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RE: st: Nonlinear regression and constraints

From   "Clive Nicholas" <>
Subject   RE: st: Nonlinear regression and constraints
Date   Wed, 29 Jun 2005 11:42:13 +0100 (BST)

Daniel Schnieder wrote:

> Without going to much into detail: my parameters are percentages. They
> can only range from 0 to 1. There may be a better solution (i.e. a
> solution that better fits the data) beyond 1, BUT, as I said, by
> definition they cannot be above 1 (or below 0). So the best solution
> that is possible has to be between 0 and 1.
> My current model gives me values which are both below 0 (I changed the
> equation a little bit, corrected a minor error, but that doesn't matter
> for the problem).

Since the response variables in your models are 0-1 proportions, you may
find the -mlbeta- routine useful. Maximum-likelihood beta-distributed
regressions have been shown to outperform other models in terms of
producing more accurate and precise results (Paolino 2001). Alas, it
cannot do constraints (I'm busy trying to knit my own, with some success
from members of the list).

This program is _not_ downloadable from SSC. To download, go:

. net from

and then click on -mlbeta-. Have fun!

help for mlbeta

Maximum likelihood estimation with Beta-distributed dependent variables

mlbeta depvar [varlist] [if exp] [in range] [, di:spersion(varlist) ]
             [, robust] [svy]


mlbeta is an implementation of Paolino's (2001) method of estimating the
effect on a beta-distributed depvar of varlist.


di:spersion(varlist) allows for the estimation of an auxiliary dispersion


. mlbeta proportion var1 var2, di(var2 var3)       (estimate model)

Paolino, Philip. 2001.  "Maximum Likelihood Estimation of Models with
Beta-distributed Dependent Variables." Political Analysis Vol. 9, No. 4,
Autumn 2001.

Jack Buckley, Department of Political Science SUNY, Stony Brook.

CLIVE NICHOLAS        |t: 0(044)7903 397793
Politics              |e:
Newcastle University  |

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