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--- readme.blupf90new [2018/08/21 20:32] – shogo
+++ readme.blupf90new [2022/05/06 01:50] – [Storing accuracy based on PEV] dani
@@ Line 1: / Line 1: @@
-====== BLUPF90TEST ======
+====== BLUPF90+ ======
-UNDER CONSTRUCTION
 ===== Summary =====
-This is a combined program of blupf90 and airemlf90.
+This program combines blupf90, remlf90, and airemlf90.\\
 \\
-\\
+See [[http://nce.ads.uga.edu/wiki/doku.php?id=readme.pregsf90|PREGSF90]] for options using genomic (SNP) information.
-See PREGSF90 with genotypes (SNP) for options.
+\\
+**Hint**: type ''blupf90+ %%--%%help'' to see all the blupf90+ options or ''blupf90+ %%--%%help-genomic'' to see all the genomic options blupf90+ can take.
 ===== Options =====
 <file>
-OPTION method VCE (default BLUP)
+OPTION method VCE (default BLUP with blupf90 options)
 </file>
-Run aoremlf90 (default running blupf90)
+Runs airemlf90 for variance component estimation (default running blupf90)
 <file>
 OPTION conv_crit 1d-12
@@ Line 25: / Line 25: @@
 OPTION EM-REML 10
 </file>
-Run EM-REML (REMLF90) for first 10 rounds to get initial variances within the parameter space (default 0).
+Runs EM-REML (REMLF90) for first 10 rounds to get initial variances within the parameter space (default 0).
 <file>
 OPTION use_yams
 </file>
-Run the program with YAMS (modified FSPAK). The computing time can be dramatically improved.
+Runs the program with YAMS (modified FSPAK). The computing time can be dramatically improved.
 <file>
 OPTION tol 1d-12
@@ Line 38: / Line 38: @@
 OPTION sol se
 </file>
-Store solutions and those standard errors.
+Stores solutions and those standard errors.
 <file>
 OPTION store_pev_pec 6
 </file>
-Store triangular matrices of standard errors and its covariances for correlated random effects such as direct-maternal effects and random-regression effects in "pev_pec_bf90".
+Stores triangular matrices of standard errors and its covariances for correlated random effects such as direct-maternal effects and random-regression effects in "pev_pec_bf90".
 <file>
 OPTION residual
@@ Line 50: / Line 50: @@
 OPTION missing -999
 </file>
-Specify the missing value (default 0) in integer.
+Specifies the missing value (default 0) in integer.
 <file>
 OPTION constant_var 5 1 2 ...
@@ Line 63: / Line 63: @@
 OPTION hetres_pos 10 11
 </file>
-Specify the position of covariables.
+Specifies the position of covariables.
 <file>
 OPTION hetres_pol 4.0 0.1 0.1
@@ Line 133: / Line 133: @@
 <file>OPTION out_se_covar_function</file>
 Indicate to store in file samples of (co)variances function for postprocessing (histogram, etc.)
+==== Storing accuracy based on PEV ====
+  OPTION store_accuracy eff
+Stores reliabilities based on PEV, where //eff// is the number of the animal effect.\\
+By default, it uses inbreeding (F) in the denominator of the reliability formula: reliability = 1-PEV/($\sigma\mathbf{}_{u}^{2}$(1 + F)) [[https://doi.org/10.1111/jbg.12470|Aguilar et al. (2020)]].\\
+It uses inbreeding based on $\mathbf{A}$ or $\mathbf{H}$ from the direct inversion of $\mathbf{A}^{-1}$ or $\mathbf{H}^{-1}$, whichever is being used.    \\
+  OPTION type 1.0
+Select 1.0 for dairy cattle (Reliability) or 0.5 for beef cattle (BIF accuracy) (default 1.0).
+  OPTION correct_accuracy_by_inbreeding filaname
+//filename// is the name of the inbreeding file if other than renf90.inb
+  OPTION correct_accuracy_by_inbreeding_direct 0
+This option turns off the inbreeding correction in the reliability formula.
+==== Omit A-inverse ====
+    OPTION omit_ainv
+This option prohibits the program from creating $\mathbf{A}^{-1}$.
+It is especially useful for GBLUP.
+For example, if you would like to perform the exact GBLUP, you can put the following options to your parameter file.
+    OPTION omit_ainv
+    OPTION TauOmega 1.0 0.0
+    OPTION AlphaBeta 0.95 0.05
+With the above options, the program doesn't create $\mathbf{A}^{-1}$ but calculates $\tau\mathbf{G}^{-1}-\omega\mathbf{A}_{22}^{-1}$. When the omega ($\omega$) is zero, only $\mathbf{G}^{-1}$ will be included in the equations. $\mathbf{G}$ is blended with $\mathbf{A}_{22}$ as $\alpha\mathbf{G}+\beta\mathbf{A}_{22}$ before the inversion ($\alpha=0.95$ and $\beta=0.05$ in this case).
+=== Details ===
+Assuming a single-trait ssGBLUP, the mixed model equations are as follows.
+\(
+\left[
+\begin{array}{ll}
+\mathbf{X}'\mathbf{X} & \mathbf{X}'\mathbf{Z}\\
+\mathbf{Z}'\mathbf{X} & \mathbf{Z}'\mathbf{Z} + \lambda\mathbf{H}^{-1}
+\end{array}
+\right]
+\left[
+\begin{array}{c}
+\mathbf{\hat{b}}\\
+\mathbf{\hat{u}}
+\end{array}
+\right]
+=
+\left[
+\begin{array}{c}
+\mathbf{X}'\mathbf{y}\\
+\mathbf{Z}'\mathbf{y}
+\end{array}
+\right]
+\)
+where $\mathbf{H}$ is a matrix combining additive genetic relationship matrices and a genomic relationship matrix.
+\(
+\mathbf{H}^{-1}
+=
+\mathbf{A}^{-1}
++
+\left[
+\begin{array}{cc}
+\mathbf{0} & \mathbf{0} \\
+\mathbf{0} & \tau\mathbf{G}^{-1}-\omega\mathbf{A}_{22}^{-1}
+\end{array}
+\right]
+\)
+If we omit $\mathbf{A}^{-1}$ and $\mathbf{A}_{22}^{-1}$, the equations are equivalent to GBLUP.
+GBLUP by BLUPF90 was not so easy because the program creates $\mathbf{A}^{-1}$ by default and there was no way to avoid this behavior.
+The new option removes $\mathbf{A}^{-1}$ from the equations so GBLUP will be easily performed.
 ===== Tricks =====