<- file stat 97discf.html -> Topics include : Group membership; classification getting worse; quadratic functions

Group Membership in DF

=======================Rich Ulrich, 7 Mar 1997==========ssc Subject: Re: Probability of Cluster Memb Message-ID: <5fps4f$k0l@usenet.srv.cis.pitt.edu> << mconklin@cresearch.com >> Michael Conklin (mconklin_1@CRESEARCH.COM) wrote: : I have a clustering program which assigns respondents to a single = : cluster. I have been asked to assign probabilities to these cluster = : memberships, that is, for each respondent determine the probability that = : this person really belongs in this cluster instead of another cluster. : Is there a general approach for doing this? One way to make sense of "clusters" which might come out of various sorts of programs, using arbitrary selection rules, is to run a "discriminant function" which operates on multivariate-normal distances. Various stat-packages or texts will describe these: The distance that a person lies from the centroid (center) of each group determines the "likelihood" (think of the y-ordinate of a normal density) of belonging to that group. The conditional Likelihood of belonging to group A is computed as [the ordinate for A], divided by [the sum of ordinates for all of the groups]. The formula can also be adjusted for "prior probabilities", or you can make computations that minimize the "Cost of mis-allocation" if it were worse to make one certain errors, compared to others. *--------

Classification (gets worse)

=======================Rich Ulrich, 31 Mar 1997==========ssc Subject: Re: Questions about Discriminant analysis: Message-ID: <5horck$21b@usenet.srv.cis.pitt.edu> Don, Central Inst for the Deaf (cid@wugate.wustl.edu) wrote: : I am testing some programs I wrote to do discriminant analysis. I am : able to use linear or quadratic decision functions. I test the program : by testing it on the training data. : What has me a little concerned is that *sometimes* my results get worse : if I add new variables. My intuition tells me that adding new varaibles : should not cause the classification rate to go down. ... : So how can adding new variables cause discriminant analysis to do worse? I think you are assuming that the "classification table" is the goal of the analysis, but mathmetically, it is NOT. If you think of two group scores as 0,1, then the mathematical goal is to minimize the *average* residual scores. When a variable is added, it will reduce the average, but it is reasonable that some residuals will increase. So, *classifications* can change for the worse, even with a Fit that has been "improved" by other criteria. Also, note that the table you see, produced by a default analysis, is not the ONLY table possible, since the cut-off line could be drawn differently for the discriminating function. "Classification tables" are useful as descriptive statistics, but they are not the goal in discriminant function. (If you have thousands of cases, you might be interested in CHAID, as an exploratory tool for maximizing the Classificiations.)

Quadratic functions?

=======================Rich Ulrich, 18 Mar 1997==========ssc Subject: Discriminant analysis: quadratic functions? Message-ID: <1680277502.3276495@invivo.edu> Andrew Siu (rsandsiu@polyu.edu.hk) wrote: : Hi. I am working on a 3-groups discriminant analysis with a sample of : around 300 cases in health care. There are 3 independent variables. : Multivariate normality assumption is OK but the assumption of equal : covariance matrices is violated (Box's M statistic in SPSS). Is the : use of quadratic functions really a better way to continue with the : analysis, instead of using linear functions? The books I read seems : to have reservations on this. Any comments or good reference on this? Nature is not designed that way. In practice, there is also the problem overfitting which especially afflicts people who have a lot more variables than you do. Have you looked at univariate transformations as a solution to unequal variances? Trimming of outliers? *----------March, 1998 comment: "Quadratic" is what you get when you allow unequal variances as an assumption of the analysis. Above, I was addressing the idea of continuous variables; if there are dichotomies, and a few have extreme divisions, then DF may be less effective than clustering, or logistic regression. "Quadratic" equations permit that one Group can be defined as an island, surrounded by another group. If that is not your model, you should seek another solution. Where nature *is* designed that way, with continuous variables, it is apt to be for one predictor at a time; and I would not expect the general, quadratic resultwith several veriables to be robust. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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