# [R] Regression with partial info about the dependent variable

From: maneesh deshpande <dmaneesh_at_hotmail.com>
Date: Wed 28 Dec 2005 - 13:54:21 EST

Hi,

I have the following problem which I would appreciate some help on.

A variable y is to be modelled as a function of a set of variables Vector(x).
The twist is that there is another variable z in the problem with the property that y(i) <= z(i).
So the data set is divided into three categories

I. y(i) = z(i)
II. Both y(i) and z(i) are known and y(i) < z(i) III. y(i) is not known but z(i) is known ( But y(i) is guaranteed to be < z(i) )

The data in categories I + II can be satisfactorily modelled via a OLS regression of the form:
y ~ Vec(x)
The question is how to incorporate the information contained in the category III data?
The category II data can be used to construct a model for y given z. Indeed log(z(i)-y(i))
is reasonably normal and so the following is a decent approximation: y(i) = z(i) + A*exp( N(0,1) )
This model can be improved by including Vec(x).

After this I am not sure how to proceed :-( :-(