Recommandation et transparence
CB
17 octobre 2019
This document is writen with rmarkdown and contain computations relative to a small experiment about algorithmic transparency policy. The reference paper is available here
The first chunk load the package we will need and include main variable recoding.
Elementary Statistics
We will use ggplot2
#create concept scores for multi-items measurement
reco_a$Confiance <- (reco_a$C_Bienveillance + reco_a$C_Competence + reco_a$C_Donnees.navigation + reco_a$C_Ethique + reco_a$C_Infos.perso)/5
reco_a$Satisfaction <- (reco_a$S_Interesse.par.produits.reco+
reco_a$S_Promoter.score+
reco_a$S_Recos.repondent.aux.besoins+
reco_a$S_Satisfaction.globale+reco_a$S_Tentation.d.achat)/5
reco_a$Understanding <- (reco_a$U_Comment+ reco_a$U_Interets+ reco_a$U_pourquoi+ reco_a$U_Technique)/4
#basic statistic with rcmdr
numSummary(reco_a[,c("Confiance", "Satisfaction", "Understanding"), drop=FALSE], statistics=c("mean", "sd", "cv"))## mean sd cv n
## Confiance 3.788462 0.8264391 0.2181463 52
## Satisfaction 4.126923 0.7441577 0.1803178 52
## Understanding 4.495192 0.8945510 0.1990017 52#comparing empirical and theoretical distribution ( density function)
g1<-ggplot(data = reco_a, aes(x=Confiance))+geom_density(fill="pink")+theme_minimal()
g1
g1 <- g1 + stat_function(fun=dnorm, color="red", args=list(mean=mean(reco_a$Confiance),
sd=sd(reco_a$Confiance)))
g1
#comparing distribution per group
g2<-ggplot(data = reco_a, aes(x=Transparence_Nominale,y=Confiance))+geom_violin()
g2
Dependant<-subset(reco_a,select=c(Confiance,Satisfaction,Understanding))
Dependant<-melt(data = Dependant)## No id variables; using all as measure variablesggplot(Dependant, aes(x = value, fill = variable)) + geom_density(alpha = 0.2)
Analyse bivariée
t test
the elementary bivariate analysis is a comparaison of two groups and is better if we test the difference. For a detailed presentation see https://uc-r.github.io/t_test
reco_a$Sexe2<-as.factor(reco_a$Sexe)
with(reco_a, plotMeans(C_Ethique, Sexe2, error.bars="se", connect=TRUE)) #with Rcmdr
t.test(C_Ethique~Sexe, alternative='two.sided', conf.level=.95, var.equal=FALSE, data=reco_a)##
## Welch Two Sample t-test
##
## data: C_Ethique by Sexe
## t = 2.0714, df = 45.122, p-value = 0.04407
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.0125981 0.8964928
## sample estimates:
## mean in group Feminin mean in group Masculin
## 3.500000 3.045455ANOVA
ANOVA is a kind of generalization of the 2-group comparisons
for details : https://bioinformatics-core-shared-training.github.io/linear-models-r/ANOVA.html
AnovaModel.1 <- aov(Satisfaction ~ Transparence_Nominale, data=reco_a)
summary(AnovaModel.1)## Df Sum Sq Mean Sq F value Pr(>F)
## Transparence_Nominale 2 4.302 2.1512 4.403 0.0174 *
## Residuals 49 23.940 0.4886
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1with(reco_a, numSummary(Satisfaction, groups=Transparence_Nominale,
statistics=c("mean", "sd")))## mean sd data:n
## 1-Aucune 4.047059 0.4718549 17
## 2-Moderee 4.500000 0.7798944 18
## 3-Forte 3.811765 0.7920561 17the test is significant à the 95% level of confidence, so we can analyse the difference. The following plot compare means of the 3 variables for the three treatments and give confidence intervals.
#preparing the data
means<- aggregate(cbind(Confiance, Satisfaction, Understanding) ~ Transparence_Nominale, data=reco_a, FUN="mean")
Sd<- aggregate(cbind(Confiance, Satisfaction, Understanding) ~ Transparence_Nominale, data=reco_a, FUN="sd")
meansM <- melt(means, id=c("Transparence_Nominale"))
SdM <- melt(Sd, id=c("Transparence_Nominale"))
SdM$sd<-SdM$value
SdM<-subset(SdM,select=c(sd))
meansM<-cbind(meansM,SdM)
#making the chart
g<- ggplot(meansM, aes(x=Transparence_Nominale, y=value, fill=variable))
g<-g+geom_bar(stat="identity", color="black", position=position_dodge())
g
g<-g+geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.2,
position=position_dodge(.9)) + labs(title="Response to transparency",x="Transparence_Nominale", y = "valeur")+ theme_classic() + scale_fill_manual(values=c('#999999','#E69F00', '#c62e0d'))
g
Correlations
for a definition of correlation see : http://www.r-tutor.com/elementary-statistics/numerical-measures/correlation-coefficient
in the following chart we represent correlation between Confiance and Satisfaction as an xy chart as a linear function (y=ax+b). Confidence intervals are represented in the grey area. We add a non linear function ( loess) in red.
ggplot(reco_a, aes(x=Confiance, y=Satisfaction)) + geom_point()+ geom_smooth(method='lm')+geom_smooth(method='gam',color="red")
M<-cor(reco_a[,c("Confiance","Satisfaction","Understanding")], use="complete")
M## Confiance Satisfaction Understanding
## Confiance 1.0000000 0.5979953 0.7107255
## Satisfaction 0.5979953 1.0000000 0.4339238
## Understanding 0.7107255 0.4339238 1.0000000corrplot(M, method="color",type="lower", order="hclust")
When we need to compute a large number of correlation, it is usefull to visualize the large matrix. In this case line and column are rearranged with the clustering function “hclust”.
read also https://rstudio-pubs-static.s3.amazonaws.com/240657_5157ff98e8204c358b2118fa69162e18.html
Mcorr <- subset(reco_a, select=c(C_Bienveillance, C_Competence, C_Donnees.navigation, C_Ethique, C_Infos.perso, C_Securite, S_Interesse.par.produits.reco, S_Promoter.score,S_Recos.repondent.aux.besoins, S_Satisfaction.globale, S_Tentation.d.achat, Transparence_Numerique, U_Comment, U_Interets,U_pourquoi,U_Technique))
M<-round(cor(Mcorr),2)
M## C_Bienveillance C_Competence
## C_Bienveillance 1.00 0.66
## C_Competence 0.66 1.00
## C_Donnees.navigation 0.59 0.76
## C_Ethique 0.67 0.64
## C_Infos.perso 0.59 0.70
## C_Securite 0.47 0.59
## S_Interesse.par.produits.reco 0.26 0.32
## S_Promoter.score 0.48 0.49
## S_Recos.repondent.aux.besoins 0.35 0.50
## S_Satisfaction.globale 0.49 0.51
## S_Tentation.d.achat 0.37 0.45
## Transparence_Numerique -0.21 -0.14
## U_Comment 0.52 0.59
## U_Interets 0.53 0.53
## U_pourquoi 0.46 0.54
## U_Technique 0.50 0.62
## C_Donnees.navigation C_Ethique C_Infos.perso
## C_Bienveillance 0.59 0.67 0.59
## C_Competence 0.76 0.64 0.70
## C_Donnees.navigation 1.00 0.63 0.86
## C_Ethique 0.63 1.00 0.59
## C_Infos.perso 0.86 0.59 1.00
## C_Securite 0.50 0.56 0.41
## S_Interesse.par.produits.reco 0.37 0.36 0.23
## S_Promoter.score 0.47 0.61 0.51
## S_Recos.repondent.aux.besoins 0.47 0.54 0.44
## S_Satisfaction.globale 0.58 0.63 0.50
## S_Tentation.d.achat 0.40 0.38 0.34
## Transparence_Numerique -0.11 -0.39 -0.05
## U_Comment 0.69 0.38 0.65
## U_Interets 0.69 0.41 0.68
## U_pourquoi 0.64 0.32 0.59
## U_Technique 0.65 0.41 0.57
## C_Securite S_Interesse.par.produits.reco
## C_Bienveillance 0.47 0.26
## C_Competence 0.59 0.32
## C_Donnees.navigation 0.50 0.37
## C_Ethique 0.56 0.36
## C_Infos.perso 0.41 0.23
## C_Securite 1.00 0.45
## S_Interesse.par.produits.reco 0.45 1.00
## S_Promoter.score 0.47 0.49
## S_Recos.repondent.aux.besoins 0.51 0.64
## S_Satisfaction.globale 0.49 0.59
## S_Tentation.d.achat 0.60 0.71
## Transparence_Numerique -0.12 -0.26
## U_Comment 0.31 0.36
## U_Interets 0.38 0.38
## U_pourquoi 0.30 0.29
## U_Technique 0.50 0.35
## S_Promoter.score
## C_Bienveillance 0.48
## C_Competence 0.49
## C_Donnees.navigation 0.47
## C_Ethique 0.61
## C_Infos.perso 0.51
## C_Securite 0.47
## S_Interesse.par.produits.reco 0.49
## S_Promoter.score 1.00
## S_Recos.repondent.aux.besoins 0.69
## S_Satisfaction.globale 0.58
## S_Tentation.d.achat 0.68
## Transparence_Numerique -0.09
## U_Comment 0.28
## U_Interets 0.43
## U_pourquoi 0.32
## U_Technique 0.20
## S_Recos.repondent.aux.besoins
## C_Bienveillance 0.35
## C_Competence 0.50
## C_Donnees.navigation 0.47
## C_Ethique 0.54
## C_Infos.perso 0.44
## C_Securite 0.51
## S_Interesse.par.produits.reco 0.64
## S_Promoter.score 0.69
## S_Recos.repondent.aux.besoins 1.00
## S_Satisfaction.globale 0.61
## S_Tentation.d.achat 0.66
## Transparence_Numerique -0.28
## U_Comment 0.36
## U_Interets 0.44
## U_pourquoi 0.36
## U_Technique 0.38
## S_Satisfaction.globale S_Tentation.d.achat
## C_Bienveillance 0.49 0.37
## C_Competence 0.51 0.45
## C_Donnees.navigation 0.58 0.40
## C_Ethique 0.63 0.38
## C_Infos.perso 0.50 0.34
## C_Securite 0.49 0.60
## S_Interesse.par.produits.reco 0.59 0.71
## S_Promoter.score 0.58 0.68
## S_Recos.repondent.aux.besoins 0.61 0.66
## S_Satisfaction.globale 1.00 0.64
## S_Tentation.d.achat 0.64 1.00
## Transparence_Numerique -0.18 0.05
## U_Comment 0.31 0.29
## U_Interets 0.38 0.35
## U_pourquoi 0.34 0.29
## U_Technique 0.30 0.34
## Transparence_Numerique U_Comment U_Interets
## C_Bienveillance -0.21 0.52 0.53
## C_Competence -0.14 0.59 0.53
## C_Donnees.navigation -0.11 0.69 0.69
## C_Ethique -0.39 0.38 0.41
## C_Infos.perso -0.05 0.65 0.68
## C_Securite -0.12 0.31 0.38
## S_Interesse.par.produits.reco -0.26 0.36 0.38
## S_Promoter.score -0.09 0.28 0.43
## S_Recos.repondent.aux.besoins -0.28 0.36 0.44
## S_Satisfaction.globale -0.18 0.31 0.38
## S_Tentation.d.achat 0.05 0.29 0.35
## Transparence_Numerique 1.00 -0.04 -0.11
## U_Comment -0.04 1.00 0.80
## U_Interets -0.11 0.80 1.00
## U_pourquoi -0.07 0.83 0.77
## U_Technique -0.03 0.85 0.69
## U_pourquoi U_Technique
## C_Bienveillance 0.46 0.50
## C_Competence 0.54 0.62
## C_Donnees.navigation 0.64 0.65
## C_Ethique 0.32 0.41
## C_Infos.perso 0.59 0.57
## C_Securite 0.30 0.50
## S_Interesse.par.produits.reco 0.29 0.35
## S_Promoter.score 0.32 0.20
## S_Recos.repondent.aux.besoins 0.36 0.38
## S_Satisfaction.globale 0.34 0.30
## S_Tentation.d.achat 0.29 0.34
## Transparence_Numerique -0.07 -0.03
## U_Comment 0.83 0.85
## U_Interets 0.77 0.69
## U_pourquoi 1.00 0.72
## U_Technique 0.72 1.00corrplot(M, method="color",type="lower", order="hclust")
Factor analysis and measurement reliability
done with Rcmdr (factanal) with 3 factors and a promax rotation that let the factor to be correlated.
more is here http://www.karlin.mff.cuni.cz/~maciak/NMST539/cvicenie8.html
or http://www.di.fc.ul.pt/~jpn/r/factoranalysis/factoranalysis.html
to do better use the package psych :
.FA <- factanal(~C_Bienveillance+C_Competence+C_Donnees.navigation+C_Ethique+C_Infos.perso+C_Securite+S_Interesse.par.produits.reco+S_Promoter.score+S_Recos.repondent.aux.besoins+S_Satisfaction.globale+S_Tentation.d.achat+U_Comment+U_Interets+U_pourquoi+U_Technique,factors=3, rotation="promax", scores="none", data=reco_a)
print(.FA)##
## Call:
## factanal(x = ~C_Bienveillance + C_Competence + C_Donnees.navigation + C_Ethique + C_Infos.perso + C_Securite + S_Interesse.par.produits.reco + S_Promoter.score + S_Recos.repondent.aux.besoins + S_Satisfaction.globale + S_Tentation.d.achat + U_Comment + U_Interets + U_pourquoi + U_Technique, factors = 3, data = reco_a, scores = "none", rotation = "promax")
##
## Uniquenesses:
## C_Bienveillance C_Competence
## 0.490 0.317
## C_Donnees.navigation C_Ethique
## 0.154 0.385
## C_Infos.perso C_Securite
## 0.174 0.521
## S_Interesse.par.produits.reco S_Promoter.score
## 0.307 0.369
## S_Recos.repondent.aux.besoins S_Satisfaction.globale
## 0.352 0.358
## S_Tentation.d.achat U_Comment
## 0.226 0.048
## U_Interets U_pourquoi
## 0.285 0.277
## U_Technique
## 0.245
##
## Loadings:
## Factor1 Factor2 Factor3
## C_Bienveillance 0.614 0.137
## C_Competence 0.704 0.157
## C_Donnees.navigation 0.823 -0.101 0.239
## C_Ethique 0.765 0.130 -0.142
## C_Infos.perso 0.932 -0.236 0.180
## C_Securite 0.310 0.464
## S_Interesse.par.produits.reco -0.388 0.973 0.216
## S_Promoter.score 0.360 0.580 -0.174
## S_Recos.repondent.aux.besoins 0.736
## S_Satisfaction.globale 0.401 0.541 -0.143
## S_Tentation.d.achat -0.136 0.962
## U_Comment 0.945
## U_Interets 0.224 0.655
## U_pourquoi 0.103 0.776
## U_Technique 0.791
##
## Factor1 Factor2 Factor3
## SS loadings 3.633 3.357 2.803
## Proportion Var 0.242 0.224 0.187
## Cumulative Var 0.242 0.466 0.653
##
## Factor Correlations:
## Factor1 Factor2 Factor3
## Factor1 1.000 -0.364 0.585
## Factor2 -0.364 1.000 -0.671
## Factor3 0.585 -0.671 1.000
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 81.51 on 63 degrees of freedom.
## The p-value is 0.0584as we obtain a confirmation of the 3-dimensionnal structure of the response (Understanding,Trust, satisfaction) we could evaluate the reliability and validity of the scales computing conbach alpha and analysing between and inter scale correlations.
A Sem model is better of course ( see the last part) to test a Confirmatory Factor Analysis
for the case of Confiance( trust) alpha is excellen( (more than 0.90)). If the security item is eliminated, there is no loss of information. We could so reduce the scale without decreae its reliability.
reliability(cov(reco_a[,c("C_Bienveillance","C_Competence","C_Donnees.navigation","C_Ethique",
"C_Infos.perso","C_Securite")], use="complete.obs"))## Alpha reliability = 0.9005
## Standardized alpha = 0.9058
##
## Reliability deleting each item in turn:
## Alpha Std.Alpha r(item, total)
## C_Bienveillance 0.8866 0.8929 0.7053
## C_Competence 0.8740 0.8773 0.8218
## C_Donnees.navigation 0.8678 0.8774 0.8235
## C_Ethique 0.8835 0.8885 0.7428
## C_Infos.perso 0.8775 0.8858 0.7678
## C_Securite 0.9057 0.9104 0.5801correlation between item and score are far over correlation between concept, there is some good discrimination between the concept, and so a good validity of the three dimensional concept of consumer reponse.
M<-subset(reco_a, select=c("Confiance", "Understanding", "Satisfaction"))
M<-round(cor(M),2)
M## Confiance Understanding Satisfaction
## Confiance 1.00 0.71 0.60
## Understanding 0.71 1.00 0.43
## Satisfaction 0.60 0.43 1.00model testing
for a quick but complete presentation http://www.sthda.com/english/articles/40-regression-analysis/168-multiple-linear-regression-in-r/
here we test two models to detect eventualy some interaction effect (and so moderating variable). The second one has an interaction effet that test the moderating effect of Purchase_frequency, The two model are then compared through an ANOVA test. ( see : https://bookdown.org/ndphillips/YaRrr/comparing-regression-models-with-anova.html)
LinearModel.2 <- lm(Confiance ~ Sexe + Transparence_Nominale, data=reco_a)
summary(LinearModel.2)##
## Call:
## lm(formula = Confiance ~ Sexe + Transparence_Nominale, data = reco_a)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.56883 -0.58208 0.06084 0.48776 1.37818
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.8218 0.2064 18.514 <2e-16 ***
## SexeMasculin -0.2530 0.2161 -1.171 0.2475
## Transparence_Nominale2-Moderee 0.4877 0.2598 1.877 0.0666 .
## Transparence_Nominale3-Forte -0.2910 0.2637 -1.103 0.2754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.768 on 48 degrees of freedom
## Multiple R-squared: 0.1872, Adjusted R-squared: 0.1364
## F-statistic: 3.685 on 3 and 48 DF, p-value: 0.01814LinearModel.3 <- lm(Confiance ~ Sexe + Transparence_Nominale +Transparence_Nominale*Sexe, data=reco_a)
summary(LinearModel.3)##
## Call:
## lm(formula = Confiance ~ Sexe + Transparence_Nominale + Transparence_Nominale *
## Sexe, data = reco_a)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.54286 -0.56714 0.08312 0.47857 1.36000
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 3.84000 0.24801 15.483
## SexeMasculin -0.29714 0.38649 -0.769
## Transparence_Nominale2-Moderee 0.45091 0.34267 1.316
## Transparence_Nominale3-Forte -0.30667 0.36035 -0.851
## SexeMasculin:Transparence_Nominale2-Moderee 0.09195 0.54145 0.170
## SexeMasculin:Transparence_Nominale3-Forte 0.03881 0.54278 0.072
## Pr(>|t|)
## (Intercept) <2e-16 ***
## SexeMasculin 0.446
## Transparence_Nominale2-Moderee 0.195
## Transparence_Nominale3-Forte 0.399
## SexeMasculin:Transparence_Nominale2-Moderee 0.866
## SexeMasculin:Transparence_Nominale3-Forte 0.943
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7843 on 46 degrees of freedom
## Multiple R-squared: 0.1877, Adjusted R-squared: 0.09944
## F-statistic: 2.126 on 5 and 46 DF, p-value: 0.07909anova(LinearModel.2,LinearModel.3)## Analysis of Variance Table
##
## Model 1: Confiance ~ Sexe + Transparence_Nominale
## Model 2: Confiance ~ Sexe + Transparence_Nominale + Transparence_Nominale *
## Sexe
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 48 28.312
## 2 46 28.294 2 0.01792 0.0146 0.9855#for illustration
level<- aggregate(cbind(Confiance, Satisfaction, Understanding) ~ Transparence_Nominale+Sexe, data=reco_a, FUN="mean")
level <- melt(level) ## Using Transparence_Nominale, Sexe as id variablesp1 <- ggplot(data = level, aes(x = Transparence_Nominale, y = value, group =Sexe, color=Sexe ))
p1<- p1 + geom_point(size=2)+geom_line(stat="identity", size=2)+facet_grid(.~variable)
p1
to improve the procedure, a classic aproach is “Process” implemented in the processr package : https://rpubs.com/markhw/processr.
It is usefull ( nd it is a growing trend) to represent graphically the results of a regression model. Jtools is usefull for this purpose with the Plot_summs function. See :
summ(LinearModel.3)| Observations | 52 |
| Dependent variable | Confiance |
| Type | OLS linear regression |
| F(5,46) | 2.13 |
| R² | 0.19 |
| Adj. R² | 0.10 |
| Est. | S.E. | t val. | p | |
|---|---|---|---|---|
| (Intercept) | 3.84 | 0.25 | 15.48 | 0.00 |
| SexeMasculin | -0.30 | 0.39 | -0.77 | 0.45 |
| Transparence_Nominale2-Moderee | 0.45 | 0.34 | 1.32 | 0.19 |
| Transparence_Nominale3-Forte | -0.31 | 0.36 | -0.85 | 0.40 |
| SexeMasculin:Transparence_Nominale2-Moderee | 0.09 | 0.54 | 0.17 | 0.87 |
| SexeMasculin:Transparence_Nominale3-Forte | 0.04 | 0.54 | 0.07 | 0.94 |
| Standard errors: OLS |
plot_summs(LinearModel.3, scale = TRUE)
Clustering
kmeans
look at this bank customer segmentation exemple https://rpubs.com/cpatinof/clusteringMktngDataCaseStudy
## K-means clustering with 3 clusters of sizes 17, 9, 26
##
## Cluster means:
## Confiance Understanding Satisfaction
## 1 3.388235 4.117647 4.070588
## 2 2.888889 3.277778 3.066667
## 3 4.361538 5.163462 4.530769
##
## Clustering vector:
## [1] 1 3 3 3 1 1 3 3 3 1 1 3 3 1 1 2 2 3 3 3 3 2 3 1 3 3 1 3 3 3 3 2 3 1 1
## [36] 3 1 3 2 3 1 2 1 2 3 3 1 1 2 3 2 1
##
## Within cluster sum of squares by cluster:
## [1] 12.162647 6.644444 24.749712
## (between_SS / total_SS = 58.1 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"## Using group as id variables
hierarchical clustering
this method come from biology and was develop to classify species :
https://cran.r-project.org/web/packages/dendextend/vignettes/Cluster_Analysis.html
# Ward Hierarchical Clustering
d <- dist(x, method = "euclidean") # distance matrix
fit <- hclust(d, method="ward.D")
plot(fit) # display dendogram
HCgroups <- cutree(fit, k=3) # cut tree into 5 clusters
# draw dendogram with red borders around the 5 clusters
rect.hclust(fit, k=3, border="red")
### Convergence test
do the two method give the same results?
just crosstabs and compute the chi² test.
KMcluster<-as.data.frame(kmeans[[1]]) #extract a component from a list
names(KMcluster)[names(KMcluster)=="kmeans[[1]]"] <- "KMcluster"
typo<-cbind(KMcluster,HCgroups)
typo$KMcluster<-as.factor(typo$KMcluster)
typo$HCgroups<-as.factor(typo$HCgroups)
.Table <- xtabs(~HCgroups+KMcluster, data=typo)
cat("\nFrequency table:\n")##
## Frequency table: print(.Table)## KMcluster
## HCgroups 1 2 3
## 1 17 0 0
## 2 0 27 3
## 3 0 0 5 .Test <- chisq.test(.Table, correct=FALSE)
print(.Test)##
## Pearson's Chi-squared test
##
## data: .Table
## X-squared = 81.25, df = 4, p-value < 2.2e-16 cat("\nExpected counts:\n")##
## Expected counts: print(.Test$expected)## KMcluster
## HCgroups 1 2 3
## 1 5.557692 8.826923 2.6153846
## 2 9.807692 15.576923 4.6153846
## 3 1.634615 2.596154 0.7692308 cat("\nChi-square components:\n")##
## Chi-square components: print(round(.Test$residuals^2, 2)) ## KMcluster
## HCgroups 1 2 3
## 1 23.56 8.83 2.62
## 2 9.81 8.38 0.57
## 3 1.63 2.60 23.27Structural equation modeling
we use Lavaan
## lavaan 0.6-5 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 33
##
## Number of observations 52
##
## Model Test User Model:
##
## Test statistic 173.278
## Degrees of freedom 102
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Confiance =~
## C_Bienveillanc 1.000 0.667 0.689
## C_Competence 0.941 0.171 5.510 0.000 0.628 0.823
## C_Donnes.nvgtn 1.449 0.238 6.089 0.000 0.966 0.923
## C_Ethique 0.815 0.172 4.725 0.000 0.543 0.697
## C_Infos.perso 1.371 0.237 5.798 0.000 0.914 0.871
## Satisfaction =~
## S_Intrss.pr.p. 1.000 0.608 0.745
## S_Promoter.scr 1.009 0.181 5.587 0.000 0.613 0.781
## S_Rcs.rpndnt.. 1.165 0.198 5.883 0.000 0.708 0.820
## S_Stsfctn.glbl 1.004 0.183 5.472 0.000 0.610 0.766
## S_Tenttn.d.cht 1.462 0.243 6.016 0.000 0.888 0.838
## Understanding =~
## U_Comment 1.000 1.011 0.962
## U_Interets 0.691 0.071 9.745 0.000 0.698 0.842
## U_pourquoi 0.773 0.075 10.353 0.000 0.781 0.861
## U_Technique 0.936 0.089 10.541 0.000 0.946 0.866
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Confiance ~
## Understanding 0.494 0.099 4.987 0.000 0.749 0.749
## Satisfaction ~
## Confiance 0.566 0.157 3.599 0.000 0.621 0.621
## Confiance ~
## Tr1 0.285 0.142 2.007 0.045 0.427 0.203
## Tr2 -0.154 0.139 -1.108 0.268 -0.232 -0.109
## Tr1 ~
## Tr2 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .C_Bienveillanc 0.491 0.103 4.783 0.000 0.491 0.525
## .C_Competence 0.188 0.043 4.351 0.000 0.188 0.323
## .C_Donnes.nvgtn 0.161 0.053 3.037 0.002 0.161 0.147
## .C_Ethique 0.311 0.065 4.768 0.000 0.311 0.514
## .C_Infos.perso 0.267 0.067 3.959 0.000 0.267 0.242
## .S_Intrss.pr.p. 0.295 0.067 4.393 0.000 0.295 0.444
## .S_Promoter.scr 0.241 0.057 4.214 0.000 0.241 0.391
## .S_Rcs.rpndnt.. 0.244 0.062 3.930 0.000 0.244 0.328
## .S_Stsfctn.glbl 0.263 0.061 4.297 0.000 0.263 0.414
## .S_Tenttn.d.cht 0.335 0.089 3.756 0.000 0.335 0.298
## .U_Comment 0.083 0.040 2.106 0.035 0.083 0.075
## .U_Interets 0.200 0.045 4.468 0.000 0.200 0.291
## .U_pourquoi 0.213 0.049 4.343 0.000 0.213 0.259
## .U_Technique 0.297 0.069 4.299 0.000 0.297 0.249
## .Tr1 0.226 0.044 5.099 0.000 0.226 1.000
## .Confiance 0.172 0.066 2.605 0.009 0.386 0.386
## .Satisfaction 0.227 0.078 2.897 0.004 0.615 0.615
## Understanding 1.021 0.219 4.664 0.000 1.000 1.000## lavaan 0.6-5 ended normally after 109 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 96
##
## Number of observations per group:
## Masculin 22
## Feminin 30
##
## Model Test User Model:
##
## Test statistic 351.125
## Degrees of freedom 204
## P-value (Chi-square) 0.000
## Test statistic for each group:
## Masculin 214.370
## Feminin 136.756
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard errors Standard
##
##
## Group 1 [Masculin]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Confiance =~
## C_Bienveillanc 1.000 0.565 0.616
## C_Competence 1.035 0.340 3.043 0.002 0.585 0.800
## C_Donnes.nvgtn 1.631 0.489 3.337 0.001 0.922 0.922
## C_Ethique 0.778 0.326 2.384 0.017 0.440 0.581
## C_Infos.perso 1.491 0.454 3.287 0.001 0.843 0.899
## Satisfaction =~
## S_Intrss.pr.p. 1.000 0.595 0.755
## S_Promoter.scr 0.953 0.248 3.838 0.000 0.567 0.808
## S_Rcs.rpndnt.. 1.114 0.278 4.002 0.000 0.663 0.841
## S_Stsfctn.glbl 0.733 0.228 3.209 0.001 0.436 0.687
## S_Tenttn.d.cht 1.363 0.339 4.018 0.000 0.811 0.844
## Understanding =~
## U_Comment 1.000 1.137 0.976
## U_Interets 0.607 0.068 8.897 0.000 0.691 0.906
## U_pourquoi 0.727 0.088 8.263 0.000 0.827 0.891
## U_Technique 1.042 0.079 13.127 0.000 1.185 0.968
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Confiance ~
## Understanding 0.376 0.128 2.935 0.003 0.756 0.756
## Satisfaction ~
## Confiance 0.523 0.279 1.874 0.061 0.497 0.497
## Confiance ~
## Tr1 0.269 0.192 1.401 0.161 0.476 0.222
## Tr2 -0.012 0.171 -0.069 0.945 -0.021 -0.010
## Tr1 ~
## Tr2 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .C_Bienveillanc 3.282 0.212 15.451 0.000 3.282 3.577
## .C_Competence 4.189 0.177 23.690 0.000 4.189 5.728
## .C_Donnes.nvgtn 3.413 0.250 13.670 0.000 3.413 3.416
## .C_Ethique 2.982 0.174 17.140 0.000 2.982 3.938
## .C_Infos.perso 3.742 0.233 16.077 0.000 3.742 3.991
## .S_Intrss.pr.p. 4.048 0.174 23.246 0.000 4.048 5.137
## .S_Promoter.scr 3.914 0.156 25.145 0.000 3.914 5.582
## .S_Rcs.rpndnt.. 4.180 0.176 23.812 0.000 4.180 5.302
## .S_Stsfctn.glbl 4.014 0.140 28.765 0.000 4.014 6.321
## .S_Tenttn.d.cht 3.806 0.214 17.785 0.000 3.806 3.961
## .U_Comment 4.227 0.248 17.018 0.000 4.227 3.628
## .U_Interets 4.682 0.162 28.820 0.000 4.682 6.145
## .U_pourquoi 4.955 0.198 25.036 0.000 4.955 5.338
## .U_Technique 4.045 0.261 15.504 0.000 4.045 3.305
## .Tr1 0.318 0.099 3.204 0.001 0.318 0.683
## .Confiance 0.000 0.000 0.000
## .Satisfaction 0.000 0.000 0.000
## Understanding 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .C_Bienveillanc 0.523 0.165 3.177 0.001 0.523 0.621
## .C_Competence 0.193 0.066 2.902 0.004 0.193 0.361
## .C_Donnes.nvgtn 0.149 0.077 1.944 0.052 0.149 0.149
## .C_Ethique 0.380 0.119 3.200 0.001 0.380 0.663
## .C_Infos.perso 0.169 0.074 2.284 0.022 0.169 0.193
## .S_Intrss.pr.p. 0.267 0.094 2.833 0.005 0.267 0.430
## .S_Promoter.scr 0.170 0.065 2.622 0.009 0.170 0.346
## .S_Rcs.rpndnt.. 0.182 0.075 2.424 0.015 0.182 0.293
## .S_Stsfctn.glbl 0.213 0.071 2.993 0.003 0.213 0.528
## .S_Tenttn.d.cht 0.266 0.111 2.401 0.016 0.266 0.288
## .U_Comment 0.064 0.039 1.649 0.099 0.064 0.047
## .U_Interets 0.104 0.035 2.964 0.003 0.104 0.178
## .U_pourquoi 0.178 0.059 3.025 0.002 0.178 0.207
## .U_Technique 0.094 0.046 2.015 0.044 0.094 0.062
## .Tr1 0.217 0.065 3.317 0.001 0.217 1.000
## .Confiance 0.121 0.081 1.500 0.134 0.379 0.379
## .Satisfaction 0.267 0.136 1.963 0.050 0.753 0.753
## Understanding 1.294 0.410 3.154 0.002 1.000 1.000
##
##
## Group 2 [Feminin]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Confiance =~
## C_Bienveillanc 1.000 0.703 0.707
## C_Competence 0.924 0.210 4.406 0.000 0.649 0.831
## C_Donnes.nvgtn 1.452 0.292 4.970 0.000 1.021 0.944
## C_Ethique 0.805 0.200 4.037 0.000 0.566 0.760
## C_Infos.perso 1.358 0.298 4.563 0.000 0.954 0.861
## Satisfaction =~
## S_Intrss.pr.p. 1.000 0.636 0.760
## S_Promoter.scr 0.980 0.236 4.149 0.000 0.623 0.745
## S_Rcs.rpndnt.. 1.130 0.254 4.443 0.000 0.719 0.791
## S_Stsfctn.glbl 1.115 0.242 4.604 0.000 0.709 0.817
## S_Tenttn.d.cht 1.531 0.314 4.881 0.000 0.974 0.861
## Understanding =~
## U_Comment 1.000 0.910 0.956
## U_Interets 0.763 0.122 6.259 0.000 0.695 0.797
## U_pourquoi 0.830 0.115 7.187 0.000 0.755 0.847
## U_Technique 0.832 0.141 5.891 0.000 0.757 0.774
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Confiance ~
## Understanding 0.582 0.149 3.904 0.000 0.753 0.753
## Satisfaction ~
## Confiance 0.602 0.202 2.983 0.003 0.665 0.665
## Confiance ~
## Tr1 0.279 0.189 1.475 0.140 0.397 0.191
## Tr2 -0.230 0.196 -1.174 0.241 -0.327 -0.150
## Tr1 ~
## Tr2 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .C_Bienveillanc 3.600 0.199 18.061 0.000 3.600 3.623
## .C_Competence 4.436 0.162 27.430 0.000 4.436 5.676
## .C_Donnes.nvgtn 3.685 0.231 15.972 0.000 3.685 3.410
## .C_Ethique 3.473 0.151 22.956 0.000 3.473 4.665
## .C_Infos.perso 4.188 0.231 18.105 0.000 4.188 3.777
## .S_Intrss.pr.p. 4.113 0.161 25.611 0.000 4.113 4.919
## .S_Promoter.scr 4.114 0.160 25.651 0.000 4.114 4.917
## .S_Rcs.rpndnt.. 4.411 0.175 25.187 0.000 4.411 4.856
## .S_Stsfctn.glbl 4.378 0.168 26.074 0.000 4.378 5.044
## .S_Tenttn.d.cht 3.836 0.220 17.437 0.000 3.836 3.394
## .U_Comment 4.400 0.174 25.310 0.000 4.400 4.621
## .U_Interets 4.800 0.159 30.157 0.000 4.800 5.506
## .U_pourquoi 4.933 0.163 30.295 0.000 4.933 5.531
## .U_Technique 3.900 0.179 21.840 0.000 3.900 3.987
## .Tr1 0.367 0.088 4.168 0.000 0.367 0.761
## .Confiance 0.000 0.000 0.000
## .Satisfaction 0.000 0.000 0.000
## Understanding 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .C_Bienveillanc 0.494 0.135 3.651 0.000 0.494 0.500
## .C_Competence 0.189 0.056 3.364 0.001 0.189 0.310
## .C_Donnes.nvgtn 0.126 0.062 2.024 0.043 0.126 0.108
## .C_Ethique 0.234 0.066 3.566 0.000 0.234 0.422
## .C_Infos.perso 0.319 0.099 3.208 0.001 0.319 0.259
## .S_Intrss.pr.p. 0.295 0.089 3.325 0.001 0.295 0.422
## .S_Promoter.scr 0.312 0.092 3.376 0.001 0.312 0.445
## .S_Rcs.rpndnt.. 0.308 0.096 3.201 0.001 0.308 0.374
## .S_Stsfctn.glbl 0.251 0.082 3.066 0.002 0.251 0.333
## .S_Tenttn.d.cht 0.329 0.121 2.713 0.007 0.329 0.258
## .U_Comment 0.078 0.054 1.455 0.146 0.078 0.086
## .U_Interets 0.277 0.081 3.443 0.001 0.277 0.365
## .U_pourquoi 0.225 0.070 3.209 0.001 0.225 0.283
## .U_Technique 0.383 0.109 3.510 0.000 0.383 0.401
## .Tr1 0.232 0.060 3.873 0.000 0.232 1.000
## .Confiance 0.184 0.090 2.041 0.041 0.373 0.373
## .Satisfaction 0.226 0.100 2.249 0.024 0.558 0.558
## Understanding 0.829 0.238 3.475 0.001 1.000 1.000