• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.705-712
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• 2005

Biplot is a graphical display of the rows and columns of an n${\times}$p data matrix. In particular, Gabriel (1995) suggested the MANOVA biplot using singular value decomposition (SVD) with the averages of response variables according to treatment groups. But his biplot may cause wrong results by disregarding them when there exist covariate effects. In this paper, we will provide the MANCOA biplot based on the SVD with the parameter estimates for MANCOVA model when there exist covariate effects.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.285-290
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• 2005

Biplot is a graphical display of the rows and columns an $n{\time}p$ data matrix. In particular, Gabriel(1981) suggested The MANOVA BIPLOT using singular value decomposition (SVD) with the averages of response variables according to treatment groups. But his biplot may cause wrong results by disregarding them when there exists covariate effects. In this paper, we will provide the MANCOVA BIPLOT based on the SVD with the parameter estimates for MANCOVA model when there exist covariate effects.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.661-668
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• 2012

For displaying multivariate numerical data on a 2D plane by the projection, principal components biplot and the GGobi are two main tools of data visualization. The biplot is very useful for capturing the global shape of the dataset, by representing $n$ observations and $p$ variables simultaneously on a single graph. The GGobi shows a dynamic movie of the images of $n$ observations projected onto a sequence of unit vectors floating on the $p$-dimensional sphere. Even though these two methods are certainly very valuable, there are drawbacks. The biplot is too condensed to describe the detailed parts of the data, and the GGobi is too burdensome for ordinary data analyses. In this paper, "the local projective display(LPD)" is proposed for visualizing multivariate numerical data. Main steps of the LDP are 1) $k$-means clustering of the data into $k$ subsets, 2) drawing $k$ principal components biplots of individual subsets, and 3) sequencing $k$ plots by Hurley's (2004) endlink algorithm for cognitive continuity.

• The Korean Journal of Applied Statistics
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• v.9 no.2
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• pp.55-72
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• 1996

It is essential in modern industry that quality and procuctivity are improved continuously. To accomplish this purpose, quality control must be maintained in all parts of a company. Recently, some tire manufacture companies are beginning to show interest in quality control. They have tried to achive some results through the statistical analysis for the experimental data which has accumulated up to now and then they strive to determine the structural relationship between the design factors in tire construction and tire performance characteristics. The measurement data obtained from the construction engineering is given in multivariate form owing to the various properties found in tire design components as wll as in performance. Also it may be existed the relationship among the multimple response variables. Thus we proposes the use of the biplot graphical display as an analytic tool of data matrices with complex respects. The proposed biplots are also availalbe to understand both the underlying structure of the data and the roles played by the different components. In particular, we consider the matter of how best to use the biplots in the maltivariate analysis of variance and multiple response data. Finally we apply this method to analyze the actual data.

• Communications for Statistical Applications and Methods
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• v.20 no.2
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• pp.129-136
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• 2013

Linear regression is the most basic statistical model for exploring the relationship between a numerical response variable and several explanatory variables. Logistic regression secures the role of linear regression for the dichotomous response variable. In this paper, we propose a biplot-type display of the multivariate data guided by the linear regression and/or the logistic regression. The figures show the directional flow of the response variable as well as the interrelationship of explanatory variables.

• The Plant Pathology Journal
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• v.24 no.3
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• pp.337-351
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• 2008

Host-pathogen interaction in rice bacterial blight pathosystem was analyzed for a better understanding of their relationship and recognition of stable pathogenicity among the populations of Xanthomonas oryzae pv. oryzae. A total number of 52 bacterial strains isolated from diseased leaf samples collected from 12 rice growing states and one Union Territory of India, were inoculated on 16 rice varieties, each possessing known genes for resistance. Analysis of variance revealed that the host genotypes(G) accounted for largest(78.4%) proportion of the total sum of squares(SS), followed by 16.5% due to the pathogen isolates(I) and 5.1% due to the $I{\times}G$ interactions. Application of the Additive Main effects and Multiplicative Interaction(AMMI) model revealed that the first two interaction principal component axes(IPCA) accounted for 66.8% and 21.5% of the interaction SS, respectively. The biplot generated using the isolate and genotypic scores of the first two IPCAs revealed groups of host genotypes and pathogen isolates falling into four sectors. A group of five isolates with high virulence, high absolute IPCA-1 scores, moderate IPCA-2 scores, low AMMI stability index '$D_i$' values and minimal deviations from additive main effects displayed in AMMI biplot as well as response plot, were identified as possessing stable pathogenicity across 16 host genotypes. The largest group of 27 isolates with low virulence, small IPCA-1 as well as IPCA-2 scores, low $D_i$ values and minimal deviations from additive main effect predictions, possessed stable pathogenicity for low virulence. The AMMI analysis and biplot display facilitated in a better understanding of the host-pathogen interaction, adaptability of pathogen isolates to specific host genotypes, identification of isolates showing stable pathogenicity and most discriminating host genotypes, which could be useful in location specific breeding programs aiming at deployment of resistant host genotypes in bacterial blight disease control strategies.

• Communications for Statistical Applications and Methods
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• v.15 no.1
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• pp.65-76
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• 2008

Biplots are the multivariate analogue of scatter plots. They approximate the multivariate distribution of a sample in a few dimensions, typically two, and they superimpose on this display representations of the variables on which the samples are measured(Gower and Hand, 1996, Chapter 1). And the relationships between the observations and variables can be easily seen. Thus, biplots are useful for giving a graphical description of the data. However, this method does not give some concise interpretations between variables and observations when the number of observations are large. Therefore, in this study, we will suggest to interpret the biplot analysis by applying the K-means clustering analysis. It shows that the relationships between the clusters and variables can be easily interpreted. So, this method is more useful for giving a graphical description of the data than using raw data.