Date:         Mon, 4 Mar 2002 15:07:23 +1100
Reply-To:     Peter Jamieson <ldolan@bigpond.net.au>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Peter Jamieson <ldolan@bigpond.net.au>
Subject:      Multinomial Logistic Regression of ranked data
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G'day All,
I am interested in learning to apply Multinomial Logistic Regression to
ranked data.
Examples of the data will initially be the results of chess tournaments such
as set out below.
There are a number of separate chess tournaments designated Event 1, Event 2
etc.
Each tournament may have from 6 to 16 competitors whose names are
abbreviated
under Player ie A, B, C etc.
For the benefit of non-chessplayers competitors receive one point for a win,
zero for a loss and half a point for a drawn game. The player(s) with the
highest number of points is(are) the winner(s).
International competitions are mostly organized by FIDE (Federation
International Des Eschec).
FIDE periodically issues an official Rating for registered players which is
updated according to their results using a formula developed by Prof Elo.
Basically if you beat other players you get more rating points, the stronger
the player you beat relative to yourself the more points you gain.
I believe tennis, golf and bridge for example may use a similar system(?).
The same cohort of players may not always be in each individual tournament.
Some events will be round-robin ie all-play-all, some may be all-play-all
twice whilst others may be
"Swiss-system" pairing where players players are matched according to their
round-by-round position on the score table.
There will be other predictor variables likely such as age, whether local or
overseas etc
but in the interest of brevity I will keep the list small to FIDE(player's
current rating), LastRank(players most recent finishing position in a
tournament) and AvL3Ranks(the player's average finishing position in his/her
last three tournaments).
"Score" is the player's point score for this tournament event.
From the data I would like to predict the odds of each of the players, X
winning an upcoming event.

Event 1
Player    FIDE     LastRank AvL3Ranks Score
A            2200            3                2.0      7.0
B            2235            4                3.7      6.5
C            2330            1                2.0      5.5
.....etc to a maximum of 16 players.

Event 2
Player    FIDE     LastRank AvL3Ranks Score
A            2200            3                2.0       9.0
B            2235            4                3.7       8.5
D            2330            1                2.0       6.5
.....etc to a maximum of 16 players.

I have looked through the past archives but did not find any similar
project.
I have located several papers in which authors discuss generating more input
data by the method of "exploding" the data for each race. However other
authors caution that this technique may not have universal applicability.
I would be interested in the lists views on this method plus any advice or
suggestions for my project.
Many thanks for your interest!
Cheers, Peter J.