###Code for lecture 34 - Factor Analysis

### Import Data

datum=read.csv(file.choose())


### exploratory factor analysis is done with the poorly name function 'factanal'

help(factanal) # note that requires the argument 'factors', which is how many factors your think there are

results2=factanal(datum,factors=2) ### lets examine what we know is truth
results2

### Uniqueness is how much each variable is unlike other variables (close to 1 = very unique)
### close to zero is not very unique (heavily correlated with other variables)
###Proportion variance and cumulative variance explain just what they mean
### Beware of results in which the cum variance is low 

###All loadings are high, and clearly group each variable into a single factor


### What happens if we don't specify enough factors

results1=factanal(datum,factors=1) #### only one factor
results1

### Note at the very bottom, the p-value that is significant, indicates a rejection of the null hypothesis
### that 1 factor is sufficient to explain the data


### what happens if we specify too many factors

results3=factanal(datum,factors=3) ### 3 factors
results3

### note third factor doesn't explain hardly any variation
### degrees of freedom for p-test is 0 - model is over-fit

### Scores for the latent variables are not produced by default
### if you want scores, then you need to include the argument:

results2=factanal(datum,factors=2,scores="regression")

results2$scores ###should give you the values of the latent variables



### Try it again, but with correlation between two latent variables

datum=read.csv(file.choose())


results2=factanal(datum,factors=2) ### lets examine what we know is truth
results2

### still works, but loadings aren't as clear-cut


results1=factanal(datum,factors=1) #### only one factor
results1

### Note at the very bottom, the p-value that is significant, indicates a rejection of the null hypothesis
### that 1 factor is sufficient to explain the data


results3=factanal(datum,factors=3) ### 3 factors
results3

### note third factor doesn't explain hardly any variation
### degrees of freedom for p-test is 0 - model is over-fit