Date:         Mon, 10 Aug 1998 16:55:11 -0500
Reply-To:     "Feinstein, Zachary" <zfeinstein@CARLSON.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         "Feinstein, Zachary" <zfeinstein@CARLSON.COM>
Subject:      logistic regression output
Content-Type: text/plain

Normally when one works with the case of a dichotomous by a dichotomous
variable design, the output from logistic regression (the Exponentiated B
weight) is the odds-ratio.  I am currently working with data that is
dichotomous by polytomous and am interested in an overall odds-ratio
statistic to describe the effect if the Gamma or Somer's D statistic is
statistically significant (the polytomous variable is ordered).
 
I can easily obtain the individual odds-ratios of the adjacent levels if I
declare the independent variable as categorical and have the contrast be the
Repeated option.  Exp(B) may be obtained if I do not declare the independent
variable as categorical and do not specify a contrast.  Interpretation of
the Exponentiated B weight in this situation is a little difficult though--
it could be interpreted as the increase in the odds as one moves from one
level of the independent variable to the next.  But this seems dependent on
even or singular-unit spacing between the values of the independent
variable.  Although my polytomous independent variable is ordered, I wish to
avoid the issue of assuming that categories are evenly spaced.
 
Another idea was to weight the odds-ratios from the repeated contrast
(stated earlier) to come up with an overall odds-ratio statistic.  This
seems like it would be okay to do, although the middle points of the
polytomous distribution would receive more weight than the end points
(weighting by the matrix size of each 2 X 2).  Also, Agresti (in his book)
commented that this would be okay to do as long as the odds-ratio is
constant across the distribution (no trend).  I cannot guarantee that with
my data; however, theoretically, there should be no reason for a trend of an
increase or decrease across levels of the polytomous variable.  I'm only
interested in finding trends such as this with my data anyway.
 
The information discussed here is for market research data- data from
questions asked of respondents.  Any information would be great and I'm
interested in not only the statistical ramifications of what I am trying to
accomplish, but also the philosophical implications (i.e. do I have to
assume the data fits the linear-logistic model if I use Exp(B) as my overall
odds-ratio from a polytomous independent variable?- yes, but it doesn't seem
reasonable to fit such a model all the time).
 
Sorry if my explanation is riddled with errors.  Thanks in advance.
 
Zachary
zfeinstein@carlson.com