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Re: st: estimating the components of a total


From   Jeph Herrin <stata@spandrel.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: estimating the components of a total
Date   Tue, 13 Mar 2012 14:29:50 -0400

Aha! It's called compositional data, and there's a way to deal with it.

thanks,
Jeph

On 3/13/2012 12:01 PM, Austin Nichols wrote:
Jeph Herrin<stata@spandrel.net>:
findit dirifit

On Tue, Mar 13, 2012 at 11:43 AM, Jeph Herrin<stata@spandrel.net>  wrote:

This is not really a Stata question, but a modelling question, though
hopefully there is a Stata command that will provide a solution.

I have a dataset which contains reported totals and subtotals from
approximately 5k respondents. For example, 5k firms are asked about their
revenues from various sources, which are then summed to create total
revenues. (Specifically, it is an electronic form which forces respondents
to provide subtotals that equal their total). However, some respondents only
report their totals, and for these I am trying to estimate the subtotals.

A basic approach would be to simply calculate the ratio for each sub
category (eg, sales revenue/total revenue) for existing data and use this to
estimate the missing values. However, because I have a lot more information
on the respondents - for instance, number of employees, assets, etc - I
think I can model the subtotal more accurately using these variables. The
problem is, the subtotals estimated this way do not sum to the total.

Concretely, let's say there are three variables -x1-,-x2-,-x3-, and that
their total t = x1 + x2 + x3. What I'd like is something like multivariable
regression


  mv x1 x2 x3 = indvar1 + indvar2 + indvar3

with the constraint that

  x1+x2+x3 = t

Does this problem have a name and/or a standard solution?

thanks,
Jeph

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