library(MASS)
arboles<-data.frame(mvrnorm(100, mu=c(30,70),
Sigma = matrix(c(1,0.7,0.7,1),ncol =2),empirical=T));arboles
## X1 X2
## 1 29.12199 69.59333
## 2 31.34742 71.59523
## 3 29.29974 70.04474
## 4 30.28608 69.54450
## 5 28.71671 68.97504
## 6 29.45941 68.57636
## 7 28.00074 68.53348
## 8 30.77024 70.20953
## 9 29.95835 68.94071
## 10 30.60133 69.85719
## 11 30.26015 70.88516
## 12 29.32369 68.98509
## 13 30.37847 70.75309
## 14 30.25995 71.08107
## 15 31.14463 71.53232
## 16 30.91592 71.07239
## 17 28.56689 68.90574
## 18 28.99949 69.97332
## 19 29.87611 70.30230
## 20 28.63684 69.34017
## 21 29.03489 69.84438
## 22 31.54077 71.39001
## 23 31.16268 71.27444
## 24 29.36901 69.29979
## 25 28.76302 68.58349
## 26 27.91468 68.04664
## 27 30.85755 70.98869
## 28 27.58590 67.08469
## 29 29.27665 70.48917
## 30 28.66615 71.02210
## 31 29.85270 70.01455
## 32 29.63017 69.57206
## 33 30.91599 71.01163
## 34 30.67326 70.28196
## 35 30.19451 68.98432
## 36 30.11325 68.84107
## 37 30.34777 69.92031
## 38 30.92681 71.25274
## 39 29.31585 70.25706
## 40 29.84553 69.94479
## 41 29.55202 70.10207
## 42 32.48445 69.45139
## 43 29.93851 69.33314
## 44 29.76089 68.68137
## 45 29.52394 70.28759
## 46 30.13833 70.06365
## 47 29.36078 69.63849
## 48 31.38426 71.78394
## 49 31.73611 71.90422
## 50 29.39307 69.19907
## 51 28.77596 70.25210
## 52 29.83210 70.92517
## 53 28.74345 69.16312
## 54 28.90442 70.06302
## 55 29.64297 69.94891
## 56 30.59011 71.04689
## 57 29.80260 69.98931
## 58 29.95453 71.25419
## 59 30.45244 69.35600
## 60 28.82598 68.96403
## 61 30.60834 70.59650
## 62 29.41618 70.07410
## 63 30.01723 69.54115
## 64 30.58869 71.07133
## 65 29.20575 69.92419
## 66 29.31579 69.04377
## 67 29.74700 69.28036
## 68 30.17043 70.08076
## 69 30.41874 70.29207
## 70 29.64457 67.72834
## 71 30.79472 70.16764
## 72 31.59076 71.30109
## 73 30.42316 69.93123
## 74 30.04516 71.04201
## 75 30.02713 70.47127
## 76 30.37738 69.25648
## 77 27.49132 67.30828
## 78 30.57008 70.74974
## 79 30.22687 70.19749
## 80 30.70677 71.15560
## 81 30.78354 69.46586
## 82 30.75035 70.46787
## 83 29.12981 69.51388
## 84 28.79221 69.38104
## 85 30.01733 70.33736
## 86 32.02282 71.60175
## 87 30.14189 69.45012
## 88 30.50537 70.68179
## 89 30.60648 70.07027
## 90 30.23933 69.89185
## 91 31.63867 70.60727
## 92 29.16013 68.40123
## 93 30.33869 69.43687
## 94 31.99900 71.55132
## 95 31.59225 70.40005
## 96 28.98697 69.24420
## 97 31.77961 70.75049
## 98 29.61383 69.75942
## 99 28.52905 69.19913
## 100 31.27831 72.36248
colnames(arboles)=c("y1.DAP","y2.EDAD")
View(arboles)
####Prueba de normalidad univariada###
norm.DAP<-shapiro.test(arboles$y1.DAP);norm.DAP
##
## Shapiro-Wilk normality test
##
## data: arboles$y1.DAP
## W = 0.99405, p-value = 0.9428
ifelse(norm.DAP$p.value<0.05, "rechazo Ho", "no rechazo Ho")
## [1] "no rechazo Ho"
norm.edad<-shapiro.test(arboles$y2.EDAD);norm.edad
##
## Shapiro-Wilk normality test
##
## data: arboles$y2.EDAD
## W = 0.98846, p-value = 0.5425
ifelse(norm.edad$p.value<0.05, "rechazo Ho", "no rechazo Ho")
## [1] "no rechazo Ho"
###prueba de normalidad bivariada###
library(royston)
## The Royston's H test has been moved to 'MVN' package.
## 'royston' package will no longer be supported. Please use
## 'MVN' package for further analysis.
norm.total<-royston.test(arboles)
ifelse(norm.total$p.value<0.05,"rechazo Ho", "no rechazo Ho")
## [1] "no rechazo Ho"
####plot#####
plot(arboles$y1.DAP,arboles$y2.EDAD)
cor(arboles$y1.DAP,arboles$y2.EDAD)
## [1] 0.7
library(psych)
describe(arboles)
## vars n mean sd median trimmed mad min max range skew
## y1.DAP 1 100 30 1 30.02 29.99 1.00 27.49 32.48 4.99 -0.03
## y2.EDAD 2 100 70 1 70.03 70.02 1.05 67.08 72.36 5.28 -0.26
## kurtosis se
## y1.DAP -0.19 0.1
## y2.EDAD 0.09 0.1
####Prueba hotelling###
library(ICSNP)
## Loading required package: mvtnorm
## Loading required package: ICS
t2arboles<-HotellingsT2(arboles, mu=c(31,73));t2arboles
##
## Hotelling's one sample T2-test
##
## data: arboles
## T.2 = 562.88, df1 = 2, df2 = 98, p-value < 2.2e-16
## alternative hypothesis: true location is not equal to c(31,73)
ifelse(t2arboles$p.value<0.05, "rechazo Ho", "no rechazo Ho")
## [1] "rechazo Ho"
######Prueba de Hotelling dos muestras independientes###
z<-cbind(arboles$y1.DAP,arboles$y2.EDAD); z
## [,1] [,2]
## [1,] 29.12199 69.59333
## [2,] 31.34742 71.59523
## [3,] 29.29974 70.04474
## [4,] 30.28608 69.54450
## [5,] 28.71671 68.97504
## [6,] 29.45941 68.57636
## [7,] 28.00074 68.53348
## [8,] 30.77024 70.20953
## [9,] 29.95835 68.94071
## [10,] 30.60133 69.85719
## [11,] 30.26015 70.88516
## [12,] 29.32369 68.98509
## [13,] 30.37847 70.75309
## [14,] 30.25995 71.08107
## [15,] 31.14463 71.53232
## [16,] 30.91592 71.07239
## [17,] 28.56689 68.90574
## [18,] 28.99949 69.97332
## [19,] 29.87611 70.30230
## [20,] 28.63684 69.34017
## [21,] 29.03489 69.84438
## [22,] 31.54077 71.39001
## [23,] 31.16268 71.27444
## [24,] 29.36901 69.29979
## [25,] 28.76302 68.58349
## [26,] 27.91468 68.04664
## [27,] 30.85755 70.98869
## [28,] 27.58590 67.08469
## [29,] 29.27665 70.48917
## [30,] 28.66615 71.02210
## [31,] 29.85270 70.01455
## [32,] 29.63017 69.57206
## [33,] 30.91599 71.01163
## [34,] 30.67326 70.28196
## [35,] 30.19451 68.98432
## [36,] 30.11325 68.84107
## [37,] 30.34777 69.92031
## [38,] 30.92681 71.25274
## [39,] 29.31585 70.25706
## [40,] 29.84553 69.94479
## [41,] 29.55202 70.10207
## [42,] 32.48445 69.45139
## [43,] 29.93851 69.33314
## [44,] 29.76089 68.68137
## [45,] 29.52394 70.28759
## [46,] 30.13833 70.06365
## [47,] 29.36078 69.63849
## [48,] 31.38426 71.78394
## [49,] 31.73611 71.90422
## [50,] 29.39307 69.19907
## [51,] 28.77596 70.25210
## [52,] 29.83210 70.92517
## [53,] 28.74345 69.16312
## [54,] 28.90442 70.06302
## [55,] 29.64297 69.94891
## [56,] 30.59011 71.04689
## [57,] 29.80260 69.98931
## [58,] 29.95453 71.25419
## [59,] 30.45244 69.35600
## [60,] 28.82598 68.96403
## [61,] 30.60834 70.59650
## [62,] 29.41618 70.07410
## [63,] 30.01723 69.54115
## [64,] 30.58869 71.07133
## [65,] 29.20575 69.92419
## [66,] 29.31579 69.04377
## [67,] 29.74700 69.28036
## [68,] 30.17043 70.08076
## [69,] 30.41874 70.29207
## [70,] 29.64457 67.72834
## [71,] 30.79472 70.16764
## [72,] 31.59076 71.30109
## [73,] 30.42316 69.93123
## [74,] 30.04516 71.04201
## [75,] 30.02713 70.47127
## [76,] 30.37738 69.25648
## [77,] 27.49132 67.30828
## [78,] 30.57008 70.74974
## [79,] 30.22687 70.19749
## [80,] 30.70677 71.15560
## [81,] 30.78354 69.46586
## [82,] 30.75035 70.46787
## [83,] 29.12981 69.51388
## [84,] 28.79221 69.38104
## [85,] 30.01733 70.33736
## [86,] 32.02282 71.60175
## [87,] 30.14189 69.45012
## [88,] 30.50537 70.68179
## [89,] 30.60648 70.07027
## [90,] 30.23933 69.89185
## [91,] 31.63867 70.60727
## [92,] 29.16013 68.40123
## [93,] 30.33869 69.43687
## [94,] 31.99900 71.55132
## [95,] 31.59225 70.40005
## [96,] 28.98697 69.24420
## [97,] 31.77961 70.75049
## [98,] 29.61383 69.75942
## [99,] 28.52905 69.19913
## [100,] 31.27831 72.36248
g<-gl(2,50,100,c("tabio","torca"));g
## [1] tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio
## [12] tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio
## [23] tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio
## [34] tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio tabio
## [45] tabio tabio tabio tabio tabio tabio torca torca torca torca torca
## [56] torca torca torca torca torca torca torca torca torca torca torca
## [67] torca torca torca torca torca torca torca torca torca torca torca
## [78] torca torca torca torca torca torca torca torca torca torca torca
## [89] torca torca torca torca torca torca torca torca torca torca torca
## [100] torca
## Levels: tabio torca
hot.arbol<-HotellingsT2(z~g, mu=c(0,0))
ifelse(hot.arbol$p.value<0.05,"rechazo Ho", "no rechazo Ho")
## [,1]
## [1,] "no rechazo Ho"
##la aproximación de Chi cuadrado se utiliza cuando se utilizan muestras con un
#n>5 y cuando el número de variables dependientes es mayor o igual a 5.
######prueba de igualdad de covarianzas####
library(biotools)
## Loading required package: rpanel
## Loading required package: tcltk
## Package `rpanel', version 1.1-4: type help(rpanel) for summary information
## Loading required package: tkrplot
## Loading required package: lattice
## Loading required package: SpatialEpi
## Loading required package: sp
## ---
## biotools version 3.1
##
mbox.arbol<-boxM(arboles,g);mbox.arbol
##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: arboles
## Chi-Sq (approx.) = 0.67914, df = 3, p-value = 0.8781
ifelse(mbox.arbol$p.value<0.05,"Rechazo Ho","no rechazo Ho") #igualdad de covaria
## [1] "no rechazo Ho"
hot.leche<-HotellingsT2(z~g, mu=c(0,0)); hot.leche #se pone cero porque en las localidades
##
## Hotelling's two sample T2-test
##
## data: z by g
## T.2 = 0.47397, df1 = 2, df2 = 97, p-value = 0.624
## alternative hypothesis: true location difference is not equal to c(0,0)
ifelse(hot.arbol$p.value<0.05,"rechazo Ho", "no rechazo Ho")
## [,1]
## [1,] "no rechazo Ho"
######igualdad de covarianzas####
var(arboles[1:50,])
## y1.DAP y2.EDAD
## y1.DAP 1.0726718 0.7617071
## y2.EDAD 0.7617071 1.1036029
var(arboles[51:100,])
## y1.DAP y2.EDAD
## y1.DAP 0.9288000 0.6417649
## y2.EDAD 0.6417649 0.9106300
library(biotools)
mbox.arbol<-boxM(arboles,g)
ifelse(mbox.arbol$p.value<0.05,"Rechazo Ho","no rechazo Ho") #igualdad de covarianzas
## [1] "no rechazo Ho"
####prueba t para dos muestras#####
arboles2<-cbind(arboles,g);arboles2
## y1.DAP y2.EDAD g
## 1 29.12199 69.59333 tabio
## 2 31.34742 71.59523 tabio
## 3 29.29974 70.04474 tabio
## 4 30.28608 69.54450 tabio
## 5 28.71671 68.97504 tabio
## 6 29.45941 68.57636 tabio
## 7 28.00074 68.53348 tabio
## 8 30.77024 70.20953 tabio
## 9 29.95835 68.94071 tabio
## 10 30.60133 69.85719 tabio
## 11 30.26015 70.88516 tabio
## 12 29.32369 68.98509 tabio
## 13 30.37847 70.75309 tabio
## 14 30.25995 71.08107 tabio
## 15 31.14463 71.53232 tabio
## 16 30.91592 71.07239 tabio
## 17 28.56689 68.90574 tabio
## 18 28.99949 69.97332 tabio
## 19 29.87611 70.30230 tabio
## 20 28.63684 69.34017 tabio
## 21 29.03489 69.84438 tabio
## 22 31.54077 71.39001 tabio
## 23 31.16268 71.27444 tabio
## 24 29.36901 69.29979 tabio
## 25 28.76302 68.58349 tabio
## 26 27.91468 68.04664 tabio
## 27 30.85755 70.98869 tabio
## 28 27.58590 67.08469 tabio
## 29 29.27665 70.48917 tabio
## 30 28.66615 71.02210 tabio
## 31 29.85270 70.01455 tabio
## 32 29.63017 69.57206 tabio
## 33 30.91599 71.01163 tabio
## 34 30.67326 70.28196 tabio
## 35 30.19451 68.98432 tabio
## 36 30.11325 68.84107 tabio
## 37 30.34777 69.92031 tabio
## 38 30.92681 71.25274 tabio
## 39 29.31585 70.25706 tabio
## 40 29.84553 69.94479 tabio
## 41 29.55202 70.10207 tabio
## 42 32.48445 69.45139 tabio
## 43 29.93851 69.33314 tabio
## 44 29.76089 68.68137 tabio
## 45 29.52394 70.28759 tabio
## 46 30.13833 70.06365 tabio
## 47 29.36078 69.63849 tabio
## 48 31.38426 71.78394 tabio
## 49 31.73611 71.90422 tabio
## 50 29.39307 69.19907 tabio
## 51 28.77596 70.25210 torca
## 52 29.83210 70.92517 torca
## 53 28.74345 69.16312 torca
## 54 28.90442 70.06302 torca
## 55 29.64297 69.94891 torca
## 56 30.59011 71.04689 torca
## 57 29.80260 69.98931 torca
## 58 29.95453 71.25419 torca
## 59 30.45244 69.35600 torca
## 60 28.82598 68.96403 torca
## 61 30.60834 70.59650 torca
## 62 29.41618 70.07410 torca
## 63 30.01723 69.54115 torca
## 64 30.58869 71.07133 torca
## 65 29.20575 69.92419 torca
## 66 29.31579 69.04377 torca
## 67 29.74700 69.28036 torca
## 68 30.17043 70.08076 torca
## 69 30.41874 70.29207 torca
## 70 29.64457 67.72834 torca
## 71 30.79472 70.16764 torca
## 72 31.59076 71.30109 torca
## 73 30.42316 69.93123 torca
## 74 30.04516 71.04201 torca
## 75 30.02713 70.47127 torca
## 76 30.37738 69.25648 torca
## 77 27.49132 67.30828 torca
## 78 30.57008 70.74974 torca
## 79 30.22687 70.19749 torca
## 80 30.70677 71.15560 torca
## 81 30.78354 69.46586 torca
## 82 30.75035 70.46787 torca
## 83 29.12981 69.51388 torca
## 84 28.79221 69.38104 torca
## 85 30.01733 70.33736 torca
## 86 32.02282 71.60175 torca
## 87 30.14189 69.45012 torca
## 88 30.50537 70.68179 torca
## 89 30.60648 70.07027 torca
## 90 30.23933 69.89185 torca
## 91 31.63867 70.60727 torca
## 92 29.16013 68.40123 torca
## 93 30.33869 69.43687 torca
## 94 31.99900 71.55132 torca
## 95 31.59225 70.40005 torca
## 96 28.98697 69.24420 torca
## 97 31.77961 70.75049 torca
## 98 29.61383 69.75942 torca
## 99 28.52905 69.19913 torca
## 100 31.27831 72.36248 torca
DAP.tabio<-matrix(subset(arboles2$y1.DAP,g=="tabio"));DAP.tabio
## [,1]
## [1,] 29.12199
## [2,] 31.34742
## [3,] 29.29974
## [4,] 30.28608
## [5,] 28.71671
## [6,] 29.45941
## [7,] 28.00074
## [8,] 30.77024
## [9,] 29.95835
## [10,] 30.60133
## [11,] 30.26015
## [12,] 29.32369
## [13,] 30.37847
## [14,] 30.25995
## [15,] 31.14463
## [16,] 30.91592
## [17,] 28.56689
## [18,] 28.99949
## [19,] 29.87611
## [20,] 28.63684
## [21,] 29.03489
## [22,] 31.54077
## [23,] 31.16268
## [24,] 29.36901
## [25,] 28.76302
## [26,] 27.91468
## [27,] 30.85755
## [28,] 27.58590
## [29,] 29.27665
## [30,] 28.66615
## [31,] 29.85270
## [32,] 29.63017
## [33,] 30.91599
## [34,] 30.67326
## [35,] 30.19451
## [36,] 30.11325
## [37,] 30.34777
## [38,] 30.92681
## [39,] 29.31585
## [40,] 29.84553
## [41,] 29.55202
## [42,] 32.48445
## [43,] 29.93851
## [44,] 29.76089
## [45,] 29.52394
## [46,] 30.13833
## [47,] 29.36078
## [48,] 31.38426
## [49,] 31.73611
## [50,] 29.39307
DAP.torca<-matrix(subset(arboles2$y1.DAP,g=="torca"));DAP.torca
## [,1]
## [1,] 28.77596
## [2,] 29.83210
## [3,] 28.74345
## [4,] 28.90442
## [5,] 29.64297
## [6,] 30.59011
## [7,] 29.80260
## [8,] 29.95453
## [9,] 30.45244
## [10,] 28.82598
## [11,] 30.60834
## [12,] 29.41618
## [13,] 30.01723
## [14,] 30.58869
## [15,] 29.20575
## [16,] 29.31579
## [17,] 29.74700
## [18,] 30.17043
## [19,] 30.41874
## [20,] 29.64457
## [21,] 30.79472
## [22,] 31.59076
## [23,] 30.42316
## [24,] 30.04516
## [25,] 30.02713
## [26,] 30.37738
## [27,] 27.49132
## [28,] 30.57008
## [29,] 30.22687
## [30,] 30.70677
## [31,] 30.78354
## [32,] 30.75035
## [33,] 29.12981
## [34,] 28.79221
## [35,] 30.01733
## [36,] 32.02282
## [37,] 30.14189
## [38,] 30.50537
## [39,] 30.60648
## [40,] 30.23933
## [41,] 31.63867
## [42,] 29.16013
## [43,] 30.33869
## [44,] 31.99900
## [45,] 31.59225
## [46,] 28.98697
## [47,] 31.77961
## [48,] 29.61383
## [49,] 28.52905
## [50,] 31.27831
t.test(DAP.tabio,DAP.torca)
##
## Welch Two Sample t-test
##
## data: DAP.tabio and DAP.torca
## t = -0.96291, df = 97.496, p-value = 0.338
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.5897182 0.2044121
## sample estimates:
## mean of x mean of y
## 29.90367 30.09633
nrow(DAP.tabio)
## [1] 50
ncol(DAP.tabio)
## [1] 1
######ver outliers multivariado####
library(mvoutlier)
## Loading required package: sgeostat
## Registered S3 methods overwritten by 'ggplot2':
## method from
## [.quosures rlang
## c.quosures rlang
## print.quosures rlang
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
## sROC 0.1-2 loaded
dd.plot(arboles)
## $outliers
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [12] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [23] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [34] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [45] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [56] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [67] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [78] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [89] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [100] FALSE
##
## $md.cla
## [1] 0.9250303 1.6276243 1.0253901 0.9617631 1.2954906 1.5602564 2.0014613
## [8] 0.8979606 1.4430747 0.9923364 1.0182641 1.0160326 0.7813462 1.2855525
## [15] 1.5356325 1.0970697 1.4387729 1.3751032 0.5586490 1.4241231 1.2089427
## [22] 1.6013082 1.3295689 0.7274505 1.4576018 2.1968962 1.0154796 2.9618263
## [29] 1.5705117 3.0462161 0.2210004 0.4391083 1.0526660 0.7235704 1.6245753
## [36] 1.7375241 0.5706715 1.2546823 1.2369658 0.1713170 0.7344723 4.0539601
## [43] 0.8756816 1.6297081 0.9911425 0.1459272 0.6504451 1.7939999 1.9861388
## [50] 0.8035447 1.9772429 1.4696946 1.2579725 1.5971412 0.4527575 1.0657945
## [57] 0.2661430 1.8013629 1.4192969 1.2117122 0.6535927 0.8932212 0.6596370
## [64] 1.0948627 1.0406183 0.9564597 0.8007316 0.1787688 0.4187440 2.8547837
## [71] 0.9632162 1.6122934 0.6635220 1.4155602 0.6338996 1.4606446 2.8301930
## [78] 0.7524142 0.2332477 1.1644187 1.7064852 0.7546385 0.8870724 1.2487352
## [85] 0.4557498 2.0394821 0.9200659 0.6829279 0.7835215 0.4541934 1.8046039
## [92] 1.6459023 1.1705984 2.0103011 1.8805099 1.0151339 1.9099524 0.3884042
## [99] 1.5054309 2.4202657
##
## $md.rob
## [1] 0.7720037 1.3172630 0.9244769 1.3518199 1.1203608 1.8899666 1.7036013
## [8] 1.1011728 1.8803341 1.3322956 0.8790948 1.1601758 0.5915650 1.1840548
## [15] 1.2547824 0.8579871 1.2313466 1.2917792 0.4103440 1.2310990 1.0918275
## [22] 1.3312623 1.0608103 0.7748677 1.4139241 1.9235289 0.7898604 2.7754961
## [29] 1.5741493 3.2728861 0.1197939 0.5514599 0.8264862 0.8656154 2.1148858
## [36] 2.2367668 0.8615869 1.0016207 1.1810181 0.1809037 0.6132780 4.7496035
## [43] 1.2288432 2.0554836 0.9097280 0.3376839 0.5372219 1.4794494 1.6211179
## [50] 0.9119853 1.9938336 1.4558633 1.0659219 1.5476975 0.3216595 0.8625148
## [57] 0.1587789 1.8217900 1.8804882 1.0797981 0.5342258 0.7843331 0.9950395
## [64] 0.8948679 0.9249441 1.0746157 1.0912946 0.3608081 0.4755758 3.4355538
## [71] 1.1922404 1.3827777 0.9575005 1.3694206 0.4803608 1.9315878 2.5487218
## [78] 0.5542817 0.2930736 0.9461251 2.1876305 0.7853458 0.7390118 1.0643843
## [85] 0.2786748 1.7578381 1.3036428 0.4925295 1.0360690 0.7454370 1.9415357
## [92] 1.8774883 1.5942187 1.7448434 2.1115339 0.8747094 1.9977489 0.3489832
## [99] 1.2924650 2.2225090
dd.plot(log(arboles[,c("y1.DAP","y2.EDAD")]))
## $outliers
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [12] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [23] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [34] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [45] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [56] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [67] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [78] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [89] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [100] FALSE
##
## $md.cla
## [1] 0.9230652 1.6113374 1.0229497 0.9751003 1.3027852 1.5764711 2.0493065
## [8] 0.9030058 1.4619851 1.0012785 1.0098455 1.0150360 0.7790652 1.2727556
## [15] 1.5227817 1.0942151 1.4532006 1.3848601 0.5494815 1.4443472 1.2153227
## [22] 1.5797197 1.3208518 0.7193577 1.4623992 2.2387648 1.0143569 3.0206119
## [29] 1.5704246 3.0710198 0.2063562 0.4293366 1.0508180 0.7319007 1.6452591
## [36] 1.7609071 0.5842092 1.2482030 1.2355028 0.1542693 0.7255136 3.9439447
## [43] 0.8862727 1.6513283 0.9842628 0.1631683 0.6402155 1.7739157 1.9557957
## [50] 0.7983094 2.0011539 1.4560524 1.2672295 1.6127331 0.4394181 1.0606758
## [57] 0.2510593 1.7815423 1.4333061 1.2140335 0.6601791 0.8873487 0.6696052
## [64] 1.0890596 1.0403379 0.9536753 0.8058638 0.1957753 0.4316754 2.9117533
## [71] 0.9672498 1.5875619 0.6761414 1.4006845 0.6269611 1.4765318 2.8938791
## [78] 0.7548246 0.2467295 1.1583889 1.7125529 0.7608208 0.8834600 1.2598686
## [85] 0.4497071 1.9911102 0.9332342 0.6859838 0.7929418 0.4681490 1.7672362
## [92] 1.6592696 1.1846185 1.9627768 1.8443527 1.0137521 1.8641736 0.3734850
## [99] 1.5296971 2.3821539
##
## $md.rob
## [1] 0.7696318 1.3060578 0.9215727 1.3689804 1.1261121 1.9217287 1.7448675
## [8] 1.1035476 1.9103595 1.3409681 0.8693454 1.1711192 0.5888971 1.1701737
## [15] 1.2463819 0.8568184 1.2428532 1.3020430 0.3985408 1.2505645 1.0982424
## [22] 1.3097900 1.0544145 0.7763795 1.4227273 1.9546890 0.7901114 2.8221389
## [29] 1.5744580 3.3017421 0.1102437 0.5544360 0.8258904 0.8715001 2.1447285
## [36] 2.2710293 0.8748102 0.9976851 1.1794037 0.1801727 0.6029754 4.6295150
## [43] 1.2481743 2.0912877 0.9019317 0.3522813 0.5287278 1.4661381 1.5983690
## [50] 0.9179704 2.0199553 1.4413140 1.0735432 1.5644324 0.3076837 0.8578929
## [57] 0.1465191 1.8011935 1.8989503 1.0825063 0.5417129 0.7776255 1.0115069
## [64] 0.8895256 0.9243093 1.0831510 1.1076142 0.3755556 0.4881845 3.5157798
## [71] 1.1936780 1.3558051 0.9696076 1.3533895 0.4711766 1.9531933 2.5948192
## [78] 0.5579827 0.3084470 0.9413486 2.1956066 0.7893482 0.7353905 1.0745810
## [85] 0.2703645 1.7065754 1.3225840 0.4970209 1.0437470 0.7596225 1.8962529
## [92] 1.9059074 1.6126723 1.6937326 2.0682152 0.8737828 1.9429542 0.3416308
## [99] 1.3153535 2.1911972
xy <- arboles[,c("y1.DAP","y2.EDAD")] # coordenadas
myarboles <- log(arboles[, c("y1.DAP","y2.EDAD")])
out.arboles<-map.plot(xy, myarboles, symb=FALSE)
out.arboles$outliers
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [12] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [23] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [34] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [45] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [56] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [67] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [78] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [89] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [100] FALSE
which(out.arboles$outliers==TRUE)
## [1] 28 30 42 70
##mbox con varianzas difernetes, se modifican datos de la base real ###
arboles3<-read.csv("E:/MAESTRÍA GEOMÁTICA UNAL/MÉTODOS MULTIVARIADOS/arboles3.csv");arboles3
## y1.DAP y2.EDAD
## 1 100.00000 500.00000
## 2 100.00000 600.00000
## 3 100.00000 600.00000
## 4 100.00000 700.00000
## 5 31.22613 70.96583
## 6 29.17756 67.62307
## 7 29.69489 69.80774
## 8 30.72601 70.39250
## 9 29.81925 71.20414
## 10 30.33947 69.91948
## 11 29.17371 70.34514
## 12 30.05829 70.79238
## 13 29.55078 68.94653
## 14 30.14137 71.13297
## 15 30.09772 68.10602
## 16 28.28280 69.95423
## 17 30.62392 69.77860
## 18 30.56126 71.11539
## 19 30.26792 70.29489
## 20 30.99743 70.10319
## 21 31.63077 71.57348
## 22 28.61379 70.20410
## 23 29.87908 69.91571
## 24 29.05957 70.01355
## 25 30.25529 70.29213
## 26 30.55576 69.90386
## 27 30.64925 70.23139
## 28 29.99646 70.17729
## 29 28.74708 68.85466
## 30 29.53504 69.83996
## 31 29.65476 69.29433
## 32 29.28896 69.53387
## 33 29.33432 69.73313
## 34 31.43666 70.97132
## 35 29.87576 70.85401
## 36 28.89247 69.30493
## 37 30.16758 69.36015
## 38 29.85290 69.96537
## 39 29.61444 70.27093
## 40 29.56664 71.02264
## 41 29.19429 69.41983
## 42 30.56264 71.07806
## 43 31.48485 72.46583
## 44 30.74595 70.09927
## 45 28.07410 68.65816
## 46 30.58726 70.48032
## 47 30.34081 70.96698
## 48 28.32970 69.38704
## 49 29.46412 70.36561
## 50 27.49464 66.56940
## 51 28.88579 69.18094
## 52 29.77453 70.46573
## 53 31.40064 70.83727
## 54 31.47604 71.08809
## 55 30.35154 68.55542
## 56 29.58612 70.34135
## 57 29.77835 69.89455
## 58 29.55675 68.99481
## 59 30.74077 70.69356
## 60 30.54432 69.57129
## 61 30.37338 70.37492
## 62 29.37278 69.13922
## 63 29.43511 68.74652
## 64 29.44560 69.70162
## 65 30.03451 69.12347
## 66 29.72585 69.88569
## 67 28.83287 69.82107
## 68 30.88588 70.76458
## 69 29.36579 68.51447
## 70 30.29081 70.06042
## 71 29.23074 69.27020
## 72 29.80536 69.96907
## 73 28.89823 69.96130
## 74 33.21748 72.23982
## 75 30.46822 69.68905
## 76 31.11455 71.82586
## 77 32.85476 71.61878
## 78 31.33164 69.89939
## 79 29.97864 70.72713
## 80 29.29297 68.99570
## 81 31.39348 69.81856
## 82 30.64165 70.94479
## 83 29.17104 68.41422
## 84 28.44670 70.04441
## 85 32.02750 71.54783
## 86 31.11716 71.05420
## 87 29.48303 69.42496
## 88 29.56931 70.13687
## 89 28.86489 68.62693
## 90 29.47127 69.62892
## 91 30.05929 70.19470
## 92 29.72441 70.12540
## 93 28.60693 68.94474
## 94 29.11514 70.45353
## 95 30.01272 69.73961
## 96 28.73206 67.81383
## 97 29.67820 68.98438
## 98 29.44732 68.35918
## 99 30.84374 71.12952
## 100 30.54691 70.42006
######prueba de igualdad de covarianzas####
mbox.arbol3<-boxM(arboles3,g);mbox.arbol3
##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: arboles3
## Chi-Sq (approx.) = 488.97, df = 3, p-value < 2.2e-16
ifelse(2.2e-16<0.05,"Rechazo Ho","no rechazo Ho") #igualdad de covaria
## [1] "Rechazo Ho"
######prueba de igualdad de covarianzas####
var(arboles3[1:50,])
## y1.DAP y2.EDAD
## y1.DAP 370.2298 2792.226
## y2.EDAD 2792.2256 21503.068
var(arboles3[51:100,])
## y1.DAP y2.EDAD
## y1.DAP 1.0867700 0.7422112
## y2.EDAD 0.7422112 0.9453209
library(biotools)
mbox.arbol<-boxM(arboles3,g)
ifelse(mbox.arbol$p.value<0.05,"Rechazo Ho","no rechazo Ho") #igualdad de covarianzas
## [1] "Rechazo Ho"
###########################################################################
###factorial completo, bloques completos, generalizados y al azar###
germ=rnorm(120, 70 ,2); germ
## [1] 71.93730 66.31486 68.53724 67.10922 69.95993 68.00244 68.21334
## [8] 69.72642 73.16099 71.38334 73.34402 67.97647 69.08663 71.58141
## [15] 68.98315 71.54040 70.25418 72.38624 70.95110 73.31673 71.37498
## [22] 73.23477 67.26619 70.78834 67.75792 71.09554 73.23581 75.06873
## [29] 70.30881 66.90380 69.42939 70.69188 71.60011 65.86823 66.34788
## [36] 68.53927 71.32948 73.27147 70.45638 69.30115 70.36132 67.16559
## [43] 70.46225 66.56699 69.39718 67.64799 70.83207 69.70786 71.74424
## [50] 69.38384 69.03722 72.97304 68.96537 73.27933 69.15313 72.51368
## [57] 67.55527 69.36992 67.97955 70.85013 71.04904 70.41014 70.99828
## [64] 71.33098 66.45227 70.13874 72.02532 70.70118 68.01788 69.91353
## [71] 72.94702 72.50269 66.46316 69.94691 68.62457 71.55954 70.72958
## [78] 67.55373 70.14681 68.43730 69.86100 73.08314 68.14168 70.40921
## [85] 72.49029 70.73779 71.25077 70.25724 71.04440 68.63795 71.34470
## [92] 74.57727 69.35732 69.49836 74.23016 68.56676 69.98838 68.38846
## [99] 68.59635 66.78296 70.35337 67.78981 73.69663 70.10184 68.21259
## [106] 73.92886 71.23719 73.02118 70.16699 73.22179 71.61555 71.13085
## [113] 67.81338 68.82444 69.60822 68.35704 70.29335 67.95400 69.68343
## [120] 68.81901
var=(gl(3, 40, 120, labels=c("V1", "V2", "V3"))); var
## [1] V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
## [24] V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V2 V2 V2 V2 V2 V2
## [47] V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2
## [70] V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3
## [93] V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3 V3
## [116] V3 V3 V3 V3 V3
## Levels: V1 V2 V3
var2<-data.frame(var)
proc=gl(2, 20, 120, labels=c("L1", "L2")); proc
## [1] L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L2 L2 L2
## [24] L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L1 L1 L1 L1 L1 L1
## [47] L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L2 L2 L2 L2 L2 L2 L2 L2 L2
## [70] L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1 L1
## [93] L1 L1 L1 L1 L1 L1 L1 L1 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2 L2
## [116] L2 L2 L2 L2 L2
## Levels: L1 L2
horm=gl(2, 10, 120, labels=c("A", "B"));horm
## [1] A A A A A A A A A A B B B B B B B B B B A A A A A A A A A A B B B B B
## [36] B B B B B A A A A A A A A A A B B B B B B B B B B A A A A A A A A A A
## [71] B B B B B B B B B B A A A A A A A A A A B B B B B B B B B B A A A A A
## [106] A A A A A B B B B B B B B B B
## Levels: A B
lgg=log10(germ)
data=data.frame(germ, var, proc, horm);data
## germ var proc horm
## 1 71.93730 V1 L1 A
## 2 66.31486 V1 L1 A
## 3 68.53724 V1 L1 A
## 4 67.10922 V1 L1 A
## 5 69.95993 V1 L1 A
## 6 68.00244 V1 L1 A
## 7 68.21334 V1 L1 A
## 8 69.72642 V1 L1 A
## 9 73.16099 V1 L1 A
## 10 71.38334 V1 L1 A
## 11 73.34402 V1 L1 B
## 12 67.97647 V1 L1 B
## 13 69.08663 V1 L1 B
## 14 71.58141 V1 L1 B
## 15 68.98315 V1 L1 B
## 16 71.54040 V1 L1 B
## 17 70.25418 V1 L1 B
## 18 72.38624 V1 L1 B
## 19 70.95110 V1 L1 B
## 20 73.31673 V1 L1 B
## 21 71.37498 V1 L2 A
## 22 73.23477 V1 L2 A
## 23 67.26619 V1 L2 A
## 24 70.78834 V1 L2 A
## 25 67.75792 V1 L2 A
## 26 71.09554 V1 L2 A
## 27 73.23581 V1 L2 A
## 28 75.06873 V1 L2 A
## 29 70.30881 V1 L2 A
## 30 66.90380 V1 L2 A
## 31 69.42939 V1 L2 B
## 32 70.69188 V1 L2 B
## 33 71.60011 V1 L2 B
## 34 65.86823 V1 L2 B
## 35 66.34788 V1 L2 B
## 36 68.53927 V1 L2 B
## 37 71.32948 V1 L2 B
## 38 73.27147 V1 L2 B
## 39 70.45638 V1 L2 B
## 40 69.30115 V1 L2 B
## 41 70.36132 V2 L1 A
## 42 67.16559 V2 L1 A
## 43 70.46225 V2 L1 A
## 44 66.56699 V2 L1 A
## 45 69.39718 V2 L1 A
## 46 67.64799 V2 L1 A
## 47 70.83207 V2 L1 A
## 48 69.70786 V2 L1 A
## 49 71.74424 V2 L1 A
## 50 69.38384 V2 L1 A
## 51 69.03722 V2 L1 B
## 52 72.97304 V2 L1 B
## 53 68.96537 V2 L1 B
## 54 73.27933 V2 L1 B
## 55 69.15313 V2 L1 B
## 56 72.51368 V2 L1 B
## 57 67.55527 V2 L1 B
## 58 69.36992 V2 L1 B
## 59 67.97955 V2 L1 B
## 60 70.85013 V2 L1 B
## 61 71.04904 V2 L2 A
## 62 70.41014 V2 L2 A
## 63 70.99828 V2 L2 A
## 64 71.33098 V2 L2 A
## 65 66.45227 V2 L2 A
## 66 70.13874 V2 L2 A
## 67 72.02532 V2 L2 A
## 68 70.70118 V2 L2 A
## 69 68.01788 V2 L2 A
## 70 69.91353 V2 L2 A
## 71 72.94702 V2 L2 B
## 72 72.50269 V2 L2 B
## 73 66.46316 V2 L2 B
## 74 69.94691 V2 L2 B
## 75 68.62457 V2 L2 B
## 76 71.55954 V2 L2 B
## 77 70.72958 V2 L2 B
## 78 67.55373 V2 L2 B
## 79 70.14681 V2 L2 B
## 80 68.43730 V2 L2 B
## 81 69.86100 V3 L1 A
## 82 73.08314 V3 L1 A
## 83 68.14168 V3 L1 A
## 84 70.40921 V3 L1 A
## 85 72.49029 V3 L1 A
## 86 70.73779 V3 L1 A
## 87 71.25077 V3 L1 A
## 88 70.25724 V3 L1 A
## 89 71.04440 V3 L1 A
## 90 68.63795 V3 L1 A
## 91 71.34470 V3 L1 B
## 92 74.57727 V3 L1 B
## 93 69.35732 V3 L1 B
## 94 69.49836 V3 L1 B
## 95 74.23016 V3 L1 B
## 96 68.56676 V3 L1 B
## 97 69.98838 V3 L1 B
## 98 68.38846 V3 L1 B
## 99 68.59635 V3 L1 B
## 100 66.78296 V3 L1 B
## 101 70.35337 V3 L2 A
## 102 67.78981 V3 L2 A
## 103 73.69663 V3 L2 A
## 104 70.10184 V3 L2 A
## 105 68.21259 V3 L2 A
## 106 73.92886 V3 L2 A
## 107 71.23719 V3 L2 A
## 108 73.02118 V3 L2 A
## 109 70.16699 V3 L2 A
## 110 73.22179 V3 L2 A
## 111 71.61555 V3 L2 B
## 112 71.13085 V3 L2 B
## 113 67.81338 V3 L2 B
## 114 68.82444 V3 L2 B
## 115 69.60822 V3 L2 B
## 116 68.35704 V3 L2 B
## 117 70.29335 V3 L2 B
## 118 67.95400 V3 L2 B
## 119 69.68343 V3 L2 B
## 120 68.81901 V3 L2 B
#with(data, aggregate(germ, list(var, horm, proc), mean)) #Igual que tapply
#tapply(data$germ, list(var, horm, proc), mean)
# H0: mu(V1)=mu(V2)=mu(V3)
modelo.3b=aov(germ~proc*var*horm, data=data)
summary(modelo.3b)
## Df Sum Sq Mean Sq F value Pr(>F)
## proc 1 0.1 0.114 0.027 0.8706
## var 2 4.4 2.177 0.511 0.6014
## horm 1 1.0 1.019 0.239 0.6258
## proc:var 2 0.6 0.281 0.066 0.9362
## proc:horm 1 19.9 19.891 4.669 0.0329 *
## var:horm 2 12.9 6.449 1.514 0.2247
## proc:var:horm 2 3.1 1.555 0.365 0.6951
## Residuals 108 460.1 4.260
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(modelo.3b)[[1]][["Pr(>F)"]][1] #Extracción del p-valor
## [1] 0.8705712
res.3b=modelo.3b$residuals
shapiro.test(res.3b) #Revisando normalidad
##
## Shapiro-Wilk normality test
##
## data: res.3b
## W = 0.98575, p-value = 0.2399
TukeyHSD(modelo.3b)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = germ ~ proc * var * horm, data = data)
##
## $proc
## diff lwr upr p adj
## L2-L1 0.06154587 -0.6854179 0.8085096 0.8705712
##
## $var
## diff lwr upr p adj
## V2-V1 -0.3185216 -1.4153374 0.7782942 0.7697491
## V3-V1 0.1359552 -0.9608606 1.2327710 0.9533145
## V3-V2 0.4544768 -0.6423390 1.5512926 0.5880822
##
## $horm
## diff lwr upr p adj
## B-A -0.1842813 -0.9312451 0.5626824 0.6258217
##
## $`proc:var`
## diff lwr upr p adj
## L2:V1-L1:V1 0.005234428 -1.888617 1.899086 1.0000000
## L1:V2-L1:V1 -0.440972119 -2.334823 1.452879 0.9842772
## L2:V2-L1:V1 -0.190836663 -2.084688 1.703015 0.9997053
## L1:V3-L1:V1 0.173938564 -1.719913 2.067790 0.9998131
## L2:V3-L1:V1 0.103206281 -1.790645 1.997058 0.9999859
## L1:V2-L2:V1 -0.446206547 -2.340058 1.447645 0.9834229
## L2:V2-L2:V1 -0.196071090 -2.089922 1.697780 0.9996636
## L1:V3-L2:V1 0.168704137 -1.725147 2.062556 0.9998392
## L2:V3-L2:V1 0.097971853 -1.795880 1.991823 0.9999891
## L2:V2-L1:V2 0.250135457 -1.643716 2.143987 0.9988996
## L1:V3-L1:V2 0.614910684 -1.278941 2.508762 0.9345755
## L2:V3-L1:V2 0.544178400 -1.349673 2.438030 0.9605720
## L1:V3-L2:V2 0.364775227 -1.529076 2.258627 0.9933959
## L2:V3-L2:V2 0.294042944 -1.599808 2.187894 0.9976080
## L2:V3-L1:V3 -0.070732283 -1.964584 1.823119 0.9999978
##
## $`proc:horm`
## diff lwr upr p adj
## L2:A-L1:A 0.8758206 -0.5148607 2.2665019 0.3589073
## L1:B-L1:A 0.6299934 -0.7606879 2.0206747 0.6394095
## L2:B-L1:A -0.1227355 -1.5134168 1.2679459 0.9956715
## L1:B-L2:A -0.2458272 -1.6365085 1.1448541 0.9672732
## L2:B-L2:A -0.9985561 -2.3892374 0.3921253 0.2454615
## L2:B-L1:B -0.7527289 -2.1434102 0.6379525 0.4944010
##
## $`var:horm`
## diff lwr upr p adj
## V2:A-V1:A -0.35366435 -2.2475157 1.540187 0.9942818
## V3:A-V1:A 0.81318764 -1.0806637 2.707039 0.8131646
## V1:B-V1:A 0.24377845 -1.6500729 2.137630 0.9990284
## V2:B-V1:A -0.03960041 -1.9334518 1.854251 0.9999999
## V3:B-V1:A -0.29749877 -2.1913501 1.596353 0.9974710
## V3:A-V2:A 1.16685199 -0.7269994 3.060703 0.4779654
## V1:B-V2:A 0.59744280 -1.2964086 2.491294 0.9418136
## V2:B-V2:A 0.31406394 -1.5797874 2.207915 0.9967287
## V3:B-V2:A 0.05616557 -1.8376858 1.950017 0.9999993
## V1:B-V3:A -0.56940919 -2.4632606 1.324442 0.9522942
## V2:B-V3:A -0.85278805 -2.7466394 1.041063 0.7808556
## V3:B-V3:A -1.11068642 -3.0045378 0.783165 0.5337270
## V2:B-V1:B -0.28337886 -2.1772302 1.610473 0.9979949
## V3:B-V1:B -0.54127723 -2.4351286 1.352574 0.9614560
## V3:B-V2:B -0.25789836 -2.1517497 1.635953 0.9987248
##
## $`proc:var:horm`
## diff lwr upr p adj
## L2:V1:A-L1:V1:A 1.26897946 -1.814921 4.352880 0.9659166
## L1:V2:A-L1:V1:A -0.10757616 -3.191477 2.976324 1.0000000
## L2:V2:A-L1:V1:A 0.66922693 -2.414674 3.753128 0.9998733
## L1:V3:A-L1:V1:A 1.15683776 -1.927063 4.240738 0.9829930
## L2:V3:A-L1:V1:A 1.73851698 -1.345384 4.822418 0.7666734
## L1:V1:B-L1:V1:A 1.50752348 -1.576377 4.591424 0.8928238
## L2:V1:B-L1:V1:A 0.24901288 -2.834888 3.332913 1.0000000
## L1:V2:B-L1:V1:A 0.73315541 -2.350745 3.817056 0.9996926
## L2:V2:B-L1:V1:A 0.45662323 -2.627277 3.540524 0.9999974
## L1:V3:B-L1:V1:A 0.69856285 -2.385338 3.782463 0.9998073
## L2:V3:B-L1:V1:A -0.02458094 -3.108482 3.059320 1.0000000
## L1:V2:A-L2:V1:A -1.37655562 -4.460456 1.707345 0.9399097
## L2:V2:A-L2:V1:A -0.59975253 -3.683653 2.484148 0.9999573
## L1:V3:A-L2:V1:A -0.11214170 -3.196042 2.971759 1.0000000
## L2:V3:A-L2:V1:A 0.46953752 -2.614363 3.553438 0.9999965
## L1:V1:B-L2:V1:A 0.23854402 -2.845357 3.322445 1.0000000
## L2:V1:B-L2:V1:A -1.01996658 -4.103867 2.063934 0.9938758
## L1:V2:B-L2:V1:A -0.53582405 -3.619725 2.548077 0.9999864
## L2:V2:B-L2:V1:A -0.81235623 -3.896257 2.271544 0.9991896
## L1:V3:B-L2:V1:A -0.57041661 -3.654317 2.513484 0.9999743
## L2:V3:B-L2:V1:A -1.29356040 -4.377461 1.790340 0.9608881
## L2:V2:A-L1:V2:A 0.77680309 -2.307098 3.860704 0.9994671
## L1:V3:A-L1:V2:A 1.26441393 -1.819487 4.348315 0.9667951
## L2:V3:A-L1:V2:A 1.84609315 -1.237807 4.929994 0.6924110
## L1:V1:B-L1:V2:A 1.61509965 -1.468801 4.699000 0.8406100
## L2:V1:B-L1:V2:A 0.35658904 -2.727312 3.440490 0.9999998
## L1:V2:B-L1:V2:A 0.84073157 -2.243169 3.924632 0.9988869
## L2:V2:B-L1:V2:A 0.56419939 -2.519701 3.648100 0.9999770
## L1:V3:B-L1:V2:A 0.80613901 -2.277762 3.890040 0.9992455
## L2:V3:B-L1:V2:A 0.08299523 -3.000905 3.166896 1.0000000
## L1:V3:A-L2:V2:A 0.48761084 -2.596290 3.571511 0.9999948
## L2:V3:A-L2:V2:A 1.06929006 -2.014611 4.153191 0.9909329
## L1:V1:B-L2:V2:A 0.83829656 -2.245604 3.922197 0.9989162
## L2:V1:B-L2:V2:A -0.42021405 -3.504115 2.663687 0.9999989
## L1:V2:B-L2:V2:A 0.06392848 -3.019972 3.147829 1.0000000
## L2:V2:B-L2:V2:A -0.21260370 -3.296504 2.871297 1.0000000
## L1:V3:B-L2:V2:A 0.02933592 -3.054565 3.113237 1.0000000
## L2:V3:B-L2:V2:A -0.69380786 -3.777708 2.390093 0.9998197
## L2:V3:A-L1:V3:A 0.58167922 -2.502221 3.665580 0.9999687
## L1:V1:B-L1:V3:A 0.35068572 -2.733215 3.434586 0.9999998
## L2:V1:B-L1:V3:A -0.90782488 -3.991725 2.176076 0.9977699
## L1:V2:B-L1:V3:A -0.42368235 -3.507583 2.660218 0.9999988
## L2:V2:B-L1:V3:A -0.70021453 -3.784115 2.383686 0.9998028
## L1:V3:B-L1:V3:A -0.45827491 -3.542176 2.625626 0.9999973
## L2:V3:B-L1:V3:A -1.18141870 -4.265319 1.902482 0.9799945
## L1:V1:B-L2:V3:A -0.23099350 -3.314894 2.852907 1.0000000
## L2:V1:B-L2:V3:A -1.48950410 -4.573405 1.594397 0.9003732
## L1:V2:B-L2:V3:A -1.00536157 -4.089262 2.078539 0.9945787
## L2:V2:B-L2:V3:A -1.28189375 -4.365794 1.802007 0.9633383
## L1:V3:B-L2:V3:A -1.03995413 -4.123855 2.043946 0.9927949
## L2:V3:B-L2:V3:A -1.76309792 -4.846999 1.320803 0.7503969
## L2:V1:B-L1:V1:B -1.25851060 -4.342411 1.825390 0.9679060
## L1:V2:B-L1:V1:B -0.77436808 -3.858269 2.309533 0.9994826
## L2:V2:B-L1:V1:B -1.05090025 -4.134801 2.033000 0.9921403
## L1:V3:B-L1:V1:B -0.80896063 -3.892861 2.274940 0.9992205
## L2:V3:B-L1:V1:B -1.53210442 -4.616005 1.551796 0.8819667
## L1:V2:B-L2:V1:B 0.48414253 -2.599758 3.568043 0.9999952
## L2:V2:B-L2:V1:B 0.20761035 -2.876290 3.291511 1.0000000
## L1:V3:B-L2:V1:B 0.44954997 -2.634351 3.533451 0.9999978
## L2:V3:B-L2:V1:B -0.27359382 -3.357494 2.810307 1.0000000
## L2:V2:B-L1:V2:B -0.27653218 -3.360433 2.807368 1.0000000
## L1:V3:B-L1:V2:B -0.03459256 -3.118493 3.049308 1.0000000
## L2:V3:B-L1:V2:B -0.75773635 -3.841637 2.326164 0.9995788
## L1:V3:B-L2:V2:B 0.24193962 -2.841961 3.325840 1.0000000
## L2:V3:B-L2:V2:B -0.48120417 -3.565105 2.602696 0.9999955
## L2:V3:B-L1:V3:B -0.72314379 -3.807044 2.360757 0.9997307