[R-sig-ME] Weighted regression in REML

Ben Bolker bbolker @ending from gm@il@com
Wed Oct 17 02:27:36 CEST 2018

  Can I please request that in general people **not** use this list to
post links to material that is (presumably) violating the
authors'/publisher's wishes? (A screenshot of a particular equation
would seem to constitute "fair use" ...)

  FWIW your statement sounds correct to me -- in the Bates et al.
JSS/lmer paper (available via vignette("lmer", package="lme4")), the
development of the estimation procedure mostly leaves the weights out
for simplicity, but says:

"To allow for case weights, we save the products X^⊤ W X, X^⊤ W y, Z^⊤ W
X, Z^⊤ W y and Z^⊤ W Z (see Table 6)."

  W is the weight matrix, so this is equivalent to multiplying X, y, Z
by W^(1/2) ...

    Ben Bolker

On 2018-10-16 05:16 PM, Nik Tuzov wrote:
> Hello:
> I'm reading the book of Searle:
> http://www.leg.ufpr.br/~eder/Variance%20Components.pdf
> I think that equation 53 on p 276 suggests that if one wants to use weights in REML, the solution is very similar to that in OLS: multiply X, Z, and Y by the square root of the weight matrixand proceed as in unweighted case. Am I right or there is more that needs to be done?
> Regards,Nik
> 	[[alternative HTML version deleted]]
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