gge biplot雙向作圖軟件方法

1、Weikai Yan, Ph. DEmail: Web: Weikai_Yan2005 “One picture is worth of 10,000 words.” Biplot is a very informative “picture” of research Weikai_Yan2005 Automobile by parameter biplot Genotype by trait biplot in terms of agricultural studies (Yan and Rajcan 2002, Crop Science ) Automobile by judge bipl

2、ot Genotype by environment biplot in terms of agricultural studies (Yan 2001, Agronomy Journal) parameter by judge biplot Genetic covariate by environment biplot (Yan and Tinker 2005, Crop Science) Weikai_Yan2005“Preference Ratings for Automobiles Manufactured in 1980”, obtained from: http:/ Rating

3、for 10 Weikai_Yan2005“Biplot”PC1 vs. PC2 (“Primary” biplot)Cars: blueparameters: red Four questions to ask before trying to interpret a biplotMathematical model? Model =1 (parameter-centered data = GGE biplot)Goodness of fit? 64%S.V.P.?SVP = 1 ( = 1), car-metric preservingAxes drawn to scale?Always

4、“Yes” by GGEbiplot Weikai_Yan2005Cosine of an angle between two parametersCorrelation between two parametersAcute angles: Positive correlationsObtuse angles: Negative correlationsRight angles: no correlation Vector lengthDiscriminating ability of the parameterA short vector:Not related to any other

5、parametersLack of variation or not well represented in the Weikai_Yan2005 Display variations that are not displayed by the “primary” biplot of PC1 vs. PC2 To check if the primary biplot is Weikai_Yan2005High: Civic_Honda Chvette_GMC Low Firebird_GMC Weikai_Yan2005Best: Continental Granfury DLPoorest

6、 Pinto Chevette M Weikai_Yan2005Best DL_VolvoPoorest Firebird Weikai_Yan2005Best DL_VolvoPoorest Firebird_GMC The average position of all Weikai_Yan2005Best in Ride Comfort Poorest in MPG Weikai_Yan2005Best in Cargo Comfort Reliability Better than average for everything except “Acceleration” Weikai_

7、Yan2005Continental is better in Ride Both are similar in Comfort Quiet AccelDL is better in everything elseEquality Weikai_Yan2005Vertices Continental DL Civic Chevette Pinto F Weikai_Yan2005Vertices Pinto Firebird DL Weikai_Yan2005Preference of 25 judges “Preference Ratings for Automobiles Manufact

8、ured in 1980”, obtained from: http:/ Weikai_Y Weikai_Yan2005Angles Similarity among judges in preferenceVector length Discriminativeness of the judges J8 and J22? Weikai_Yan2005Little variation is left for PC3 and PC4The main biplot is adequate Weikai_Yan2005Similarity among cars in the eye of the W

9、eikai_Yan2005DL and imported car lovers 14 judgesContinental and Eldorado lovers 7 judgesPinto and Chevette Lover J24Why? Weikai_Yan2005What are the bases of the preference of the judges? Weikai_Y Weikai_Yan2005The angle between a judge and a parameter: Positive attitude: acute angles Negative attit

10、ude: obtuse angles Indifference: a right angle Weikai_Yan2005The most important thing for different judges Braking “J24” MPG 6 Reliability 8 Quietness 6 Ride Weikai_Yan2005In case the primary biplot is not Weikai_Yan2005(Gabriel, 1971)Or 3D-biplots for rank-3 matrix!Biplot analysis is a very powerfu

11、l tool, Weikai_Yan2005 Revealing linear patterns, generating hypotheses Patterns among rows Patterns among columns Interactions between rows and Weikai_Yan2005 Revealing non-linear relationships among variables Hypothesis test(Hypothesis test is NOT always necessary) Weikai_Yan2005BiplotAnalysisStatisticalTestsDecisionsHypothesis TestingPattern discoveryHypothesis generatingData inspection & Weikai_Yan2005 Biplot analysis has evolved into an elegant, powerful, generic tool for research data exploration Using user-friendly software GGEbiplot, biplot a