[EMAIL PROTECTED] (Seymann, Richard) wrote in message news:<[EMAIL PROTECTED]>... > This isn't exactly a statistics question, but at least one possible solution > might employ a statistics tool. > > Here's the problem: > > In order to assign roommates, admitted freshmen are given a list of ten > characteristics and asked to rank-order their preferences from 1 for most > important to 10 for least important. The objective is to match roommates' > interests and preferences as closely as possible. Whatever matching > algorithm is used, it will be run independently for the four combinations of > male smokers, female smokers, male non-smokers, and female non-smokers. > > So, for each student we would expect a permutation of the integers from 1 to > 10, and if any two students submitted the same permutation, they'd be a > perfect match. My initial reaction is to calculate pair-wise correlation > coefficients and then sort through the correlation matrix to make roommate > pairings based on the magnitude (positive) of r, but I'm sure there must be > other approaches. Any comments, ideas, or suggestions would be welcome.
Depends on how you want to weight matches/mismatches. There are other measures/kinds of correlation you might find useful. For example, the spearman correlation corresponds to squaring the differences in rating. Taking absolute values of difference in rating would correspond to Spearman's footrule. Counting 1 for each exact match and 0.5 for each "difference of rank = 1" would be another measure. And so on. There's a myriad of possible similarity/distance measures you might use. Consider also that close matching on some criteria might matter more than on others. Further, consider that close matches on the top-rated items might matter more than on lower rated items (e.g. I might insist that my top rated item be in your top two, but not care much where my middle-rated item is in your list). These sort of decisions aren't statistical. They come from what you want to achieve. Glen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
