estimating variance components for arbitrarily defined var/covar matrices
Ben: Perhaps I am misunderstanding, but isn't this essentially the same
as a problem that I asked you about, some years ago, about which you
said that it cannot currently be done in lme4?
I guess that in my old question to you, Z*Z' was the identity matrix, so
the current question is perhaps a generalization of my question.
The catch, it seems to me, is that var(e) is ill-defined --- you can
replace var(e) by var(e) - zeta and Z*Z*VG by Z*Z'*VG + zeta*I for any
zeta such that
-delta < zeta < var(e)
where delta = min(diag(Z*Z'*VG)), and have an equivalent model.
Is it not so? If not, what am I misunderstanding?
In my question to you I asked if one could constrain var(e) to be zero
so as to make the model well defined, and you said no, one could not,
because of the way lmer does its estimation.
cheers,
Rolf
On 26/02/15 13:12, Ben Bolker wrote:
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 I haven't actually tried any problems like this, but 1. in principle this is possible 2. There's a hack at http://stackoverflow.com/questions/19327088/reproducing-results-from-previous-answer-is-not-working-due-to-using-new-version/19382162#19382162 3. you might take a look at the pedigreemm package for another example. There *might* be something else in the Reverse Depends/Suggests list at http://cran.r-project.org/web/packages/lme4/index.html , but nothing jumps out at me. Steve Walker is in the very early stages of working on a phylogenetic model with a similar structure. Looking forward to seeing what other people have to say ... Ben On 15-02-25 06:42 PM, Matthew Keller wrote:
Hi all, This is a typical problem in genetics and I'm trying to figure out whether there's any way to solve it using lmer or similar, and if not, why it isn't possible. Often in genetics, we have an n-by-n matrix (n=sample size) of genetic relationships, where the diagonal is how related you are to yourself (~1, depending on inbreeding) and off-diagonals each pairwise relationship. I'd like to be able to use lmer or some other function in R to estimate the variance attributable to this genetic relationship matrix. Thus: y = b0 + b*X + g*Z + error where y is a vector of observations, b is a vector of fixed covariate effects and g is a vector of random genetic effects. X and Z are incidence matrices for b & g respectively, and we assume g ~ N(0, VG). The variance of y is therefore var(y) = Z*Z' * VG + I*var(e) Z*Z' is the observed n-by-n genetic relationship matrix. Given an observed Z*Z' genetic relationship matrix, is there a way to estimate VG? I guess this boils down to, if we have an observed n-by-n matrix of similarities, can we use mixed models in R to get the variance in y that is explained by that similarity? Thanks in advance! [[alternative HTML version deleted]]
_______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
-----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.11 (GNU/Linux) iQEcBAEBAgAGBQJU7mTeAAoJEOCV5YRblxUHZ+8IAJbS6sHtOIHM1zJcql0jcizh IpPKXsu4x0jhEnhH4RIxLDwumHXKZQyZeGOYWDeD+wgE/mNUHqeWRiGYp8Qd8w+m IR6uaswTp5wVP/HcMfRB5cTeFVkhoXQ3aRa0nOZrwI7V4d5HTIRmg5NvCb9Kro7n ZM4ONyLEETHMXfOUgeDAA7SOWrGmoNschOBuMdhD/jaajo2Cf3QOI4owaq/vQ+D4 fW41afw5lWXOgck6MLDck77R+8IELxIrbfYWauxPJp47CyHHPS27pCH3PoHX7S7B LF5VJXL+Ta7gS3luig8Sou/fkXdt/NdHs1CqDP7EJ2B7VBM/1BasMMju13Y0ork= =4RMa -----END PGP SIGNATURE-----
_______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
Rolf Turner Technical Editor ANZJS Department of Statistics University of Auckland Phone: +64-9-373-7599 ext. 88276 Home phone: +64-9-480-4619