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<p class="MsoNormal">Hi Metafor users,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I have a data set with missing values for ArgMean:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> tmp.dat.Arg3$ArgMean<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">  [1]     NA     NA  53.00  58.50     NA     NA     NA     NA<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">  [9]     NA     NA     NA  76.40  71.70  85.70  84.10  61.90<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[17]  62.20 153.00 153.00 144.00 143.00  63.00  60.00  58.50<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[25]  60.70  80.60  92.30  67.39  68.66  87.49  78.42  71.30<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[33]  69.12  71.30  69.80  68.60  79.22     NA     NA  83.00<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[41]  97.00 117.00 115.00  83.00  95.00 115.00 106.00  75.77<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[49]  74.05  74.05  84.96  91.85 102.18  98.70  86.30  98.90<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[57]  87.20  53.70  80.00  53.70  80.30     NA     NA  59.00<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[65]  61.00  47.00  53.00 100.40 103.30 111.40  89.20 102.70<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[73]     NA     NA  61.50  60.50  54.40  69.10  68.30  63.80<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[81] 111.00 107.00 113.00 109.00  59.80  84.50  57.40  83.80<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[89]  56.00  63.00  71.00  68.00  56.00  64.00  70.00  67.00<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[97]  82.40  82.80  94.20     NA     NA     NA  77.50  80.94<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[105]  78.80 110.30  73.00  97.60  73.00  77.70  63.00  63.00<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[113]  77.00  87.00  63.00  62.00  76.00  80.00  65.90  62.57<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height:11.25pt;background:white;word-break:break-all">
<span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[121]  68.00  79.00  60.00  72.00  67.00  71.00<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">My 4-level model using rma.mv function is:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">> </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">(tmp.CD <- rma.mv(ArgMean, ArgSEMtrDP^2, data=tmp.dat.Arg3,<o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                   mods = ~  <o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                     cArgDI + <o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                     factor(Breed) +  <o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                     factor(Breed)*cArgDI + <o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                     factor(Stage) +     <o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                     factor(Stage)*cArgDI + <o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                     factor(CD) +<o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                     factor(CD)*cArgDI,<o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                   random = ~1|laboratory/experiment/study,<o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibcpb"><span style="font-family:"Lucida Console";color:blue">+ </span></span><span class="gghfmyibcob"><span style="font-family:"Lucida Console";color:blue">                   method = "REML"))</span></span><span style="font-family:"Lucida Console";color:black"><o:p></o:p></span></pre>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The model is solved with the rma.mv function and indeed I get a warning message:<o:p></o:p></p>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span style="font-family:"Lucida Console";color:#C5060B"><br></span><span class="gghfmyibgob"><span style="font-family:"Lucida Console";color:#C5060B">Warning message:<o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibgob"><span style="font-family:"Lucida Console";color:#C5060B">In rma.mv(ArgMean, ArgSEMtrDP^2, data = tmp.dat.Arg3, mods = ~cArgDI +  :<o:p></o:p></span></span></pre>
<pre style="line-height:11.25pt;background:white;word-break:break-all"><span class="gghfmyibgob"><span style="font-family:"Lucida Console";color:#C5060B">  Rows with NAs omitted from model fitting.</span></span><span style="font-family:"Lucida Console";color:black"><o:p></o:p></span></pre>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Cook’s distance and robust functions work fine.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Upon calculation of I^2 statistic, I get the following:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> # Calculation of I^2 statistic<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> W <- diag(1/tmp.dat.Arg3$ArgSEMtrDP^2)<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> X <- model.matrix(tmp.CD)<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:#C5060B;mso-fareast-language:EN-CA">Error in W %*% X : non-conformable arguments<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> 100 * sum(tmp.CD$sigma2) /
<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">+   (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:#C5060B;mso-fareast-language:EN-CA">Error in diag(P) : object 'P' not found<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA"><o:p> </o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> # Separation of total variance by cluster<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> 100 * tmp.CD$sigma2 / (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:#C5060B;mso-fareast-language:EN-CA">Error in diag(P) : object 'P' not found<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-line-height-alt:0pt"><span style="font-size:12.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">>
<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">If I remove NA values for ArgMean, then I can solve I^2 statistic:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> tmp.dat.Arg3 <- subset (tmp.dat.Arg3,ArgMean > 0)<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA"><o:p> </o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA"><o:p> </o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> # Calculation of I^2 statistic<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> W <- diag(1/tmp.dat.Arg3$ArgSEMtrDP^2)<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> X <- model.matrix(tmp.CD)<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> 100 * sum(tmp.CD$sigma2) /
<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">+   (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[1] 93.233<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA"><o:p> </o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> # Separation of total variance by cluster<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:blue;mso-fareast-language:EN-CA">> 100 * tmp.CD$sigma2 / (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))<o:p></o:p></span></p>
<p class="MsoNormal" style="word-break:break-all"><span style="font-size:10.0pt;font-family:"Lucida Console";color:black;mso-fareast-language:EN-CA">[1]  0.0000022494 90.8175748834  2.4158304680<o:p></o:p></span></p>
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<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Is it possible to get I^2 statistic directly without removing NA values?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The residual heterogeneity is very high and it might be normal given the data analyzed ??. It is a meta-analysis on 108 raw treatment means from 44 studies, clustered within 29 experiments, themselves clustered within 16 laboratories. The
 effect of factor CD (type of studies) on the relationship was NS and is shown below:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-CA"><img width="468" height="357" id="Image_x0020_1" src="cid:image001.jpg@01D31106.A455D1C0"></span><o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Best,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Roger <span style="font-family:"Segoe UI Symbol","sans-serif"">
☺<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:13.5pt;font-family:"Kaufmann Bd BT";color:navy;mso-fareast-language:FR-CA">Roger Martineau, mv Ph.D.</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Centre de recherche et de développement</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">sur le bovin laitier et le porc</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Agriculture et agroalimentaire Canada/Agriculture and Agri-Food Canada</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Téléphone/Telephone: 819-780-7319</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR-CA" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Télécopieur/Facsimile: 819-564-5507</span><span lang="FR-CA" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">2000, Rue Collège / 2000, College Street</span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Sherbrooke (Québec)  J1M 0C8</span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA">Canada</span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy;mso-fareast-language:FR-CA"><a href="mailto:roger.martineau@agr.gc.ca"><span style="color:blue">roger.martineau@agr.gc.ca</span></a></span><span lang="EN-US" style="mso-fareast-language:FR-CA"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-CA"> <o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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