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re: st: toeplitz


From   Joseph Coveney <jcoveney@bigplanet.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   re: st: toeplitz
Date   Thu, 13 Jul 2006 18:07:45 +0900

David Airey asked (on Tue, 20 May 2003):

If this helps anyone answering my question about an equivalent model
statement to SAS proc mixed,

u + Alpha_1(i) + Alpha_2(i) + M_{i}+ e_m(i) where
u = grand mean
Alpha = polygenic effects random (13 of them)
M = QTL effect fixed
e_m = random error

proc mixed data=a;
model trait = m1;
random alpha1-alpha13/type=TOEP(1);

I found this explanation of toeplitz:

TYPE=TOEP<(q)>

specifies a banded Toeplitz structure. This can be viewed as a
moving-average structure with order equal to q-1. The TYPE=TOEP
option is a full Toeplitz matrix, which can be viewed as an
autoregressive structure with order equal to the dimension of
the matrix. The specification TYPE=TOEP(1) is the same as , s^2 I,
where I is an identity matrix, and it can be useful for specifying
the same variance component for several effects.

Probably not...

--------------------------------------------------------------------------------

Would it be something analogous to the following?  (See also
www.stata.com/statalist/archive/2006-06/msg00847.html )

Joseph Coveney

clear
set more off
quietly update
assert r(inst_exe) >= date("2006-07-06", "ymd")
assert r(inst_ado) >= date("2006-07-11", "ymd")
set seed `=date("2006-07-13", "ymd")'
set obs 200
forvalues i = 1/3 {
    generate float u`i' = 2 * invnorm(uniform())
}
generate float y12 = u2 - u1 + invnorm(uniform())
generate float y23 = u3 - u2 + invnorm(uniform())
drop u*
generate int id = _n
reshape long y, i(id) j(occasion)
generate byte u1 = -(occasion == 12)
generate byte u2 = 1 - 2 * (occasion == 23)
generate byte u3 = (occasion == 23)
xtmixed y || id: u1 u2 u3, cov(identity) noconstant ///
  collinear nolrtest nolog
exit


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