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From |
"easycalcs" <[email protected]> |

To |
[email protected] |

Subject |
Re: st: random coefficient models |

Date |
Tue, 21 Oct 2003 23:10:23 -0000 |

Apologies for several similar earlier postings on GLS - I wasn't sure that any had gone thru'. I'm bringing this posting to the top. My request is for a procedure that will estimate k that will maximize the log-likelihood function, being a function of the residual sum of squares viz [y(i)/w(i)-1/w(i)-x(i)/w(i)]^2, as w(i) is a function of k (see below)! Come on you Stata coders, someone can surely help. Thanks. Also, in reply to Professor Stephen P. Jenkins, once k is known Var [(n(i)] can be backed out. --- In [email protected], "easycalcs" <easycalcs@y...> wrote: > There's no need at the estimation stage to know the variance of e (i) > or n(i): > > Substititute for b1(i) in the y equation and obtain > > y = b0+Bx(i)+v(i) > > where v(i)=e(i)+x(i)n(i) > > The new equation has a heteroskedastic error > Var[v(i)]= Var[e(i)]+x(i)^2Var[(n(i)] = Var[e(i)]{1+kx(i)^2} > where k= Var[e(i)]/Var[n(i)] > > If e(i) and n(i) are iid ~ normally, a loglikelihood formulation can > be set up. If the weights are computed as w(i)=(1+kx(i))^1/2 the > weighted least squares is y(i)/w(i) on 1/w(i) and x(i)/w(i). A > concentrated loglikelihood may be established (with unknown paramter > k) where the residual sum of (weighted) least is formulated in terms > of the unknown parameter k. This is then maximised wrt k! > > Does anyone have the formulation/Stata specification proc for such a > concentrated loglikelihood function? I'm not a Stata coder! Thanks. > > GM,Reading(aka easycalcs) > > > --- In [email protected], "Stephen P. Jenkins" > <stephenj@e...> wrote: > > On Mon, 20 Oct 2003 12:54:33 -0400 Steven Devaney > > <DevaneySP@n...> wrote: > > > > > Hello again > > > > > > Off-list I was asked to clarify what I meant. > > > > > > What I am interested in is whether anyone knows about or has > written an MLE procedure for estimating B in the set-up? > > > > > > y(i) = b0 + b1(i) + e(i) > > > > > > where > > > > > > b1(i) = B + n(i) > > > > > > I was hoping to use Hildreth and Houck, but cannot constrain > xtrchh so that t = 1. > > > > If t = 1 (single cross-section), can you identify the variance of > the > > b1(i), or equivalently the variance of the n(i) ? > > > > > > Stephen > > ---------------------- > > Professor Stephen P. Jenkins <stephenj@e...> > > Institute for Social and Economic Research (ISER) > > University of Essex, Colchester, CO4 3SQ, UK > > Tel: +44 (0)1206 873374. Fax: +44 (0)1206 873151. > > http://www.iser.essex.ac.uk > > > > * > > * For searches and help try: > > * http://www.stata.com/support/faqs/res/findit.html > > * http://www.stata.com/support/statalist/faq > > * http://www.ats.ucla.edu/stat/stata/ > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: random coefficient models***From:*"easycalcs" <[email protected]>

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