On 13 Apr 2000, Wen-Feng Hsiao wrote:
> Suppose I have an aggregation model which is in the following form:
> Y = X11 * X12 + X21 * X22.
It may be that you're not getting answers because many of us are not at
all sure of the question. (For example, the phrase "aggregation model"
is not familiar to me.) Your "Subject:" question (linear or
interactive?) suggests that you're thinking in terms of multiple linear
regression as a means of analyzing your model; but then your example,
of aggregating the knowledge of two persons, conflicts with my view of
how "persons" ought to be represented (as cases, not as variables) in a
multiple regression problem.
And in most models that involve interaction, if X1 and X2 are
variables (predictors) whose product (or interaction) is part of a
regression model, one would usually expect to see X1 and X2 separately as
also part of the model -- at least initially, if only to verify that
their fitted coefficients are indistinguishable from zero.
Similarly, one would usually expect to find an intercept
modelled, or the absence of an intercept commented on explicitly.
> This model could be thought as an aggregation of two knowledge, namely
> X1. and X2.. Each knowledge contains two pieces of information
> (attributes). For example, X1 contains X11 ans X12. Now if X.1 is the
> height, and X.2 is the weight of a person. Then, the aggregation of any
> two persons, say, Student1(height=170cm, weight=60kg),
> Student2(height=180cm, weight=68kg) can be represented by
>
> Y = 170*60+180*68=22440.
While I think I know what "170 cm" and "60 kg" mean, I'm not at all sure
that I can interpret the idea of their product (10200 kg-cm?), let alone
the sum of two such entities accumulated for what I would ordinarily
think of as two cases.
> My question: a model as the above form is linear or interactive? I doubt
> it is not a linear model. Since it is not in this form: Y= c1 X1 + c2 X2,
> where c1 and c2 are constant. I doubt it is not a pure interactive form,
> since X.1 and X.2 are dependent. Sorry for this stupid question.
By "X.1 and X.2 are dependent" do you mean merely that they have non-zero
correlation? In the sense in which I've been accustomed to using "pure
interaction", it refers to an interaction term which is uncorrelated with
bothof the terms from which it is constructed. In your example that
cannot be the case -- X1*X2 will have a strong positive correlation with
X1, and also with X2, for human heights and weights. A "pure
interaction" term would be, for example, the residual from a regression
analysis predicting X1*X2 from X1 and X2 -- that is, the "error"
from the model
X1*X2 = a + b1*X1 + b2*X2 + error
where a, b1, and b2 are determined by the regression analysis.
I'm not sure whether this will help, because I'm still not sure I
understand what you're trying to ask; however, I do think I understand
the two answers I've seen offered.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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