library(reshape2) # melt
library(MASS) # lda
library(psy) # cronbach
library(psych) # KMO
##
## Attaching package: 'psych'
## The following object is masked from 'package:psy':
##
## wkappa
library(Hmisc) # correlation matrix
## Warning: package 'Hmisc' was built under R version 3.4.2
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
## Loading required package: ggplot2
##
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
##
## %+%, alpha
##
## Attaching package: 'Hmisc'
## The following object is masked from 'package:psych':
##
## describe
## The following objects are masked from 'package:base':
##
## format.pval, round.POSIXt, trunc.POSIXt, units
library(psych) #KMO
library(Hmisc) # correlation matrix
cat("\014") # cleans screen
rm(list=ls(all=TRUE)) # remove variables in working memory
setwd("C:/Users/Erik Ernesto Vazquez/Downloads") # sets working directory
MainStudy<-read.csv("DataSetPretest.csv", header=T) # reads raw data from Qualtrics
MainStudy<-subset(MainStudy,MainStudy$Q23>0) ## Valid responses
## Reliability of Background Atmoshpherics measures urban/street
MainStudyMelt1BA<-melt(MainStudy,id.vars=c("ResponseId","Q13_1","Q33_1"),
measure.vars=c("Q13_1","Q33_1"),
variable.name="BA", value.name="Item1")
MainStudyMelt2BA<-melt(MainStudy,id.vars=c("ResponseId","Q13_4","Q33_4"),
measure.vars=c("Q13_4","Q13_4"),
variable.name="BA", value.name="Item2")
MainStudyMelt3BA<-melt(MainStudy,id.vars=c("ResponseId","Q13_5","Q33_5"),
measure.vars=c("Q13_5","Q13_5"),
variable.name="BA", value.name="Item3")
cronbach(cbind(MainStudyMelt1BA$Item1,MainStudyMelt2BA$Item2,MainStudyMelt3BA$Item3)) ## Cronbach 0.72
## $sample.size
## [1] 424
##
## $number.of.items
## [1] 3
##
## $alpha
## [1] 0.7204019
cronbach(cbind(MainStudyMelt2BA$Item2,MainStudyMelt3BA$Item3)) ## Cronbach 0.8786
## $sample.size
## [1] 424
##
## $number.of.items
## [1] 2
##
## $alpha
## [1] 0.8786803
## The photo above has urban/street aesthetics (4)
## The background style of the photo above is urban/street (5)
## Reliability of Background Atmoshpherics measures prof/studio
MainStudyMelt1BA<-melt(MainStudy,id.vars=c("ResponseId","Q13_2","Q33_2"),
measure.vars=c("Q13_2","Q33_2"),
variable.name="BA", value.name="Item1")
MainStudyMelt2BA<-melt(MainStudy,id.vars=c("ResponseId","Q13_3","Q33_3"),
measure.vars=c("Q13_3","Q13_3"),
variable.name="BA", value.name="Item2")
MainStudyMelt3BA<-melt(MainStudy,id.vars=c("ResponseId","Q13_6","Q33_6"),
measure.vars=c("Q13_6","Q13_6"),
variable.name="BA", value.name="Item3")
cronbach(cbind(MainStudyMelt1BA$Item1,MainStudyMelt2BA$Item2,MainStudyMelt3BA$Item3)) ## Cronbach 0.77
## $sample.size
## [1] 424
##
## $number.of.items
## [1] 3
##
## $alpha
## [1] 0.7728367
cronbach(cbind(MainStudyMelt2BA$Item2,MainStudyMelt3BA$Item3)) ## Cronbach 0.85
## $sample.size
## [1] 424
##
## $number.of.items
## [1] 2
##
## $alpha
## [1] 0.8514981
## The photo above has studio/professional aesthetics (3)
## The background style of the photo above is studio/professional (6)
## The highest from the both BA measures is that of urban/street, so,
## we will evaluate using those measures
## Reliability of Model Commoness measures
MainStudyMelt1MC<-melt(MainStudy,id.vars=c("ResponseId","Q17_1","Q37_1","Q40_1"),
measure.vars=c("Q17_1","Q37_1","Q40_1"),
variable.name="MC", value.name="Item1")
MainStudyMelt2MC<-melt(MainStudy,id.vars=c("ResponseId","Q17_2","Q37_2","Q40_2"),
measure.vars=c("Q17_2","Q37_2","Q40_2"),
variable.name="MC", value.name="Item2")
MainStudyMelt3MC<-melt(MainStudy,id.vars=c("ResponseId","Q17_3","Q37_3","Q40_3"),
measure.vars=c("Q17_3","Q37_3","Q40_3"),
variable.name="MC", value.name="Item3")
MainStudyMelt4MC<-melt(MainStudy,id.vars=c("ResponseId","Q17_6","Q37_6","Q40_6"),
measure.vars=c("Q17_6","Q37_6","Q40_6"),
variable.name="MC", value.name="Item4")
cronbach(cbind(MainStudyMelt1MC$Item1,MainStudyMelt2MC$Item2,MainStudyMelt3MC$Item3,MainStudyMelt4MC$Item4)) ## Cronbach 0.855
## $sample.size
## [1] 636
##
## $number.of.items
## [1] 4
##
## $alpha
## [1] 0.8558307
cronbach(cbind(MainStudy$Q19_1,MainStudy$Q19_2,MainStudy$Q19_3,MainStudy$Q19_4)) ## Authenticity Cronbach .92
## $sample.size
## [1] 212
##
## $number.of.items
## [1] 4
##
## $alpha
## [1] 0.928113
cronbach(cbind(MainStudy$Q18_1,MainStudy$Q18_2,MainStudy$Q18_3)) ## Purchase Intent .95
## $sample.size
## [1] 212
##
## $number.of.items
## [1] 3
##
## $alpha
## [1] 0.9592214
## Averages
MainStudy$BackgroundUrbanPhotoUrban<-(MainStudy$Q13_4+MainStudy$Q13_5)/2
MainStudy$BackgroundUrbanPhotoStudio<-(MainStudy$Q33_4+MainStudy$Q33_5)/2
MainStudy$ModelCommonessPhotoCommon<-(MainStudy$Q17_1+MainStudy$Q17_2+MainStudy$Q17_3+MainStudy$Q17_6)/4
MainStudy$ModelCommonessPhotoThin<-(MainStudy$Q37_1+MainStudy$Q37_2+MainStudy$Q37_3+MainStudy$Q37_6)/4
MainStudy$ModelCommonessPhotoOW<-(MainStudy$Q40_1+MainStudy$Q40_2+MainStudy$Q40_3+MainStudy$Q40_6)/4
summary(MainStudy)
## StartDate EndDate Status
## 10/10/2017 18:12: 3 10/10/2017 20:55: 3 Min. :0
## 10/10/2017 18:18: 3 10/10/2017 20:56: 3 1st Qu.:0
## 10/10/2017 20:50: 3 10/11/2017 2:53 : 3 Median :0
## 10/10/2017 20:51: 3 10/10/2017 18:15: 2 Mean :0
## 10/11/2017 2:45 : 3 10/10/2017 18:21: 2 3rd Qu.:0
## 10/10/2017 19:05: 2 10/10/2017 19:12: 2 Max. :0
## (Other) :195 (Other) :197
## IPAddress Progress Duration..in.seconds. Finished
## 103.25.44.2 : 7 Min. :100 Min. : 120.0 Min. :1
## 37.187.147.158 : 3 1st Qu.:100 1st Qu.: 191.5 1st Qu.:1
## 103.25.44.30 : 2 Median :100 Median : 255.0 Median :1
## 117.213.36.33 : 2 Mean :100 Mean : 384.2 Mean :1
## 157.50.22.36 : 2 3rd Qu.:100 3rd Qu.: 346.2 3rd Qu.:1
## 101.100.169.163: 1 Max. :100 Max. :8576.0 Max. :1
## (Other) :195
## RecordedDate ResponseId RecipientLastName
## 10/10/2017 20:55: 3 R_0ieuzoFFIvgBtCN: 1 Mode:logical
## 10/10/2017 20:56: 3 R_0In7CgSbEOgdst3: 1 NA's:212
## 10/11/2017 2:53 : 3 R_0kffRK83bUuFDwt: 1
## 10/10/2017 18:15: 2 R_10wSeDmahwyPdns: 1
## 10/10/2017 18:21: 2 R_12f1jrwrXArmrrl: 1
## 10/10/2017 19:12: 2 R_12GsZl8WqhIwMvn: 1
## (Other) :197 (Other) :206
## RecipientFirstName RecipientEmail ExternalReference LocationLatitude
## Mode:logical Mode:logical Mode:logical Min. : 1.00
## NA's:212 NA's:212 NA's:212 1st Qu.:13.08
## Median :28.67
## Mean :26.62
## 3rd Qu.:39.15
## Max. :56.74
##
## LocationLongitude DistributionChannel UserLanguage Q1
## Min. :-157.839 anonymous:212 : 4 Min. :2
## 1st Qu.: -84.308 EN:208 1st Qu.:2
## Median : 2.339 Median :2
## Mean : -6.852 Mean :2
## 3rd Qu.: 77.621 3rd Qu.:2
## Max. : 121.061 Max. :2
##
## Q2 Q13_1 Q13_2 Q13_3
## Min. :2 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:3.000
## Median :2 Median :4.000 Median :4.000 Median :4.000
## Mean :2 Mean :4.222 Mean :4.415 Mean :4.627
## 3rd Qu.:2 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.250
## Max. :2 Max. :9.000 Max. :9.000 Max. :9.000
##
## Q13_4 Q13_5 Q13_6 Q27_First.Click
## Min. :1.000 Min. :1.000 Min. :1.000 Min. : 0.024
## 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.000 1st Qu.: 2.138
## Median :4.000 Median :4.000 Median :5.000 Median : 5.896
## Mean :4.236 Mean :4.217 Mean :4.953 Mean : 8.682
## 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:7.000 3rd Qu.:11.356
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :66.995
##
## Q27_Last.Click Q27_Page.Submit Q27_Click.Count Q33_1
## Min. : 2.284 Min. : 15.71 Min. : 1.00 Min. :1.000
## 1st Qu.: 14.226 1st Qu.: 17.53 1st Qu.: 6.00 1st Qu.:3.000
## Median : 24.482 Median : 27.85 Median : 8.00 Median :6.000
## Mean : 31.290 Mean : 36.28 Mean :10.77 Mean :5.741
## 3rd Qu.: 38.674 3rd Qu.: 41.22 3rd Qu.:11.00 3rd Qu.:8.000
## Max. :453.643 Max. :455.13 Max. :58.00 Max. :9.000
##
## Q33_2 Q33_3 Q33_4 Q33_5
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:3.00
## Median :3.500 Median :4.000 Median :6.000 Median :6.00
## Mean :3.995 Mean :4.156 Mean :5.599 Mean :5.83
## 3rd Qu.:5.000 3rd Qu.:6.000 3rd Qu.:8.000 3rd Qu.:9.00
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :9.00
##
## Q33_6 Q28_First.Click Q28_Last.Click Q28_Page.Submit
## Min. :1.000 Min. : 0.025 Min. : 2.421 Min. : 15.65
## 1st Qu.:2.000 1st Qu.: 2.418 1st Qu.: 13.430 1st Qu.: 17.38
## Median :4.000 Median : 6.284 Median : 21.818 Median : 24.54
## Mean :4.198 Mean : 8.879 Mean : 27.655 Mean : 32.06
## 3rd Qu.:6.000 3rd Qu.: 9.578 3rd Qu.: 34.772 3rd Qu.: 36.60
## Max. :9.000 Max. :337.450 Max. :344.416 Max. :345.63
##
## Q28_Click.Count Q17_1 Q17_2 Q17_3
## Min. : 1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.: 6.00 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
## Median : 7.00 Median :5.000 Median :4.000 Median :4.000
## Mean :10.66 Mean :5.024 Mean :4.514 Mean :4.349
## 3rd Qu.:11.00 3rd Qu.:7.000 3rd Qu.:6.000 3rd Qu.:6.000
## Max. :55.00 Max. :9.000 Max. :9.000 Max. :9.000
##
## Q17_4 Q17_5 Q17_6 Q29_First.Click
## Min. :1.00 Min. :1.000 Min. :1.000 Min. : 0.160
## 1st Qu.:3.75 1st Qu.:5.000 1st Qu.:3.000 1st Qu.: 2.392
## Median :5.00 Median :8.000 Median :5.000 Median : 6.074
## Mean :5.25 Mean :6.778 Mean :4.844 Mean : 8.495
## 3rd Qu.:7.00 3rd Qu.:9.000 3rd Qu.:7.000 3rd Qu.: 9.069
## Max. :9.00 Max. :9.000 Max. :9.000 Max. :119.381
##
## Q29_Last.Click Q29_Page.Submit Q29_Click.Count Q37_1
## Min. : 2.119 Min. : 15.70 Min. : 1.00 Min. :1.000
## 1st Qu.: 15.516 1st Qu.: 17.82 1st Qu.: 6.00 1st Qu.:3.000
## Median : 24.754 Median : 27.47 Median : 7.00 Median :5.000
## Mean : 30.910 Mean : 43.14 Mean :10.12 Mean :5.241
## 3rd Qu.: 35.372 3rd Qu.: 37.77 3rd Qu.:10.00 3rd Qu.:8.000
## Max. :563.095 Max. :1716.94 Max. :38.00 Max. :9.000
##
## Q37_2 Q37_3 Q37_4 Q37_5
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:4.000
## Median :5.000 Median :5.000 Median :4.000 Median :8.000
## Mean :4.882 Mean :4.689 Mean :4.642 Mean :6.472
## 3rd Qu.:7.000 3rd Qu.:7.000 3rd Qu.:6.000 3rd Qu.:9.000
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :9.000
##
## Q37_6 Q30_First.Click Q30_Last.Click Q30_Page.Submit
## Min. :1.000 Min. : 0.000 Min. : 0.00 Min. : 15.68
## 1st Qu.:3.000 1st Qu.: 2.288 1st Qu.: 12.62 1st Qu.: 18.34
## Median :5.000 Median : 5.284 Median : 25.51 Median : 27.72
## Mean :5.113 Mean : 8.083 Mean : 29.85 Mean : 33.89
## 3rd Qu.:7.000 3rd Qu.: 9.014 3rd Qu.: 34.98 3rd Qu.: 37.38
## Max. :9.000 Max. :286.460 Max. :342.58 Max. :344.11
##
## Q30_Click.Count Q40_1 Q40_2 Q40_3
## Min. : 0.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.: 6.00 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.000
## Median : 7.00 Median :4.000 Median :4.000 Median :4.000
## Mean :10.45 Mean :4.538 Mean :3.915 Mean :4.269
## 3rd Qu.:10.00 3rd Qu.:6.000 3rd Qu.:5.000 3rd Qu.:6.000
## Max. :55.00 Max. :9.000 Max. :9.000 Max. :9.000
##
## Q40_4 Q40_5 Q40_6 Q31_First.Click
## Min. :1.000 Min. :1.000 Min. :1.000 Min. : 0.000
## 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:3.000 1st Qu.: 2.219
## Median :7.000 Median :6.000 Median :4.000 Median : 6.423
## Mean :6.127 Mean :5.632 Mean :4.146 Mean : 9.606
## 3rd Qu.:8.000 3rd Qu.:8.000 3rd Qu.:5.250 3rd Qu.: 10.302
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :391.058
##
## Q31_Last.Click Q31_Page.Submit Q31_Click.Count Q19_1
## Min. : 0.00 Min. : 15.65 Min. : 0.00 Min. :1.000
## 1st Qu.: 16.29 1st Qu.: 19.41 1st Qu.: 6.00 1st Qu.:3.000
## Median : 27.67 Median : 30.70 Median : 8.00 Median :4.000
## Mean : 32.27 Mean : 36.89 Mean :10.68 Mean :4.028
## 3rd Qu.: 38.96 3rd Qu.: 41.97 3rd Qu.:11.00 3rd Qu.:5.000
## Max. :396.40 Max. :397.78 Max. :56.00 Max. :9.000
##
## Q19_2 Q19_3 Q19_4 Q18_1
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.000
## Median :4.000 Median :4.000 Median :4.000 Median :5.000
## Mean :4.019 Mean :4.462 Mean :3.972 Mean :5.274
## 3rd Qu.:5.000 3rd Qu.:6.000 3rd Qu.:5.000 3rd Qu.:8.000
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :9.000
##
## Q18_2 Q18_3 Q20 Q21
## Min. :1.000 Min. :1.000 Min. :1.000 Min. : 2.0
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:11.0
## Median :5.000 Median :5.000 Median :3.000 Median :12.0
## Mean :5.108 Mean :5.005 Mean :3.519 Mean :11.3
## 3rd Qu.:7.000 3rd Qu.:7.000 3rd Qu.:5.000 3rd Qu.:12.0
## Max. :9.000 Max. :9.000 Max. :9.000 Max. :15.0
##
## Q22 Q23 Q24 Q24_6_TEXT Q25
## 2 :74 Min. :1.000 Min. :1.000 :178 1990 : 16
## 1 :68 1st Qu.:1.000 1st Qu.:1.000 Asian : 8 1991 : 16
## 3 :44 Median :1.000 Median :3.000 Indian : 8 1992 : 16
## 4 :12 Mean :1.052 Mean :3.269 asian : 3 1989 : 14
## 5 : 6 3rd Qu.:1.000 3rd Qu.:5.000 indian : 3 1985 : 11
## 6 : 4 Max. :2.000 Max. :6.000 India : 2 1983 : 10
## (Other): 4 (Other): 10 (Other):129
## Q26 Q26_8_TEXT BackgroundUrbanPhotoUrban
## 1,4,6 : 18 :199 Min. :1.000
## 2,3,4,6 : 16 Twitter : 3 1st Qu.:2.500
## 4 : 14 twitter : 2 Median :4.000
## 4,6 : 13 Whatsapp: 2 Mean :4.226
## 1,2,3,4,5,6: 12 Ravelry : 1 3rd Qu.:5.500
## 1,2,3,4,6 : 11 tumblr : 1 Max. :9.000
## (Other) :128 (Other) : 4
## BackgroundUrbanPhotoStudio ModelCommonessPhotoCommon
## Min. :1.000 Min. :1.000
## 1st Qu.:3.500 1st Qu.:3.250
## Median :5.500 Median :4.750
## Mean :5.715 Mean :4.683
## 3rd Qu.:8.500 3rd Qu.:6.000
## Max. :9.000 Max. :9.000
##
## ModelCommonessPhotoThin ModelCommonessPhotoOW
## Min. :1.000 Min. :1.000
## 1st Qu.:3.500 1st Qu.:3.000
## Median :5.250 Median :4.000
## Mean :4.981 Mean :4.217
## 3rd Qu.:6.500 3rd Qu.:5.250
## Max. :9.000 Max. :8.750
##
## Mainipulation Check / Pretest 1
t.test(MainStudy$BackgroundUrbanPhotoUrban,MainStudy$BackgroundUrbanPhotoStudio,paired=T) ## significant difference between the two backgrounds
##
## Paired t-test
##
## data: MainStudy$BackgroundUrbanPhotoUrban and MainStudy$BackgroundUrbanPhotoStudio
## t = -6.3464, df = 211, p-value = 1.325e-09
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.950461 -1.025954
## sample estimates:
## mean of the differences
## -1.488208
t.test(MainStudy$ModelCommonessPhotoCommon,MainStudy$ModelCommonessPhotoThin,paired=T) ## significant difference between the thin model and normal model
##
## Paired t-test
##
## data: MainStudy$ModelCommonessPhotoCommon and MainStudy$ModelCommonessPhotoThin
## t = -3.118, df = 211, p-value = 0.002075
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4869742 -0.1097239
## sample estimates:
## mean of the differences
## -0.2983491
t.test(MainStudy$ModelCommonessPhotoCommon,MainStudy$ModelCommonessPhotoOW,paired=T) ## significant difference between the overweight model and normal model
##
## Paired t-test
##
## data: MainStudy$ModelCommonessPhotoCommon and MainStudy$ModelCommonessPhotoOW
## t = 3.2736, df = 211, p-value = 0.001241
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.1853058 0.7462980
## sample estimates:
## mean of the differences
## 0.4658019
# VALIDITY all variables
validity<-cbind(MainStudy$Q13_4,MainStudy$Q13_5,
MainStudy$Q17_1,MainStudy$Q17_2,MainStudy$Q17_3,MainStudy$Q17_4,
MainStudy$Q19_1,MainStudy$Q19_2,MainStudy$Q19_3,MainStudy$Q19_4,
MainStudy$Q18_1,MainStudy$Q18_2,MainStudy$Q18_3)
factanal(validity,4,rotation="varimax") ## 4 factors explain more than 70% of the variance
##
## Call:
## factanal(x = validity, factors = 4, rotation = "varimax")
##
## Uniquenesses:
## [1] 0.005 0.362 0.684 0.460 0.005 0.869 0.126 0.269 0.320 0.102 0.116
## [12] 0.083 0.133
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4
## [1,] 0.132 0.987
## [2,] 0.227 0.765
## [3,] 0.471 0.292
## [4,] 0.161 0.305 0.647
## [5,] 0.217 0.211 0.950
## [6,] 0.251 -0.236
## [7,] 0.881 0.210 0.178 0.146
## [8,] 0.780 0.176 0.157 0.259
## [9,] 0.679 0.447 0.102
## [10,] 0.893 0.233 0.166 0.131
## [11,] 0.356 0.856 0.153
## [12,] 0.353 0.871 0.186
## [13,] 0.377 0.836 0.158
##
## Factor1 Factor2 Factor3 Factor4
## SS loadings 3.191 2.946 1.669 1.659
## Proportion Var 0.245 0.227 0.128 0.128
## Cumulative Var 0.245 0.472 0.600 0.728
##
## Test of the hypothesis that 4 factors are sufficient.
## The chi square statistic is 50.24 on 32 degrees of freedom.
## The p-value is 0.0212
KMO(validity)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = validity)
## Overall MSA = 0.85
## MSA for each item =
## [1] 0.61 0.61 0.91 0.80 0.78 0.57 0.86 0.89 0.93 0.86 0.89 0.86 0.90
summary(prcomp(validity)) ## 4 components explain more than 80% of the variance
## Importance of components%s:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 5.5267 3.1664 2.6467 2.39744 1.89055 1.77853
## Proportion of Variance 0.4598 0.1509 0.1055 0.08653 0.05381 0.04762
## Cumulative Proportion 0.4598 0.6108 0.7162 0.80274 0.85655 0.90417
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 1.23423 1.06517 1.04831 0.95885 0.86186 0.7199
## Proportion of Variance 0.02293 0.01708 0.01654 0.01384 0.01118 0.0078
## Cumulative Proportion 0.92710 0.94418 0.96072 0.97456 0.98575 0.9936
## PC13
## Standard deviation 0.65460
## Proportion of Variance 0.00645
## Cumulative Proportion 1.00000
screeplot(prcomp(validity),type="lines")
biplot(prcomp(validity,scale.=T),cex=0.8,xlabs=rep(".",nrow(validity)))
rcorr(as.matrix(validity))
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 1.00 0.78 0.08 0.10 0.09 0.10 0.31 0.27 0.22 0.30 0.08 0.09
## [2,] 0.78 1.00 0.02 0.08 0.10 0.02 0.32 0.35 0.20 0.33 0.04 0.06
## [3,] 0.08 0.02 1.00 0.41 0.40 0.06 0.22 0.18 0.37 0.24 0.47 0.49
## [4,] 0.10 0.08 0.41 1.00 0.72 -0.06 0.33 0.34 0.35 0.29 0.42 0.44
## [5,] 0.09 0.10 0.40 0.72 1.00 -0.18 0.38 0.46 0.34 0.37 0.40 0.44
## [6,] 0.10 0.02 0.06 -0.06 -0.18 1.00 -0.03 -0.07 0.08 0.00 0.18 0.12
## [7,] 0.31 0.32 0.22 0.33 0.38 -0.03 1.00 0.77 0.74 0.89 0.52 0.52
## [8,] 0.27 0.35 0.18 0.34 0.46 -0.07 0.77 1.00 0.67 0.80 0.46 0.46
## [9,] 0.22 0.20 0.37 0.35 0.34 0.08 0.74 0.67 1.00 0.72 0.65 0.63
## [10,] 0.30 0.33 0.24 0.29 0.37 0.00 0.89 0.80 0.72 1.00 0.53 0.54
## [11,] 0.08 0.04 0.47 0.42 0.40 0.18 0.52 0.46 0.65 0.53 1.00 0.90
## [12,] 0.09 0.06 0.49 0.44 0.44 0.12 0.52 0.46 0.63 0.54 0.90 1.00
## [13,] 0.13 0.09 0.47 0.41 0.41 0.17 0.53 0.51 0.65 0.56 0.87 0.89
## [,13]
## [1,] 0.13
## [2,] 0.09
## [3,] 0.47
## [4,] 0.41
## [5,] 0.41
## [6,] 0.17
## [7,] 0.53
## [8,] 0.51
## [9,] 0.65
## [10,] 0.56
## [11,] 0.87
## [12,] 0.89
## [13,] 1.00
##
## n= 212
##
##
## P
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 0.0000 0.2474 0.1635 0.1734 0.1429 0.0000 0.0000 0.0012
## [2,] 0.0000 0.7273 0.2537 0.1639 0.7462 0.0000 0.0000 0.0030
## [3,] 0.2474 0.7273 0.0000 0.0000 0.4000 0.0015 0.0075 0.0000
## [4,] 0.1635 0.2537 0.0000 0.0000 0.3553 0.0000 0.0000 0.0000
## [5,] 0.1734 0.1639 0.0000 0.0000 0.0087 0.0000 0.0000 0.0000
## [6,] 0.1429 0.7462 0.4000 0.3553 0.0087 0.6433 0.3058 0.2241
## [7,] 0.0000 0.0000 0.0015 0.0000 0.0000 0.6433 0.0000 0.0000
## [8,] 0.0000 0.0000 0.0075 0.0000 0.0000 0.3058 0.0000 0.0000
## [9,] 0.0012 0.0030 0.0000 0.0000 0.0000 0.2241 0.0000 0.0000
## [10,] 0.0000 0.0000 0.0004 0.0000 0.0000 0.9499 0.0000 0.0000 0.0000
## [11,] 0.2234 0.5187 0.0000 0.0000 0.0000 0.0095 0.0000 0.0000 0.0000
## [12,] 0.2140 0.3791 0.0000 0.0000 0.0000 0.0735 0.0000 0.0000 0.0000
## [13,] 0.0564 0.2101 0.0000 0.0000 0.0000 0.0157 0.0000 0.0000 0.0000
## [,10] [,11] [,12] [,13]
## [1,] 0.0000 0.2234 0.2140 0.0564
## [2,] 0.0000 0.5187 0.3791 0.2101
## [3,] 0.0004 0.0000 0.0000 0.0000
## [4,] 0.0000 0.0000 0.0000 0.0000
## [5,] 0.0000 0.0000 0.0000 0.0000
## [6,] 0.9499 0.0095 0.0735 0.0157
## [7,] 0.0000 0.0000 0.0000 0.0000
## [8,] 0.0000 0.0000 0.0000 0.0000
## [9,] 0.0000 0.0000 0.0000 0.0000
## [10,] 0.0000 0.0000 0.0000
## [11,] 0.0000 0.0000 0.0000
## [12,] 0.0000 0.0000 0.0000
## [13,] 0.0000 0.0000 0.0000
# VALIDITY without purchase intent
validity<-cbind(MainStudy$Q13_4,MainStudy$Q13_5,
MainStudy$Q17_1,MainStudy$Q17_2,MainStudy$Q17_3,
MainStudy$Q19_1,MainStudy$Q19_2,MainStudy$Q19_4)
factanal(validity,3,rotation="varimax") ## 3 factors explain more than 70% of the variance
##
## Call:
## factanal(x = validity, factors = 3, rotation = "varimax")
##
## Uniquenesses:
## [1] 0.381 0.005 0.778 0.304 0.253 0.154 0.286 0.064
##
## Loadings:
## Factor1 Factor2 Factor3
## [1,] 0.178 0.766
## [2,] 0.176 0.982
## [3,] 0.152 0.446
## [4,] 0.137 0.822
## [5,] 0.222 0.834
## [6,] 0.876 0.228 0.165
## [7,] 0.760 0.301 0.214
## [8,] 0.934 0.191 0.164
##
## Factor1 Factor2 Factor3
## SS loadings 2.371 1.750 1.655
## Proportion Var 0.296 0.219 0.207
## Cumulative Var 0.296 0.515 0.722
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 16.33 on 7 degrees of freedom.
## The p-value is 0.0223
KMO(validity)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = validity)
## Overall MSA = 0.73
## MSA for each item =
## [1] 0.60 0.61 0.81 0.69 0.72 0.77 0.86 0.74
summary(prcomp(validity)) ## 3 components explain more than 80% of the variance
## Importance of components%s:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 4.0236 2.8915 2.3136 1.88315 1.15895 1.05199 0.9147
## Proportion of Variance 0.4354 0.2248 0.1440 0.09537 0.03612 0.02976 0.0225
## Cumulative Proportion 0.4354 0.6603 0.8042 0.89957 0.93570 0.96546 0.9880
## PC8
## Standard deviation 0.66917
## Proportion of Variance 0.01204
## Cumulative Proportion 1.00000
screeplot(prcomp(validity),type="lines")
biplot(prcomp(validity,scale.=T),cex=0.8,xlabs=rep(".",nrow(validity)))
rcorr(as.matrix(validity))
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 1.00 0.78 0.08 0.10 0.09 0.31 0.27 0.30
## [2,] 0.78 1.00 0.02 0.08 0.10 0.32 0.35 0.33
## [3,] 0.08 0.02 1.00 0.41 0.40 0.22 0.18 0.24
## [4,] 0.10 0.08 0.41 1.00 0.72 0.33 0.34 0.29
## [5,] 0.09 0.10 0.40 0.72 1.00 0.38 0.46 0.37
## [6,] 0.31 0.32 0.22 0.33 0.38 1.00 0.77 0.89
## [7,] 0.27 0.35 0.18 0.34 0.46 0.77 1.00 0.80
## [8,] 0.30 0.33 0.24 0.29 0.37 0.89 0.80 1.00
##
## n= 212
##
##
## P
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 0.0000 0.2474 0.1635 0.1734 0.0000 0.0000 0.0000
## [2,] 0.0000 0.7273 0.2537 0.1639 0.0000 0.0000 0.0000
## [3,] 0.2474 0.7273 0.0000 0.0000 0.0015 0.0075 0.0004
## [4,] 0.1635 0.2537 0.0000 0.0000 0.0000 0.0000 0.0000
## [5,] 0.1734 0.1639 0.0000 0.0000 0.0000 0.0000 0.0000
## [6,] 0.0000 0.0000 0.0015 0.0000 0.0000 0.0000 0.0000
## [7,] 0.0000 0.0000 0.0075 0.0000 0.0000 0.0000 0.0000
## [8,] 0.0000 0.0000 0.0004 0.0000 0.0000 0.0000 0.0000