding sheep compared with that of sheep fed ad libitum.

• 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 Transactions of the Korean Institute of Electrical Engineers P
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• v.67 no.4
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• pp.183-190
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• 2018

Predicting accurate electricity prices is an important task in the electricity trading market. To address the electricity price forecasting problem, various approaches have been proposed so far and it is known that linear regression-based approaches are the best. However, the use of such linear regression-based methods is limited due to low accuracy and performance. In traditional linear regression methods, it is not practical to find a nonlinear regression model that explains the training data well. If the training data is complex (i.e., small-sized individual data and large-sized features), it is difficult to find the polynomial function with n terms as the model that fits to the training data. On the other hand, as a linear regression model approximating a nonlinear regression model is used, the accuracy of the model drops considerably because it does not accurately reflect the characteristics of the training data. To cope with this problem, we propose a new electricity price forecasting method that divides the entire dataset to multiple split datasets and find the best linear regression models, each of which is the optimal model in each dataset. Meanwhile, to improve the performance of the proposed method, we modify the proposed localized linear regression method in the map and reduce way that is a framework for parallel processing data stored in a Hadoop distributed file system. Our experimental results show that the proposed model outperforms the existing linear regression model. Specifically, the accuracy of the proposed method is improved by 45% and the performance is faster 5 times than the existing linear regression-based model.