Analyzing Ranked Data: Correlation and Factor Analysis?

I had survey respondents rank a series of items in order of importance, from 1 to 7. So, if a respondent assigned a score of 1 to one variable, then none of the other variables could get a 1 as well. The dataset is replicated in test.data below. I have three questions:

1. Should I interpret this as ranked data rather than interval data? I think so, but I am not sure.
2. If they are ranked data, is it sensible to use either the Wilcoxon-Mann-Whitney U or Kruskal-Wallis test to test for differences in median (?) rankings depending on the levels of the predictor variable?
3. If they are ranked data, could I construct a correlation matrix using Spearman's Rho?
4. If that is possible, could I use a factor analysis on that correlation matrix to possibly reduce the dataset and measure some hypothesized underlying constructs?

I have tried to do these steps basicallly using the steps below, although I see now that there is a paper and an R package suggesting the possibility of performing factor analysis on ranked data.

Thank you for your suggestions.

library(psych)
#Create Data frame
test.data<-replicate(10, sample(seq(1,6,1), replace=F))

#transpose
test.data<-t(test.data)

#data frame
test.data<-data.frame(test.data)

#Provide names
names(test.data)<-c('item1', 'item2', 'item3', 'item4', 'item5', 'item6’)

#Some predictors
test.data$gender<-factor(sample(c('M', 'F'), replace=T,size=10)) test.data$position<-factor(sample(c('Journ', 'Pol'), replace=T, size=10))

#Correlation Matrix
cor.matrix<-cor(test.data[,1:6], method=c('spearman'))

#Factor Analysis
plot(eigen(cor.matrix)\$values, type='o')

fa(cor.matrix, method='pa', rotate='none', nobs=nrow(test.data))

#Kruskal-Wallis or Mann-Whitney depending on predictor levels
lapply(test.data[,1:6], function(x) kruskal.test(x~position, data=test.data))
• The first link declines opening. Do you have the full article which you can share? – ttnphns Mar 13 '15 at 20:38
• – spindoctor Mar 13 '15 at 21:06
• Pardon me, I meant to have the second article "Factor analysis...". Do you have a pdf that you could share? – ttnphns Mar 14 '15 at 7:32
• – spindoctor Mar 20 '15 at 14:18