On Wed, 24 Mar 2004 16:17:24 +0100, Torsten Franz <[EMAIL PROTECTED]> wrote:
> Hi, > > I've got a problem I need assistance for: > I've got a number of objects which are defined by several > parameters/variables. The parameters belong to different scales (metric, > ordinal, nominal). How can I express the degree of the homogeneity or > similarity of the objects? I suppose you could express it *subjectively* by using the opinions of experts. That could be a good starting point, in any case. > I'd like as result a number between 0 (unequal in all parameters) and 1 > (identical objects). At least the ordinal parameters should be regarded. Well, you could end up with a single number; you start with more. Suppose that you start out with multiple numbers, which each describe one dimension of difference. [ Simple example: distance apart in longitude; latitude; altitude.] Do you want to weight them the same? Do you want to add together those differences, or what? If some differences are correlated, do you want to count that differently? This is basically the problem tackled by 'cluster analysis.' Personally, I think that clustering algorithms are too arbitrary, and their solutions need a whole separate analysis in order to describe them. If you place objects into groups that are 'rather similar', then you can use 'discriminant function' or logistic regression in order to set up equations that have numbers: you can use those to assign distances. Discussions you may read about Discriminant function should make it clear that there is not an absolute answer to the question, "How many dimensions does it take?" - in order to describe the differences. ( I hope that you do understand 'dimensions' here in the mathematical and statistical way.) -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html - I need a new job, after March 31. Openings? - . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
