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<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Hi,<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>I attach an implementation of an idea proposed by
Gulnara. It uses weighted least squares to compute the REML heritability estimate.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>The function is found in &#8220;REMLrotateFun.R&#8221;
and some example code is found in &#8220;ExampleCode_REMLrotate.R&#8221; that
uses the data in &#8220;RemlEx.RData&#8221;.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>If someone would be interested in trying it (and
possibly also suggest improvements), I would appreciate it.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>It works for linear mixed models having a polygenic
random effect and iid residuals. It seems to be very fast. The example I attach
contains 680 observations.<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Is this a new algorithm or has it been done already?<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p>&nbsp;</o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Best wishes,<o:p></o:p></span></font></p>

<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Lars Rönnegård<o:p></o:p></span></font></p>

<p class=MsoNormal><st1:place w:st="on"><st1:PlaceName w:st="on"><font size=2
  face=Arial><span lang=EN-GB style='font-size:10.0pt;font-family:Arial'>Dalarna</span></font></st1:PlaceName><font
 size=2 face=Arial><span lang=EN-GB style='font-size:10.0pt;font-family:Arial'>
 <st1:PlaceType w:st="on">University</st1:PlaceType></span></font></st1:place><font
size=2 face=Arial><span lang=EN-GB style='font-size:10.0pt;font-family:Arial'><o:p></o:p></span></font></p>

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