Booklet of Code and Output for STAD29/STA 1007 Final Exam

Transcription

1 Booklet of Code and Output for STAD29/STA 1007 Final Exam

2 List of Figures in this document by page: List of Figures 1 Raisins data Boxplot of raisin data Raisin data t-test Radiation data and logistic regression Radiation data predictions Management training data (part) and interaction plot Management training boxplots Management training analyses of variance Transplant data (some) Fitting a proportional-hazards model for liver transplant data Model 2 for liver transplant data Predictions for transplant model Plotting survival curve Some of the flea beetle data MANOVA of the flea beetle data Discriminant analysis of the flea beetle data Plot of discriminant analysis for flea beetles Predicted species membership for flea beetles Termite data (some) Repeated-measures ANOVA for termite data Interaction plot for termite data European protein consumption Hierarchical cluster analysis of protein data Map of Europe in K-means clustering of European protein data with five clusters Metric multidimensional scaling map of protein data More output from metric scaling of protein data Non-metric multidimensional scaling map of protein data Some of the personality scales inventory Personality scales principal component analysis and scree plot Personality scales factor analysis Personality scales biplot

3 raisin=read.table("raisins.txt",header=t) raisin brand raisins 1 generic 25 2 generic 26 3 generic 25 4 generic 28 5 generic 26 6 generic 28 7 generic 28 8 generic 27 9 generic generic generic generic generic generic sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid sunmaid 30 Figure 1: Raisins data 2

4 attach(raisin) boxplot(raisins~brand) generic sunmaid Figure 2: Boxplot of raisin data 3

5 t.test(raisins~brand,alternative="l") Welch Two Sample t-test data: raisins by brand t = , df = 24.64, p-value = alternative hypothesis: true difference in means is less than 0 95 percent confidence interval: -Inf sample estimates: mean in group generic mean in group sunmaid Figure 3: Raisin data t-test 4

6 radiation=read.table("radiation.txt",header=t) radiation rems survived died attach(radiation) response=cbind(died,survived) radiation.1=glm(response~rems,family="binomial") summary(radiation.1) Call: glm(formula = response ~ rems, family = "binomial") Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(> z ) (Intercept) <2e-16 *** rems <2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: on 9 degrees of freedom Residual deviance: on 8 degrees of freedom AIC: Number of Fisher Scoring iterations: 4 Figure 4: Radiation data and logistic regression 5

7 new.rems=seq(0,900,100) radiation.new=data.frame(rems=new.rems) predict(radiation.1,radiation.new) predict(radiation.1,radiation.new,type="response") Figure 5: Radiation data predictions 6

8 train=read.table("training.txt",header=t) head(train) trained situation rating 1 yes standard 85 2 yes standard 91 3 yes standard 80 4 yes standard 78 5 no standard 53 6 no standard 49 attach(train) interaction.plot(trained,situation,rating) mean of rating situation standard emergency no yes trained Figure 6: Management training data (part) and interaction plot 7

9 boxplot(rating~trained+situation) no.emergency yes.emergency no.standard yes.standard Figure 7: Management training boxplots 8

10 train.1=aov(rating~trained*situation) summary(train.1) Df Sum Sq Mean Sq F value Pr(>F) trained e-07 *** situation trained:situation Residuals Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 train.2=aov(rating~trained+situation) summary(train.2) Df Sum Sq Mean Sq F value Pr(>F) trained e-08 *** situation Residuals Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 library(survival) data("transplant") head(transplant,n=12) Figure 8: Management training analyses of variance age sex abo year futime event 1 47 m B death 2 55 m A ltx 3 52 m B ltx 4 40 f O ltx 5 70 m O censored 6 66 f O ltx 7 41 f A ltx 8 55 m O ltx 9 50 m A ltx m A ltx m A ltx m A censored attach(transplant) Figure 9: Transplant data (some) 9

11 period=cut(transplant$year, c(1989, 1994, 1997, 2000), labels=c('90-94', '95-97', '98-99')) data.frame(year,period)[1:6,] year period y=surv(futime,event=="ltx") y.1=coxph(y~age+sex+abo+period) summary(y.1) Call: coxph(formula = y ~ age + sex + abo + period) n= 797, number of events= 618 (18 observations deleted due to missingness) coef exp(coef) se(coef) z Pr(> z ) age sexf abob *** aboab aboo e-15 *** period < 2e-16 *** period < 2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 exp(coef) exp(-coef) lower.95 upper.95 age sexf abob aboab aboo period period cordance= 0.73 (se = ) Rsquare= (max possible= 1 ) Likelihood ratio test= on 7 df, p=0 Wald test = on 7 df, p=0 Score (logrank) test = on 7 df, p=0 Figure 10: Fitting a proportional-hazards model for liver transplant data 10

12 y.2=coxph(y~abo+period) summary(y.2) Call: coxph(formula = y ~ abo + period) n= 815, number of events= 636 coef exp(coef) se(coef) z Pr(> z ) abob *** aboab aboo e-14 *** period < 2e-16 *** period < 2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 exp(coef) exp(-coef) lower.95 upper.95 abob aboab aboo period period cordance= (se = ) Rsquare= (max possible= 1 ) Likelihood ratio test= on 5 df, p=0 Wald test = on 5 df, p=0 Score (logrank) test = on 5 df, p=0 Figure 11: Model 2 for liver transplant data periods=levels(period) abos=levels(abo) transplant.new=expand.grid(period=periods,abo=abos) pp=survfit(y.2,transplant.new) Figure 12: Predictions for transplant model 2 11

13 lines=c(1,2,4) colours=c("black","blue","red","green") clty=expand.grid(line=lines,colour=colours,stringsasfactors=t) plot(pp,col=clty$colour,lty=clty$line) legend(x=1000,y=1,legend=periods,title="period",lty=lines) legend(x=1500,y=1,legend=abos,title="blood group", col=colours[c(1,3,4,2)],pch=3) Period Blood group A B AB O Figure 13: Plotting survival curve 12

14 fleabeetles=read.table("fleabeetles.txt",header=t) fleabeetles[c(1:6,24:30),] Width Angle Species Figure 14: Some of the flea beetle data attach(fleabeetles) y=cbind(width,angle) fleabeetles.1=manova(y~species) summary(fleabeetles.1) Df Pillai approx F num Df den Df Pr(>F) Species < 2.2e-16 *** Residuals Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Figure 15: MANOVA of the flea beetle data 13

15 library(mass) fleabeetles.2=lda(species~width+angle) fleabeetles.2 Call: lda(species ~ Width + Angle) Prior probabilities of groups: Group means: Width Angle Coefficients of linear discriminants: LD1 LD2 Width Angle Proportion of trace: LD1 LD Figure 16: Discriminant analysis of the flea beetle data 14

16 plot(fleabeetles.2) LD LD1 Figure 17: Plot of discriminant analysis for flea beetles 15

17 fleabeetles.3=predict(fleabeetles.2) pp=round(fleabeetles.3$posterior,3) p.all=cbind(fleabeetles,pp) p.all[1:35,] Width Angle Species p.all[36:74,] Width Angle Species Figure 18: Predicted species membership for flea beetles 16

18 termites=read.csv("termites.csv",header=t) head(termites) dish dose day1 day2 day4 day5 day6 day7 day8 day10 day11 day12 day day14 day Figure 19: Termite data (some) response=as.matrix(termites[,3:15]) library(car) attach(termites) termites.1=lm(response~dose) days=colnames(response) days.df=data.frame(days) termites.2=manova(termites.1,idata=days.df,idesign=~days) termites.2 Type II Repeated Measures MANOVA Tests: Pillai test statistic Df test stat approx F num Df den Df Pr(>F) (Intercept) e-09 *** dose ** days * dose:days Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Figure 20: Repeated-measures ANOVA for termite data 17

19 detach(termites) library(tidyr) termites.tidy=gather(termites,day,termite,day1:day15) attach(termites.tidy) interaction.plot(day,dose,termite) mean of termite dose 5 10 day1 day4 day6 day8 day11 day13 day15 day Figure 21: Interaction plot for termite data 18

20 protein=read.table("euro-protein.txt",header=t) protein RedMeat WhiteMeat Eggs Milk Fish Cereals Starch Nuts Fr.Veg Albania Austria Belgium Bulgaria Czechoslovakia Denmark E Germany Finland France Greece Hungary Ireland Italy Netherlands Norway Poland Portugal Romania Spain Sweden Switzerland UK USSR W Germany Yugoslavia Figure 22: European protein consumption 19

21 protein.s=scale(protein) protein.d=dist(protein.s) protein.1=hclust(protein.d,method="ward.d") plot(protein.1) Cluster Dendrogram ght Finland Norway Denmark Sweden Hungary USSR Poland Czechoslovakia E Germany Switzerland Austria Netherlands Ireland Belgium W Germany France UK Albania Bulgaria Romania Yugoslavia Greece Italy Portugal Spain protein.d hclust (*, "ward.d") Figure 23: Hierarchical cluster analysis of protein data 20

22 Figure 24: Map of Europe in

23 protein.2=kmeans(protein.s,5,nstart=20) sort(protein.2$cluster) Austria Belgium France Ireland Netherlands Switzerland UK W Germany Denmark Finland Norway Sweden Greece Italy Portugal Spain Czechoslovakia E Germany Hungary Poland USSR Albania Bulgaria Romania Yugoslavia g.1=cutree(protein.1,5) g.2=protein.2$cluster table(g.1,g.2) g.2 g Figure 25: K-means clustering of European protein data with five clusters 22

24 protein.3=cmdscale(protein.d) countries=row.names(protein) plot(protein.3,xlim=c(-3,5),xlab="x",ylab="y") text(protein.3,countries,pos=4) Portugal y France Norway Poland Denmark E Germany Belgium UK W Germany Sweden Finland Czechoslovakia Switzerland Austria Ireland Netherlands Spain USSR Italy Hungary Greece RomaniaYugoslavia Bulgaria Albania x Figure 26: Metric multidimensional scaling map of protein data 23

25 protein.4=cmdscale(protein.d,2,eig=t) protein.5=cmdscale(protein.d,3,eig=t) protein.4$gof [1] protein.5$gof [1] Figure 27: More output from metric scaling of protein data 24

26 library(mass) protein.6=isomds(protein.d) initial value iter 5 value final value converged protein.6$stress [1] plot(protein.6$points,xlab="x",ylab="y",xlim=c(-3,5)) text(protein.6$points,countries,pos=4) Portugal y France Norway Denmark Belgium UK Finland E Germany Poland W Germany Spain Italy Greece Czechoslovakia USSR Ireland Sweden Netherlands Switzerland Austria Hungary Romania Bulgaria Yugoslavia Albania x Figure 28: Non-metric multidimensional scaling map of protein data 25

27 library(psych) data(epi.bfi) head(epi.bfi) epie epis epiimp epilie epineur bfagree bfcon bfext bfneur bfopen bdi traitanx stateanx dim(epi.bfi) [1] Figure 29: Some of the personality scales inventory 26

28 epi.bfi.1=princomp(epi.bfi,cor=t) plot(epi.bfi.1,type="l") epi.bfi.1 Variances Comp.1 Comp.3 Comp.5 Comp.7 Comp.9 Figure 30: Personality scales principal component analysis and scree plot 27

29 epi.bfi.2=factanal(epi.bfi,3,scores="r") epi.bfi.2 Call: factanal(x = epi.bfi, factors = 3, scores = "r") Uniquenesses: epie epis epiimp epilie epineur bfagree bfcon bfext bfneur bfopen bdi traitanx stateanx Loadings: Factor1 Factor2 Factor3 epie epis epiimp epilie epineur bfagree bfcon bfext bfneur bfopen bdi traitanx stateanx Factor1 Factor2 Factor3 SS loadings Proportion Var Cumulative Var Test of the hypothesis that 3 factors are sufficient. The chi square statistic is on 42 degrees of freedom. The p-value is 2.36e-47 Figure 31: Personality scales factor analysis 28

30 biplot(epi.bfi.2$scores,epi.bfi.2$loadings) Factor epie epis epiimp bfext bfagree bfopen stateanx 214 bdi bfneur epineur traitanx bfcon epilie Factor1 Figure 32: Personality scales biplot 29