From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
Subject: Re: Binary Correlations. Was: Levels of Measurement?
Reply-To: thompson@atlas.socsci.umn.edu
Organization: Economics Department, University of Minnesota
Date: Fri, 18 Dec 1992 20:30:45 GMT

thompson@atlas.socsci.umn.edu (T. Scott Thompson) writes:

>Perhaps someone interested in the levels of measurement question might
>be able to help me too.

>I have been acting as informal statistical consultant for my wife, who
>is a physician with only an elementary statistical background, in a
>project where she wants measures of association between a fairly large
>number of binary variables in a sample with n=500 and in a subsample
>with n = 260.  (These numbers may increase in the future.)  

>We have been calculating standard Pearson correlation coefficients,
>which to my way of thinking are as good as anything else at describing
>binary associations, since scaling is not an issue for binary data.  I
>do not claim to have studied the issue in depth, however.

[stuff deleted]

>What is "the right way" to do this from the point of view of
>statistical theory?

Many thanks to those who have responded so far.  I will summarize your
responses to the net sometime in the future.  (Probably in early
January.)

Since a few people have e-mailed me with requests for more detail
about the problem/data, here is a summary:

The sample consists of data taken from the charts of pediatric
patients who were seen in the pediatric outpatient clinic at one of
the large public hospitals in Minnesota on certain days chosen at
random.  The variables include age and sex of the child, various
variables summarizing the history of contact with the pediatrics
clinic (i.e.  whether or not it is their first visit, whether or not
this is their primary care clinic, etc.).  These variables are used to
define the smaller subsample, which can be thought of as the group
that regularly visits the clinic for medical treatment, and for whom
the medical history appears to be reasonably complete.

(Yes, we know that there is a selectivity problem.  No. We are not
doing anything about it yet.  Any suggestions on how to handle it are
welcome.)

The remaining variables consist of binary indicators coded from the
patient's chart for whether or not the patient has certain "morbidity
factors."  These come in three flavors, which I can loosely describe
as "clinical conditions" (e.g. ear infections), "developmental
conditions" (e.g. whether or not the child was born premature, whether
or not the child's physical growth is delayed, diagnosis of speech
problems), and "social conditions" (e.g. whether or not the mother is
a teenager, whether or not the child has been refered to a family
protection agency because of child abuse, whether or not the child has
been placed in a foster home).  There are about 150 morbidities
altogether, of which about 20 have an estimated incidence greater than
2 percent.  We are mostly looking at these 20.

The main goal, as nearly as I can tell, is to find patterns in the
diagnostic groups, i.e. patterns of association among the morbidities
and among the groups of morbidities.  Presumably these will be used to
help identify the kinds of services that the hospital should be
providing, and to aid in detection of problems that might otherwise go
unnoticed in the usual chaos of the clinic.

As you might surmise from the above, the clinic serves a largely poor,
inner city population, and most of the patients are seen on a "walk
in" basis.
--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209
Newsgroups: sci.math.stat