BOOKS OF RtfiDIfGS - PAHO/WHO

\'nKV 111,I No. 2, IIIJ·,ri
- 43 -
Lroups when tlhey caliirot le pautitionedil
further either because the samnple sizes are .
too sinall or the remaiiiuiig variation is
either tio low to Ibe redticedl ltirther or iunexplainable
iii teris of the variables in the
data base. Each observation is contained in
one and only one of these terminal groups.
with a predict.ld value eqtual to thie mean of
the group. That is, ifykj is the value of 'the
dependent variable for thejth observation
within the kth group, then
Yk =- k * ek (2.1)
whereYk is the mean tbr all menihers in the
kth grolip und ue is thte error it: Usillg ' lo
predict or estimnate Yk,. This proceldure
minimizes the sulin of the (ek,)- over all
observations. Thlis, individial oblservations
tend to have Iv¿alules close to thle incai¡
valite of tlie terminal grotup to whichl they
belong.
It was decited that the approach had he
be implemented on an inutiractive basis to
accommodate a hligh level of physician iiitervention.
This was an important considleration
since group formation using this
algorithm is biasically iterative in niature.
Since no computer system existed that
could handie large data bases efficiently in
the interactive mode, a new technology
was developed called AUTOGRP. 20 AU-
TOCRP supports a facility allowing onne to
·invoke a;n algorithm that determines pirtitions
hbased on the variance redluction
criterion c' tée? AID algorithm. This coinmand,
o¡ capability, of the system is referred
to as the CLASSIFY tacility.
' Mathematically, the algorithm can be
'described as follows20 : Each observation in'
Ia.data set has a value of the independent
yariable X and a value of the dependent
variable Y. lf there ;iare N possible distinict
values of the independent variable, then
'ihe subset of observations, or records, that
'has each value X, (1 . i - N) is called a
'category. If there are Mi observations in the
Ith actcgryv (1 ~ i ', N), ithe toital sitan tl'
squares (TSSQ) of the data with respect to
DI)C (:O()NS' UCI'I()N
the dependent variable is denlled as
N m 1
T;SSQ = (Y -Y)
i=l j=l
(2.2)
where Yu is the value of the dependent
variable for thejth ol)servation in the ith
category of independent variable, and
N
Y = 1
i .
i = 1 j=1
y',
N
i=l
M, IE (2.3)
or the meanis valtiue of the dependent variable
in the entire data set. The data set can
be partitioned on the basis of the independent
variable into G groups, where
each group is the uniúín of speci'ied
categories. That is, we can define the mapping
of categories to groups with sets Rk (1
< k 1 G), such that
Rk n Rk = 0,k# k'
G
U R = {i,2,3 .... N}>
k=l
The "within group sium of squares"
(WGSSQ) is the total of the sqluared deviations
(diffe'trences) of each group's observations
from the group mean with respect to
the dependent variable anad cain )e expressed
as
.WGSSQ (k) =
where
i R
i o Ry
Mj
j l
(Yjj - Y,, . 1 :r k 4; C. (2.4)
WGSSQ (k) = within group sum of
squares for the kth group
Ilk = set of a;ill ategories of the indtcpendent
variable in the kth group and