BIPLOT ANALYSIS OF AUTOMOBILE EVALUATION DATA Weikai Yan, Ph. D Email: [email protected]@ggebiplot.com Web: .

BIPLOT ANALYSIS OF BIPLOT ANALYSIS OF AUTOMOBILE EVALUATION AUTOMOBILE EVALUATION

DATADATA

Weikai Yan, Ph. DEmail: [email protected]

Web: www.ggebiplot.com

Weikai_Yan2005www.ggebiplot.com

Why biplot?Why biplot?

• “One picture is worth of 10,000 words.”

• Biplot is a very informative “picture” of research data


Three types of biplot will be Three types of biplot will be used in this studyused in this study

• Automobile by parameter biplot– Genotype by trait biplot in terms of agricultural studies

(Yan and Rajcan 2002, Crop Science )

• Automobile by judge biplot– 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)


Car by parameter tableCar by parameter table

“'Preference Ratings for Automobiles Manufactured in 1980”, obtained from: http://ftp.sas.com/techsup/download/sample/samp_lib/statsampPrincipal_Components_Analysis_of.html

Rating for 10 parameters


Car by parameter biplotCar by parameter biplot“Biplot”• PC1 vs. PC2 (“Primary”

biplot)• Cars: blue• parameters: red

Four questions to ask before trying to interpret a biplot

• Mathematical model? – Model =1 (parameter-

centered data = GGE biplot)

• Goodness of fit? – 64%

• S.V.P.?– SVP = 1 ( = 1), car-metric

preserving• Axes drawn to scale?

– Always “Yes” by GGEbiplot


Relationships among Relationships among parameters parameters

• Cosine of an angle between two parameters

– Correlation between two parameters

• Acute angles: Positive correlations

• Obtuse angles: Negative correlations

• Right angles: no correlation

• Vector length– Discriminating ability

of the parameter– A short vector:

• Not related to any other parameters

• Lack of variation or not well represented in the biplot


Biplot of PC3 vs. PC4Biplot of PC3 vs. PC4

• Display variations that are not displayed by the “primary” biplot of PC1 vs. PC2

• To check if the primary biplot is adequate


Rank cars based on Rank cars based on anyany parameterparameter

“MPG”“MPG”• High:

– Civic_Honda

– Chvette_GMC

– …

• Low– Firebird_GMC


Rank cars based on Rank cars based on anyany parameterparameter

“Ride”“Ride”• Best:

– Continental

– Granfury

– DL

• Poorest– Pinto

– Chevette

– Mustang


Rank cars based on Rank cars based on anyany two two parameters parameters

“MPG” and “RIDE”“MPG” and “RIDE”• Best

– DL_Volvo

• Poorest– Firebird


Rank cars on all parameters Rank cars on all parameters

• Best– DL_Volvo

• Poorest– Firebird_GMC

The average position of all parameters


The parameter profile of The parameter profile of anyany car: car:

“Ford Continental”“Ford Continental”• Best in

– Ride

– Comfort

• Poorest in– MPG


The parameter profile of The parameter profile of anyany car: car:

“Volvo DL”“Volvo DL”• Best in

– Cargo

– Comfort

– Reliability

• Better than average for everything except “Acceleration”


Compare Compare anyany two cars: two cars:“Volvo DL” vs. “Volvo DL” vs. “Continental”“Continental”

• Continental is better in– Ride

• Both are similar in– Comfort

– Quiet

– Accel

• DL is better in everything else

Equality line


Which car gets the Which car gets the highesthighest scoresscores

for what?for what?• Vertices

– Continental

– DL

– Civic

– Chevette

– Pinto

– Firebird


Which car gets the Which car gets the lowestlowest scoresscores

for what?for what?• Vertices

– Pinto

– Firebird

– DL


Car by judge dataCar by judge data(personal preference)(personal preference)

Preference of 25 judges

“'Preference Ratings for Automobiles Manufactured in 1980”, obtained from: http://ftp.sas.com/techsup/download/sample/samp_lib/statsampPrincipal_Components_Analysis_of.html


Car by judge biplotCar by judge biplot


Similarity among judgesSimilarity among judgesin terms of car preferencesin terms of car preferences

• Angles– Similarity among

judges in preference

• Vector length– Discriminativeness of

the judges

– J8 and J22?


Biplot of PC3 vs. PC4Biplot of PC3 vs. PC4

• Little variation is left for PC3 and PC4

• The main biplot is adequate


Similarity among carsSimilarity among carsfrom the eyes of the judgesfrom the eyes of the judges

• Similarity among cars in the eye of the judges


Genotype evaluation:Genotype evaluation: “who favors what most?”“who favors what most?”

• DL and imported car lovers– 14 judges

• Continental and Eldorado lovers– 7 judges

• Pinto and Chevette Lover– J24

Why?


Joint two-way table Joint two-way table of of “car by parameter” + “car by “car by parameter” + “car by

judge”judge”What are the bases of the preference of the judges?

ExplanatoryExplanatoryvariablesvariables

ResponseResponsevariablesvariables


Response variable by Response variable by explanatory variable tableexplanatory variable table

(correlation coefficients)(correlation coefficients)


Parameter by judge biplotParameter by judge biplot

• The angle between a judge and a parameter: – Positive attitude:

acute angles

– Negative attitude: obtuse angles

– Indifference: a right angle


parameter by judge biplotparameter by judge biplotWho values what most?Who values what most?

• The most important thing for different judges– Braking

• “J24”

– MPG• 6

– Reliability• 8

– Quietness• 6

– Ride• 4


A rotating A rotating 3D-biplot3D-biplot

In case the primary biplot is not adequate…


“Any two-way table can be analyzed using a 2D-biplot as soon as it can be sufficiently approximated by a rank-2 matrix.”

(Gabriel, 1971)

Or 3D-biplots for rank-3 matrix!

Limitations ofLimitations ofBiplot AnalysisBiplot Analysis

Biplot analysis is a very powerful tool, but…


What can biplots do? What can biplots do?

• Revealing linear patterns, generating hypotheses– Patterns among rows– Patterns among columns– Interactions between rows and columns


What biplots cannot do?What biplots cannot do?

• Revealing non-linear relationships among variables

• Hypothesis test(Hypothesis test is NOT always necessary)


Biplot Analysis & Statistical Biplot Analysis & Statistical testtest

are complementary are complementary

BiplotAnalysis

StatisticalTests

Decisions

Hypothesis Testing

Pattern discoveryHypothesis generating

Data inspection & visualization

Research dataResearch data


ConclusionsConclusions

• Biplot analysis has evolved into an elegant, powerful, generic tool for research data exploration

• Using user-friendly software GGEbiplot, biplot analysis is easy and fun. GGEbiplot beta is freely available at www.ggebiplot.com. Visit www.ggebiplot.com for more about biplot analysis.

• Don’t be discouraged by the math; you don’t have to know how a car is made to drive it

BIPLOT ANALYSIS OF AUTOMOBILE EVALUATION DATA Weikai Yan, Ph. D Email: [email protected]@ggebiplot.com Web: .

Documents

judge biplot slide

environment biplot yan

parameter biplot biplot

mpg slide

gmc slide

adequate slide

biplot of pc3

parameter biplot genotype