Hello all,
I have used Principal Component Analysis to create a new variable that is like an index of a personal characteristic.
The factor loadings of the variables used to create this index are all positive. However, the factor scores ( i.e the "index" for each observation -using predict command after factor analysis) have a range between -1 and 1. I would like them to be 0 to 1 instead so I can interpret data correctly.
Any idea/command on how I can figure this out? Thanks!!
Hello Carmen,
If your chief concern is how to linearly re-express a score that is currently from x to y in range onto a scale that is 0 to 1 in range, this transform will do that for you:
new score = (old score - minimum old score) / (maximum old score - minimum old score)
Good luck with your work.
Hello David. Thank you! This worked. However I still have negative values. What should I do with them? Interpret them as the student has no observed characteristic? Or use the absolute value of all values?
I would appreciate your insight. David Morse
You can use the modified factor analysis (also called weighted factor analysis) to create an index. The primary advantage of this method is that it allows the highest possible variation with the smallest possible number of factors and overcomes the weakness of defining a common weight for all the indicator variables. Usually, this method gives values between 0 and 1 (or 0-100%). An example of how to calculate the urbanization index can be found here:
Article Development of an urban intensity index to facilitate urban ...
Hello again, Carmen,
I'm not sure how you're still getting negative values after the re-expression. Note that you'd have to re-express the factor/component scores for each factor separately (as they are unlikely to all have the same local maximum and minimum values). Maybe I'm missing what you're trying to do.
Don't ignore negative numbers, and don't replace them with their absolute value! There really isn't any need to fret over the fact that the original numbers have both positive and negative values; this won't impact the meaningfulness of the scores as indicators of amount of the attribute/component in question.
Good luck finishing your project.
Carmen, you shouldn't tamper with output scores from PCA which usually results from factor components that have been so rotated that they are at right angles to each other. In order words, they are mutually independent.
Just use the output figures as they are. Secondly, any method of new variable creation that is not rotated to be at right angles with each other still retains correlation attributes. The new variables so created are not really independent new variables
In effect, I am not sure that use of modified factor analysis in this research will achieve the desired objective of creating new independent set of variables that are really orthogonal. The factors must have to be rotated to be at right angles to each other.
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