Factor Analysis Discussion
DIRECTIONS:
Discuss what you have learned about factor analysis. If this method applies to your current or future research plans, include these speculations in your discussion.
You may want to discuss such aspects as the logic of the method, the primary purposes of the method, the various steps involved, the matrices produced, the reasons for rotation, and so on. Other points of interest related to factor analysis are certainly welcome here.
READ:
Factor Analysis
As we know, Factor Analysis is a process used to discover the underlying nature of the inter-relationships between variables present in a correlation matrix. The goal of the analysis is to reduce a large number of correlated variables to a much smaller number of factors. Each factor represents a theoretical dimension upon which highly correlated variables are grouped together. So, Factor Analysis attempts to reduce the redundancy present in the correlation matrix by producing a smaller set of factors, which can then be interpreted.
But, the initial solution from the process is often difficult to interpret. For that reason, factors must be rotated to provide a better overall picture of the data. Rotation is a mathematical procedure that redistributes the factor loadings, without reducing the total amount of variance accounted for by the factors. Essentially, rotation attempts to make variables load highly on only one factor, and low on the remaining factors. This is usually referred to as "Simple Structure."
One way to visualize the effects of rotation is to look at the cows and the barn on the farmland in the animation. There is a fixed amount of "grass" for the cows to eat, and regardless of WHERE the cows and barn are placed on the farm, the total amount of grass remains the same.
Just as moving the cows from one area to another doesn't change the amount of grass available for them to eat, rotating the factors does not change the total amount of variance that is accounted for. But rotating the factors can make them more interpretable, as now variables that load highly on one may have small loadings on another.
Let's say that you have questions about how quickly or how steadily the cows eat. It might be helpful to put them in specific spots in the field so you can observe them more easily. This doesn't change the amount of grass available for the cows to eat, but it may well improve your ability to understand the information you gather.
Just as a farmer may want to see his cows and therefore not have them behind the barn or a clump of trees, so too, will a researcher need to see his or her factors clearly, which can be done with simple structure.
So, think of rotation as essentially doing the same thing; the "cows" represent the factors, and the "grass" represents the variability accounted for by the factors. Just as repositioning the cows has no effect on the total amount of grass eaten, repositioning the factors accounts for the same amount of variance as the unrotated factors, but now allows for simple structure.
Again, this means that variables load highly on one factor, and low on the remaining factors. The researcher can then examine the variables that load highly on a particular factor, and attempt to give a name to the dimension that it seems to suggest.
Credits
Subject Matter Expert:
Barry Trunk
Interactive Design:
Christina DiMeo
Instructional Designer:
Felicity Pearson
Project Manager:
Wade Fields
Voice Talent:
Brent Berheim
