############ I.  SWLS Download and Data Preparation



# Survey URL:



# http://rss.acs.unt.edu:8080/users/psychometric/survey/satisfy_life/





survey.data<-read.delim('http://bayes.acs.unt.edu:8083:8083/BayesContent/class/splus/swls.txt', fill=TRUE)



# Create data frame 

survey.df<-as.data.frame(survey.data)



# Reverse code SWLS items 



library(car)

survey.df$Q1<-recode(survey.df$Q1,'7=1;6=2;5=3;4=4;3=5;2=6;1=7; ',as.factor.result=FALSE)

survey.df$Q2<-recode(survey.df$Q2,'7=1;6=2;5=3;4=4;3=5;2=6;1=7; ',as.factor.result=FALSE)

survey.df$Q3<-recode(survey.df$Q3,'7=1;6=2;5=3;4=4;3=5;2=6;1=7; ',as.factor.result=FALSE)

survey.df$Q4<-recode(survey.df$Q4,'7=1;6=2;5=3;4=4;3=5;2=6;1=7; ',as.factor.result=FALSE)

survey.df$Q5<-recode(survey.df$Q5,'7=1;6=2;5=3;4=4;3=5;2=6;1=7; ',as.factor.result=FALSE)



# Create table of frequencies and display



survey.table<-table(survey.df$Q4, survey.df$Q5)

survey.table



# Display as proportions of total N



prop.table(survey.table)



# Test for independence



summary(survey.table)



# Plot barchart 



barplot(survey.table)



###################################################



############# II.  Data Exploration of SWLS





# SWLS scores



swls.scores<-apply(as.matrix(cbind(survey.df$Q1,survey.df$Q2,survey.df$Q3,survey.df$Q4,survey.df$Q5)), 1, sum)



summary(swls.scores)



survey.df<-cbind(survey.df, swls.scores)



par(mfrow=c(1,1))



# Fit regression



survey.df.lm<-lm(survey.df$employ_other~survey.df$swls.scores)

summary(survey.df.lm)



# Plot a scatterplot



scatterplot(jitter(survey.df$employ_other)~jitter(survey.df$swls.scores), data=survey.df)





######################################################





############# III.  Summary statistics of SWLS items



survey.df<-data.frame(cbind(survey.df, swls.scores))



swls.items<-data.frame(survey.df$Q1,survey.df$Q2, survey.df$Q3,survey.df$Q4, survey.df$Q5)



# Summary statistics of SWLS items and the SWLS scores



summary(swls.items.scores)



# Correlation the SWLS items with the SWLS scores



cor(swls.items.scores)



# Total test variance



var(swls.scores)



# Sum of the entries in the variance/covariance matrix



cov(swls.items)

sum(cov(swls.items))



# Scatterplot matrix of SWLS items



scatterplot.matrix(~jitter(Q1)+jitter(Q2)+jitter(Q3)+jitter(Q4)+jitter(Q5)+jitter(swls.scores), reg.line=lm, smooth=TRUE, span=0.5, diagonal = 'density', data=survey.df)



#######################################################



############# IV.   Exploratory Factor Analysis





swls.items<-data.frame(survey.df$Q1,survey.df$Q2, survey.df$Q3,survey.df$Q4, survey.df$Q5)



summary(swls.items)

cor(swls.items)

cov(swls.items)

S<-cov(swls.items)



# Exploratory Factor Analysis (EFA) - 1 factor  



library(stats)

factanal1.fit<-factanal(swls.items, factors=1, scores='regression')

factanal1.fit



swls.items<-cbind(swls.items, factanal1.fit$scores)



# Scatterplot matrix of SWLS items with Factor 1 scores



scatterplot.matrix(~jitter(survey.df.Q1)+jitter(survey.df.Q2)+jitter(survey.df.Q3)+jitter(survey.df.Q4)+jitter(survey.df.Q5)+jitter(Factor1), reg.line=lm, smooth=TRUE, span=0.5, diagonal = 'density', data=swls.items)





########################################################



################ V.   Confirmatory Factor Analysis of SWLS Items





swls.items<-data.frame(survey.df$Q1,survey.df$Q2, survey.df$Q3,survey.df$Q4, survey.df$Q5)



# Confirmatory factor analysis (CFA) - 1 factor  



library(sem)



swls.cor<-cor(swls.items)



swls.cor[upper.tri(swls.cor)] <- 0



R.swls<-swls.cor



model.swls<-matrix(c('F1->Q1','lam11',NA,

                     'F1->Q2','lam21',NA,

                     'F1->Q3','lam31',NA,

                     'F1->Q4','lam41',NA,

                     'F1->Q5','lam51',NA,

                     'Q1<->Q1','th1',NA,

                     'Q2<->Q2','th2',NA,

                     'Q3<->Q3','th3',NA,

                     'Q4<->Q4','th4',NA, 

                     'Q5<->Q5','th5',NA,

                     'F1<->F1',NA,1),

                ncol=3, byrow=T)



obs.vars.swls<-c('Q1','Q2','Q3','Q4','Q5') 

sem.swls<-sem(model.swls, R.swls, 161, obs.vars.swls)

summary(sem.swls)





############################################################################





# Generalizability and Reliability Using SEM Framework





swls.items<-data.frame(survey.df$Q1,survey.df$Q2, survey.df$Q3,survey.df$Q4, survey.df$Q5)



# Confirmatory factor analysis (CFA) - 1 factor  



library(sem)

swls.cov<-cov(swls.items)

swls.cov

sum(swls.cov)



swls.cov[upper.tri(swls.cov)] <- 0



S.swls<-swls.cov



model.swls<-matrix(c('F1->Q1','lam11',NA,

                     'F1->Q2','lam21',NA,

                     'F1->Q3','lam31',NA,

                     'F1->Q4','lam41',NA,

                     'F1->Q5','lam51',NA,

                     'Q1<->Q1','th1',NA,

                     'Q2<->Q2','th2',NA,

                     'Q3<->Q3','th3',NA,

                     'Q4<->Q4','th4',NA, 

                     'Q5<->Q5','th5',1,

                     'F1<->F1',NA,1),

                ncol=3, byrow=T)



obs.vars.swls<-c('Q1','Q2','Q3','Q4','Q5') 

sem.swls<-sem(model.swls, S.swls, 161, obs.vars.swls, start.tol=1E-10)

summary(sem.swls)



# Loadings (first 5 elements) and Uniqueness/Error Variance (second 5 elements)

# Note that the Uniqueness/Error terms are the 'psi-squared' terms in McDonald's book



sem.swls$coeff





omega.partA<-sum(sem.swls$coeff[1:5])^2

omega.partA



omega.partB<-sum(c(sem.swls$coeff[6],sem.swls$coeff[7],sem.swls$coeff[8],sem.swls$coeff[9],sem.swls$coeff[10]))

omega.partB



# Calculate total test variance based on loadings and errors



total.swls.var<-omega.partA+omega.partB

total.swls.var



# Calculate McDonald's Omega coefficient



omega.swls<-(omega.partA)/(omega.partA+omega.partB)

omega.swls



# Calculate Cronbach's alpha



library(psy)

cronbach(swls.items