 The Arts Engagement Project at
The University of Michigan

# Principal Components Analysis

We used a Principle Components Analysis (PCA) in R (‘prcomp’ function) to integrate multiple variables and conduct an analysis for each question and set of responses. PCA is a multivariate statistical technique that extracts important information about the inter-correlations of multiple variables and re-represents that information as new variables called principle components. These new principle components can then be used to show the similarity and graphic relationships between variables as a way of exploring the data. Because PCA condenses multiple variables into fewer dimensions, the new principle components may also be used to integrate new descriptions of the combined variables. These reified principle components may then be used as covariates to estimate relationships with other variables such as demographic factors.

Twenty-seven dictionary-based variables (LIWC, AIC, and Docuscope) were not relevant and were excluded from the analysis, leaving a total of 221 dictionary-based variables in the PCA. This was in addition to the measures of topic prevalence, which each had different numbers of topic variables depending on the question/response type. In order to remove variables with high numbers of 0s (no observations), we set a 0.3 maximum threshold, leaving variable columns with 70% or more observations in the analysis. The number of responses and variables included for each question in the analysis are provided in Table 1. Because of the different scales used by the different dictionaries and topic measures (for example, topic prevalence is 0-1 while AIC is measured on a scale from 1-7), the PCA was based on a correlation matrix. The data were also centered around zero and rotated.

```#install.packages("corrplot")
#install.packages("ggplot2")
#install.packages("plotly")
install.packages("factoextra")
install.packages("FactoMineR")

library(ggplot2)   # plotting;
library(plotly)
library(haven)     # SPSS/.sav file import
library(dplyr)     # data manipulation
library("corrplot")#
library(stringr)   # string manipulation
library(labelled)
library("FactoMineR")
library("factoextra")```
```#data <- read.csv('pcadata.csv')
ls()```
1. ‘data’
2. ‘df’
```data <- df
#print the dimension of the dataframe
dim(data)```
1. 4828
2. 7288
```stripnames <- function(data, question) {
data <- data %>% select(starts_with(question))
varnames <- names(data)
newnames <- varnames
for (i in seq(2, length(varnames))) {
newnames[i] <- substr(varnames[i], gregexpr("\\.\\.", varnames[i])[]+2, nchar(varnames[i]))
}
names(data) <- newnames
return(data)
}

mergeQuestion <- function(data, question) {
if(substr(question, 3,3) == '_') {
question <- substr(question, 4, nchar(question))
}
# if you're aware of other prefixes, add them here
yrs <- c('','fl_','f1_','f2_','so_','jr_','sr_','sl_')
mergeddf <- data.frame()
for(yr in yrs) {
qyr <- paste0(yr, question)
if(data %>% select(starts_with(qyr)) %>% ncol == 0) { next }
tempdf <- stripnames(df, qyr)
names(tempdf) <- question
mergeddf <- bind_rows(mergeddf, tempdf)
}
return(mergeddf)
}

stripVars <- function(data) {
#remove irrelavant variables
removenames <- names(data %>% select(matches("AIC..Words|AIC..IC_Differentiation|AIC..IC_Integration|AIC..DIAL_Differentiation|AIC..DIAL_Integration|AIC..ELAB_Differentiation|AIC..ELAB_Integration|docuscope..OralCues|docuscope..DialogCues|docuscope..XWordTokens|docuscope..XPunctuationTokens|docuscope..XTokens|LIWC..WC|LIWC..Sixltr|LIWC..Dic|LIWC..WPS|LIWC..swear|LIWC..netspeak|LIWC..assent|LIWC..nonflu|LIWC..filler|LIWC..AllPunc|LIWC..Period|LIWC..Comma|LIWC..Colon|LIWC..SemiC|LIWC..QMark|LIWC..Exclam|LIWC..Dash|LIWC..Quote|LIWC..Apostro|LIWC..Parenth|LIWC..OtherP")))
data <- data[ , !names(data) %in% removenames]
return(data)
}

#example input for parameter question: "sr_career"
#threshold: set the threshold for cos2. only variables with cos2> threshold will be kept in biplots
#percent: set the percentage of 0 in a column; columns with percentage of 0 values > percent will be removed
pca_biplot <- function(question,threshold,percent) {

if(substr(question, 3,3) == '_') {
question <- substr(question, 4, nchar(question))
}

# select columns relevant to the question
data_subset <- mergeQuestion(data, question) %>% stripVars
print(dim(data_subset))
#create file for eigenvales and output
eigfile <- paste(question,"_eigenvalues.txt", sep="")
sink(eigfile, append=FALSE, split=TRUE)

#remove rows with no response
data_subset <- data_subset[complete.cases(data_subset),]
print(dim(data_subset))
# replace NULL with 0
# this shouldnt be necessary -- investigate if so
# data_subset[is.na(data_subset)] <- 0

#remove columns with percentage of 0 values > percent
data_subset <- data_subset[ lapply( data_subset, function(x) sum(x==0) / length(x) ) < percent ]

print(dim(data_subset))

print(names(data_subset))

#scale all the variables
data_subset[, -c(1)] <- scale(data_subset[, -c(1)])

#create new dataframe pcadata to store scaled variables

#remove columns that only have NULL; columns that only have 0 after scaling will become NULL

#fit PCA uses correlatio matrix, rotation, centered
pca.fit <- prcomp(pcadata2, retx= TRUE, center=TRUE, scale=TRUE)
eig.val <- get_eigenvalue(pca.fit)

#get variable contributions
var <- get_pca_var(pca.fit)
#print(var\$contrib)
#print(var\$coord)
#print(pca.fit)

# Print Eigenvalues and variable contributions and close sink
print(eig.val)

sink(append=TRUE, type="message")
sink()

# Export into a TXT file
write.infile(pca.fit, file=paste(question,"_pca_results.txt", sep=""), sep = "\t")

#print screeplot
pdf(file=paste(question,"_screeplot.pdf", sep=""))
screeplot=fviz_eig(pca.fit, addlabels = TRUE, ylim = c(0, 50))
print(screeplot)
dev.off()

#make biplot for PC1&2
p12=fviz_pca_var(pca.fit, axes = c(1, 2), col.var = "cos2", alpha.var="cos2", select.var = list(cos2 = threshold),
repel = TRUE # Avoid text overlapping
)+ xlim(-1, 1) + ylim (-1, 1)

#make biplot for PC3&4
p34=fviz_pca_var(pca.fit, axes = c(3, 4), col.var = "cos2", alpha.var="cos2", select.var = list(cos2 = threshold),
repel = TRUE # Avoid text overlapping
)+ xlim(-1, 1) + ylim (-1, 1)

#print biplot
pdf(file=paste(question,"_biplot12.pdf", sep=""))
print(p12)
dev.off()

#print biplot
pdf(file=paste(question,"_biplot34.pdf", sep=""))
print(p34)
dev.off()

#print charts of variable contrib and cos2

pdf(file=paste(question,"_corr_cos2_viz.pdf", sep=""))
corrcos2viz <- corrplot(var\$cos2, is.corr=FALSE, tl.cex = .5)
print(corrcos2viz)
dev.off()

pdf(file=paste(question,"_corr_contrib_viz.pdf", sep=""))
corrcontribviz <- corrplot(var\$contrib, is.corr=FALSE, tl.cex = .5)
print(corrcontribviz)
dev.off()

# Contributions of variables to PC1
pdf(file=paste(question,"_contributionPC1.pdf", sep=""))
c1=fviz_contrib(pca.fit, choice = "var", axes = 1, top = 10)
print(c1)
dev.off()
# Contributions of variables to PC2
pdf(file=paste(question,"_contributionPC2.pdf", sep=""))
c2=fviz_contrib(pca.fit, choice = "var", axes = 2, top = 10)
print(c2)
dev.off()
# Contributions of variables to PC3
pdf(file=paste(question,"_contributionPC3.pdf", sep=""))
c3=fviz_contrib(pca.fit, choice = "var", axes = 3, top = 10)
print(c3)
dev.off()
# Contributions of variables to PC4
pdf(file=paste(question,"_contributionPC4.pdf", sep=""))
c4=fviz_contrib(pca.fit, choice = "var", axes = 4, top = 10)
print(c4)
dev.off()
# Contributions of variables to PC5
pdf(file=paste(question,"_contributionPC5.pdf", sep=""))
c5=fviz_contrib(pca.fit, choice = "var", axes = 5, top = 10)
print(c5)
dev.off()

###### interactive pca plot

#make biplot with individual dots
test2<-fviz_pca_biplot(res.pca, axes = c(1, 2), geom=c('point','text'), col.ind = "light blue",
pointshape = 19, pointsize = 2,alpha.ind = 0.3,
label = "var",
alpha.var ="cos2", select.var = list(cos2 = threshold),
col.var = "cos2",gradient.cols = c("blue", "red")

)

#labs(fill = "identity")# Change legend title

pp=ggplotly(p=test2,width=800,height=800)
ppp=style(pp,text=mytext,hoverinfo="text", traces = c(1,2,3))
htmlwidgets::saveWidget(as_widget(ppp), paste(question,"_plotly12.html", sep=""))

test3<-fviz_pca_biplot(res.pca, axes = c(3, 4), geom=c('point','text'), col.ind = "light blue",
pointshape = 19, pointsize = 2,alpha.ind = 0.3,
label = "var",
alpha.var ="cos2", select.var = list(cos2 = threshold),
col.var = "cos2",gradient.cols = c("blue", "red")

)

pp=ggplotly(p=test3,width=800,height=800)
ppp=style(pp,text=mytext,hoverinfo="text", traces = c(1,2,3))
htmlwidgets::saveWidget(as_widget(ppp), paste(question,"_plotly34.html", sep=""))
}
```
```#example input for parameter question: "career"
#1st is threshold: set the threshold for cos2. only variables with cos2> threshold will be kept in biplots
#2nd is percent: set the percentage of 0 in a column; columns with percentage of 0 values > percent will be removedpca_biplot('barriers',0.3,0.4)
pca_biplot('career',0.2,0.3)
pca_biplot('development',0.2,0.3)
pca_biplot('othergrowth',0.2,0.3)
pca_biplot('society',0.2,0.3)
pca_biplot('role',0.2,0.3)
pca_biplot('barriers',0.2,0.3)
pca_biplot('feel',0.2,0.3)
pca_biplot('definition',0.2,0.3)
pca_biplot('aftercollege4',0.2,0.3)
pca_biplot('behavior2',0.2,0.3)
pca_biplot('change',0.2,0.3)
pca_biplot('childhood2',0.2,0.3)```