SPSS offers a certain metric to assess predictor or variable importance in clustering. How it is calculated has already been answered in the following thread:
The information provided by SPSS does not go beyond this:
So far, I think I have understood that it uses the p-value (of an F-Test) of a given variable and contrasts it to the p-value of another variable used in clustering to determine its importance. I have several questions sorted in the following for clarity:
a) Why does this metric use the decimal logarithm (of p-values) and why is there a negative sign in front of it?
b) "The importance of field i": does field simply mean variable?
c) For the denominator: why does it take the maximum value from j∈Ω (so the smallest p-value of any other variable used except the variable from the nominator)?
d) "where Ω denotes the set of predictor and evaluation fields": What concretely do "set of predictor" and "evaluation fields" mean? Why doesn't it say "set of predictors", in the sense of "number of predictors"?
e) What is the "minimal double value"? Is this an established term?
f) This study uses predictor importance and sets a cutoff level at 0.4 (and then clusters again only with the variables >=0.4). Is there any rule that tells us above which level variables are important? Or is the 0.4 chosen arbitrarily as a question of taste?