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--- how_to_run_pure_gblup [2019/06/07 00:30] – yutaka
+++ how_to_run_pure_gblup [2019/06/07 01:34] – yutaka
@@ Line 15: / Line 15: @@
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-where $\mathbf{y}$ is a vector of observations, $\mathbf{b}$ is a vector of fixed effects (typically a single $\mu$), $\mathbf{u}$ is a vector of additive genetic effects, $\mathbf{e}$ is a vector of residual effects. We assume $\mathrm{var}(\mathbf{y})=\mathrm{var}(\mathbf{u})+\mathrm{var}(\mathbf{e})=\mathbf{G}\sigma_{u}^{2}+\mathbf{R}\sigma_{e}^{2}$ where $\mathbf{G}$ is the genomic relationship matrix, $\mathbf{R}$ is a diagonal matrix (typically $\mathbf{I}$), $\sigma_{u}^{2}$ is the additive genetic variance, and $\sigma_{e}^{2}$ is the residual variance. The system of mixed model equations (MME) is shown as follows.
+where $\mathbf{y}$ is a vector of observations, $\mathbf{X}$ is a design matrix relating the fixed effects to the observations (typically $\mathbf{1}$), $\mathbf{b}$ is a vector of fixed effects (typically a single $\mu$), $\mathbf{u}$ is a vector of additive genetic effects, $\mathbf{e}$ is a vector of residual effects. We assume $\mathrm{var}(\mathbf{y})=\mathrm{var}(\mathbf{u})+\mathrm{var}(\mathbf{e})=\mathbf{G}\sigma_{u}^{2}+\mathbf{R}\sigma_{e}^{2}$ where $\mathbf{G}$ is the genomic relationship matrix, $\mathbf{R}$ is a diagonal matrix (typically $\mathbf{I}$), $\sigma_{u}^{2}$ is the additive genetic variance, and $\sigma_{e}^{2}$ is the residual variance. The system of mixed model equations (MME) is shown as follows.
 $$
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 \right]
 $$
-Note that $\mathbf{R}^{-1}=\mathbf{I}/\sigma_{e}^{2}$.
+Note that $\mathbf{R}^{-1}=\mathbf{I}/\sigma_{e}^{2}$ in the typical case.
 ===== A way to build MME in blupf90 =====
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 The blupf90 program is designed to solve the animal model that has the inverse of the numerator relationship matrix ($\mathbf{A}^{-1}$). Also, this program is extended to perform the single-step GBLUP analysis including the inverse of a subset pedigree matrix for genotyped animals ($\mathbf{A}_{22}^{-1}$) as well as $\mathbf{G}^{-1}$.
-Regardless of the above GBLUP model, the program literally creates the following MME.
+Regardless of whether you need the pedigree relationships, the program literally creates the following MME.
 $$
@@ Line 69: / Line 69: @@
 When all animals are genotyped, you will see $\mathbf{A}^{-1}=\mathbf{A}_{22}^{-1}$, and therefore, the two pedigree matrices will be canceled out in MME; only $\mathbf{G}^{-1}$ remains there in theory.
-One restriction to run GBLUP in blupf90 is that this program always requires the pedigree file to create $\mathbf{G}^{-1}$ even though the pedigree information is not used. Also, the program literally calculates $\mathbf{A}^{-1}$ and $\mathbf{A}_{22}^{-1}$, and adds them to MME even though these matrices will be numerically cancelled out. It means you have to prepare a pedigree file to run GBLUP, and the pedigree can be dummy.
+One restriction to run GBLUP in blupf90 is that this program always requires the pedigree file to create $\mathbf{G}^{-1}$ even though the pedigree information is not used. Also, the program literally calculates $\mathbf{A}^{-1}$ and $\mathbf{A}_{22}^{-1}$, and adds them to MME even though these matrices will be numerically canceled out. It means you have to prepare a pedigree file to run GBLUP, and the pedigree can be a dummy.
 ==== Procedure to run GBLUP ====
@@ Line 97: / Line 97: @@
 The parameter file for renumf90 is as follows.
-It has three OPTIONs that changes the behavior of blupf90 to have the correct $\mathbf{G}^{-1}$ for GBLUP.
+It has three OPTIONs that change the behavior of blupf90 to have the correct $\mathbf{G}^{-1}$ for GBLUP.
 <file text renum.txt>
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 First of all, you do not provide any pedigree file in this parameter file.
 The renumf90 program creates a dummy pedigree file that has only animal ID but no parent ID.
-This dummy pedigree actually creates the pedigree relationships $\mathbf{A}^{-1}=\mathbf{I}$ and $\mathbf{A}_{22}^{-1}=\mathbf{I}$, which will be cancelled out in the end.
+This dummy pedigree actually creates the pedigree relationships $\mathbf{A}^{-1}=\mathbf{I}$ and $\mathbf{A}_{22}^{-1}=\mathbf{I}$, which will be canceled out in the end.
 The first two options define the blending of matrices.
@@ Line 145: / Line 145: @@
 We call this adjustment //tuning// to obtain the final matrix.
 $$
-\mathbf{G}_{\mathrm{final}} = a\mathbf{G}_{\mathrm{updated}} + b\mathbf{J}
+\mathbf{G}_{\mathrm{final}} \leftarrow a\mathbf{G}_{\mathrm{updated}} + b\mathbf{J}
 $$
-The constants $a$ and $b$ are tuning parameters. It is critical for genomic prediction when the genotyped animals are form only the last generation but you have the historical pedigree (i.e. incompatible $\mathbf{G}$ and $\mathbf{A}_{22}$).
+The constants $a$ and $b$ are tuning parameters. It is critical for genomic prediction when the genotyped animals are from only the last generation but you have the historical pedigree (i.e. incompatible $\mathbf{G}$ and $\mathbf{A}_{22}$).
 Using the dummy pedigree, this tuning is nonsense, and therefore, you should turn it off by the option.
@@ Line 155: / Line 155: @@
 You don't have to use any other options to run GBLUP.
-If you have more complicated situations, it might be reasonable to use [[http://nce.ads.uga.edu/wiki/doku.php?id=undoc:blupf90|''OPTION omit_ainv'']]. But again, if you are satisfied with above method, you don't need the extra option.
+If you have more complicated situations, it might be reasonable to use [[http://nce.ads.uga.edu/wiki/doku.php?id=undoc:blupf90|''OPTION omit_ainv'']]. But again, if you are satisfied with the above method, you don't need the extra option.