Statistics for everyone: ch.25 Factor Analysis

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ch.25 Factor Analysis

Before we start Factor Analysis, let’s reload the States data in the package carData to put the data in its first state.

Let’s choose Factor analysis.

Select all variables.

Select to have 1 factor.

The results show that the p value is very low for the hypothesis that one factor is sufficient. So let’s specify factor as two.

Again, as you execute the command, specify factor as two.

I’ve specified it as two factors, and it seems almost certain that dollars, pay, and percent will belong to factor2. SATM and SATV belong to factor1, pop is a bit vague.

Let’s try changing the method of rotation in ‘Options’ to Promax.

This will show you this result: It seems reasonable that dollars and pay belong to factor2, and SATM and SATV belong to factor1.

At this point, draw the matrix scatter plot that we saw earlier and you will get an idea. Among the variables, you can see that dollars and pay are very consistent, showing a positive relationship, and SATM and SATV are also very consistent, showing a positive relationship with each other.

Dollars and pay are something similar, so I think we can put them together. I think SATM and SATV could be combined in a similar way. By the way, percent seems to be similar to dollars and pay, but it feels something a little different, and pop is not like anything else.

Let’s say you have student performance data. Both English and French grades are likely to have similar grades as a language, and Math and Physical grades are likely to have similar grades. If you have a similar distribution like this (which may or may not actually be the case), you can lump the highly correlated things together and represent them as one common factor.

As another example, let’s say you have data that expresses a person’s personality with multiple scores. Even in this case, you will be able to tie together certain scores that have a high relationship with each other. (Happiness and Satisfaction, for example)

In this way, you can use factor analysis when you want to tie things together and express things that are highly related. For reference, the principal component analysis we learned earlier has similarities to the factor analysis because we want to bundle these variables together and represent them in 2 component. They are often confused in this regard.

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