1、2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,1,Applied Multivariate Quantitative Methods,Summarization of Multivariate Data By Jen-pei Liu, PhD Division of Biometry, Department of Agronomy, National Taiwan University and Wei-Chie Chie, MD, PhD Department of Public Health Nationa
2、l Taiwan University,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,2,Summarization of Multivariate Data,Limitations of Graphical Presentation Two-dimensional only At one time, only three variables Not possible for one variable plotting another three at the same time No simple way
3、to describe the relationship among more than four or more variables,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,3,Summarization of Multivariate Data,Plotting index variables Reduction of the number of variables to a few index variables Principal components Principal component 2
4、 against principal component 1 Principal component 3 versus other two Key difference between the objects may be lost in the reduction Index variables may not have any meaningful interpretation,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,4,2018/10/9,Copyright by Jen-pei Liu, PhD
5、 and Wei-Chu Chie, MD, PhD,5,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,6,Summarization of Multivariate Data,The draftmans plot A plots of the variables for each variable against variable for each of other variables The individual graphs are small enough so that they can be vi
6、ewed at the same time Only need two-dimensional plots Can not depict aspects of the data that would only be apparent when three or more variables are considered together,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,7,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD,
7、PhD,8,Summarization of Multivariate Data,The Representation of Individual Data Points Each of the objects for which variables are measured by a symbol Different characteristics of this symbol varying according to different variables: faces (Chernoff, 1973) or stars (Welsch, 1976) Advantage: displayi
8、ng all variables simultaneously Disadvantage: depending strongly on the order in which objects are displayed and the order in which variables are assigned to different aspects of the symbols Few statistical packages to produce such graphs,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD,
9、 PhD,9,Summarization of Multivariate Data,Example: Prehistoric Thai dog: faces Mandible breadth eye size Mandible height nose size Length of first molar brow size Breadth of first molar ear size Length from first to third molar mouth size Length from first to fourth premolars the amount of smile,201
10、8/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,10,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,11,Summarization of Multivariate Data,Stars Six variables were assigned to rays according to the order of Mandible breadth (six oclock) Mandible height (clockwise) Leng
11、th of first molar Breadth of first molar Length from first to third molar Length from first to fourth premolars,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,12,Summarization of Multivariate Data,Profiles of variables Plotting the values for variables Horizontal axis: variables V
12、ertical axis: values of measurements Values of objects are connected by line Plotting the bars Horizontal axis: objects Vertical axis: values of measurements Values of variables for each object are grouped together Only for variables with the same units,2018/10/9,Copyright by Jen-pei Liu, PhD and We
13、i-Chu Chie, MD, PhD,13,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,14,2018/10/9,Copyright by Jen-pei Liu, PhD and Wei-Chu Chie, MD, PhD,15,Summarization of Multivariate Data,Summary Difficulty for plotting results of all variables simultaneously Index variables Draftmans plots Use of symbols for individual data points Profiles of variables,
