"Donald F. Burrill" wrote:
>
> Comments embedded in original post...
>
> > Kenneth Benoit wrote:
> >
> > Perhaps someone can help me with this problem. I am trying to solve for
> > a number of parameters in three equations which are linked through
> > composition of the data. each model yields different parameter
> > estimates when estimated alone since the parameters are overidentified.
> > I'd be happy for any advice on the problem!
> >
> > Ken Benoit
> >
> > ---------------------------------------------------------
> > Kenneth Benoit http://benoit.tcd.ie
> > Department of Political Science mailto:[EMAIL PROTECTED]
> > Trinity College Tel: 353-1-608-2491
> > Dublin 2, Ireland Fax: 353-1-677-0546
>
> > Consider a system where:
> >
> > Y1 = X0 + (1-g11)b1 X1 + g21b2X2 + g31b3X3
> >
> > Y2 = X4 + g12b1 X1 + (1-g22)b2X2 + g32b3X3
> >
> > Y3 = X5 + g13b1 X1 + g23b2X2 + (1-g33)b3X3
>
> It is not clear that this is possible. From the constraints below,
> Y1 + Y2 + Y3 = X0 + X4 + X5 = 1; it follows that the other 9
> terms must add to zero. But the gij are all nonnegative, and from the
> description below so must be the bi; then can X1, X2, and/or X3 be
> negative? If not, then every one of the 9 terms must equal zero.
>
> > and: (I take it that ³ means < or =. and " means 'for all')
> >
> > 1 = Y1 + Y2 + Y3, 0 ³ Yi ³ 1.0 "i
> > 1 = X0 + X4 + X5, 0 ³ Xi ³ 1.0 "i
> > 1 = g11 + g12 + g13, 0 ³ gij ³ 1.0 "i,j
> > 1 = g21 + g22 + g33
> ^^^ This should read g23 ?
> > 1 = g31 + g32 + g33
> >
> > GOAL: To estimate g's and b's. Problems: overidentification; effects
> > of the data items and some of the parameters summing to 1 which I
> > still don't fully understand.
>
> > Background: This is for a voting transition study in Italy, where the
> > b's represent a the proportion of voters following a rational
> > proximity model, and the g's represent the discrete probability
> > distribution according to which non-rational voters distribute their
> > votes to one of three electoral coalitions (corresponding to the Y's).
>
> It is not clear to me why it is reasonable to multiply the g's by the
> b's. Seems to be representing the proportion of (those voters who vote
> rationally) who are voting non-rationally, which on the face of it would
> seem to be a contradiction in terms.
>
> > I have data for all of the Y's and X's, which are proportions.
> >
> > Possible ways to simplify:
> >
> > * Set gij's to constants before estimation.
> > * Set gij = g* " i,j.
> > * Set b3 = 1.
> > * Set b1 = b2.
> >
> > -----------------------------------------------------------------------
> > File translated fromTEXby TTH,version 2.56.
> > On 26 Nov 1999, 14:00.
>
> ------------------------------------------------------------------------
> 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
Hi and thanks very much for responding to my original post. It took me
so long to respond because I was travelling. I am still working on the
problem though and no closer to a solution of the original framework.
It's not an extremely complicated model but takes a long time to
explain. If you are curious or willing to look more at the setup from
my original e-mail I'd be happy to mail you the 5-page working draft
with the model and also a brief explanation of the data and the voting
district structure. I'll wait for word from you first before sending
anything.
Many thanks,
Ken
---------------------------------------------------------
Kenneth Benoit http://benoit.tcd.ie
Department of Political Science mailto:[EMAIL PROTECTED]
Trinity College Tel: 353-1-608-2491
Dublin 2, Ireland Fax: 353-1-677-0546
