| MABM_16M_MAM_November-06-2014_a November 6, 2014 |
| Obs | animal | sire | dam | afa | afb | sex | wwt |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1.00 | 0.00 | 1 | 289 |
| 2 | 2 | 0 | 0 | 0.00 | 1.00 | 2 | 245 |
| 3 | 3 | 0 | 2 | 0.50 | 0.50 | 2 | 256 |
| 4 | 4 | 1 | 0 | 0.50 | 0.50 | 2 | 261 |
| 5 | 5 | 1 | 2 | 0.50 | 0.50 | 1 | 292 |
| 6 | 6 | 1 | 3 | 0.75 | 0.25 | 1 | 286 |
| MABM_16M_MAM_November-06-2014_a November 6, 2014 |
| Model_3_Animal multibreed_eqvar_res_add_uneqvar_nadd_November-06-2014_a November 6, 2014 |
| ANIMAL BREEDING NOTES |
| CHAPTER 16M ALL MODELS |
| MULTIBREED ANIMAL MODELS WITH: |
| 1) UNEQUAL RESIDUAL, ADDITIVE, AND NONADDITIVE GENETIC VARIANCES |
| 2) EQUAL RESIDUAL VARIANCES, UNEQUAL ADDITIVE AND NONADDITIVE GENETIC VARIANCES |
| 3) EQUAL RESIDUAL AND ADDITIVE GENETIC VARIANCES, UNEQUAL NONADDITIVE GENETIC VARIANCES |
| 4) EQUAL RESIDUAL AND ADDITIVE GENETIC VARIANCES, NO RANDOM NONADDITIVE GENETIC EFFECTS |
| Mauricio A. Elzo, University of Florida, elzo@animal.ufl.edu |
| Read input dataset (SAS file) |
OBS animal sire dam afa afb sex wwt
------ --------- --------- --------- --------- --------- --------- ---------
1 1.0000 0 0 1.0000 0 1.0000 289.0000
2 2.0000 0 0 0 1.0000 2.0000 245.0000
3 3.0000 0 2.0000 0.5000 0.5000 2.0000 256.0000
4 4.0000 1.0000 0 0.5000 0.5000 2.0000 261.0000
5 5.0000 1.0000 2.0000 0.5000 0.5000 1.0000 292.0000
6 6.0000 1.0000 3.0000 0.7500 0.2500 1.0000 286.0000
|
| datmat = matrix of input data |
| datmat | ||||||
|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 0 | 1 | 289 |
| 2 | 0 | 0 | 0 | 1 | 2 | 245 |
| 3 | 0 | 2 | 0.5 | 0.5 | 2 | 256 |
| 4 | 1 | 0 | 0.5 | 0.5 | 2 | 261 |
| 5 | 1 | 2 | 0.5 | 0.5 | 1 | 292 |
| 6 | 1 | 3 | 0.75 | 0.25 | 1 | 286 |
| Enter Parameters for Current Run |
| Enter restronsol = 1 to impose restrictions on solutions to solve the MME, else = 0 if not |
| restronsol |
|---|
| 0 |
| No restrictions imposed on solutions to solve MME |
| Define number of traits = nt = 1 (DO NOT CHANGE; This program is for single traits ONLY !! |
| nt |
|---|
| 1 |
| Enter nanim = Number of animals |
| nanim |
|---|
| 6 |
| Enter nrec = Number of records |
| nrec |
|---|
| 6 |
| Enter nf = Number of fixed effects in the MME |
| nf |
|---|
| 6 |
| Enter nga = Number of random additive genetic effects in the MME |
| nga |
|---|
| 6 |
| ngn = Number of random nonadditive genetic effects in the MME |
| ngn |
|---|
| 6 |
| Enter uneqresvar = 1 if unequal residual variances else uneqresvar = 0 |
| uneqresvar |
|---|
| 0 |
| Enter uneqaddvar = 1 if unequal residual variances else uneqaddvar = 0 |
| uneqaddvar |
|---|
| 0 |
| Compute neq = nf+nga+ngn = total number of MME |
| neq |
|---|
| 18 |
| Define pedigf = pedigree file with breed composition of animals, sires, and dams |
| pedigf | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 2 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 3 | 0 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 4 | 1 | 0 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 5 | 1 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 6 | 1 | 3 | 0.75 | 0.25 | 1 | 0 | 0.5 | 0.5 |
| Construct xf = matrix of fixed and random effects |
| Construct fixed effects in matrix xf |
| xf | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Construct random additive genetic effects in matrix xf |
| xf | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Construct random nonadditive genetic effects in matrix xf |
| xf | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| Make x = xf, i.e., use computed xf |
| x | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| veaa | vebb | veab |
|---|---|---|
| 49 | 49 | 0 |
| TRICK: make r=diag(ve=1) for models with common residual variance |
| r = matrix of residual covariances |
| r | |||||
|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| invr = inverse of matrix of residual covariances |
| invr | |||||
|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| Read yf = vector of records |
| yf |
|---|
| 289 |
| 245 |
| 256 |
| 261 |
| 292 |
| 286 |
| Make y = yf, i.e., use read yf |
| y |
|---|
| 289 |
| 245 |
| 256 |
| 261 |
| 292 |
| 286 |
| Compute xtinvr = x transpose times r |
| xtinvr | |||||
|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0.5 | 0.5 | 0.5 | 0.75 |
| 0 | 1 | 0.5 | 0.5 | 0.5 | 0.25 |
| 0 | 0 | 1 | 1 | 1 | 0.5 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 1 | 0.5 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0.5 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| Compute xtinvr = x transpose times r times x |
| xtinvrx | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 6 | 3.25 | 2.75 | 3.5 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 2.5 | 2 | 0.5 | 0 | 0 | 0 |
| ROW2 | 3.25 | 2.3125 | 0.9375 | 1.875 | 2.25 | 1 | 1 | 0 | 0.5 | 0.5 | 0.5 | 0.75 | 1.375 | 1 | 0.375 | 0 | 0 | 0 |
| ROW3 | 2.75 | 0.9375 | 1.8125 | 1.625 | 0.75 | 2 | 0 | 1 | 0.5 | 0.5 | 0.5 | 0.25 | 1.125 | 1 | 0.125 | 0 | 0 | 0 |
| ROW4 | 3.5 | 1.875 | 1.625 | 3.25 | 1.5 | 2 | 0 | 0 | 1 | 1 | 1 | 0.5 | 2.25 | 2 | 0.25 | 0 | 0 | 0 |
| ROW5 | 3 | 2.25 | 0.75 | 1.5 | 3 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1.5 | 1 | 0.5 | 0 | 0 | 0 |
| ROW6 | 3 | 1 | 2 | 2 | 0 | 3 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW7 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW8 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW9 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW10 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW11 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW12 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| ROW13 | 2.5 | 1.375 | 1.125 | 2.25 | 1.5 | 1 | 0 | 0 | 0 | 1 | 1 | 0.5 | 2.25 | 1 | 0.25 | 0 | 0 | 0 |
| ROW14 | 2 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 0 |
| ROW15 | 0.5 | 0.375 | 0.125 | 0.25 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0.25 | 0 | 0.25 | 0 | 0 | 0 |
| ROW16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Enter intrabreed and interbreed additive genetic variances |
| vaaa | vabb | vaab |
|---|---|---|
| 36 | 36 | 0 |
| Compute vaf = vector of multibreed additive genetic variances |
| pedigf | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 2 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 3 | 0 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 4 | 1 | 0 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 5 | 1 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 6 | 1 | 3 | 0.75 | 0.25 | 1 | 0 | 0.5 | 0.5 |
| vaf |
|---|
| 36 |
| 36 |
| 36 |
| 36 |
| 36 |
| 36 |
| Compute daf = vector of computed residual additive genetic variances |
| Recall: (Ga)-1 = (I - 1/2 P') (Da)-1 (I - 1/2 P) |
| daf |
|---|
| 36 |
| 36 |
| 27 |
| 27 |
| 18 |
| 18 |
| Make da = daf, i.e., use computed da |
| Compute dainv = inverse of da |
| dainv = inverse of matrix of residual additive genetic variances |
| dainv |
|---|
| 0.0277778 |
| 0.0277778 |
| 0.037037 |
| 0.037037 |
| 0.0555556 |
| 0.0555556 |
| Enter intrabreed and interbreed nonadditive genetic variances |
| vnab |
|---|
| 16 |
| Compute vnf = vector of multibreed additive genetic variances |
| vnf |
|---|
| 16 |
| 16 |
| 16 |
| 16 |
| 16 |
| 16 |
| Compute dnf = vector of computed residual nonadditive genetic variances |
| Recall: (Gn)-1 = (I - 1/2 P') (Dn)-1 (I - 1/2 P) |
| dnf |
|---|
| 16 |
| 16 |
| 12 |
| 12 |
| 8 |
| 8 |
| Make dn = dnf, i.e., use computed dn |
| Compute dninv = inverse of dn |
| dninv = inverse of matrix of residual nonadditive genetic variances |
| dninv |
|---|
| 0.0625 |
| 0.0625 |
| 0.0833333 |
| 0.0833333 |
| 0.125 |
| 0.125 |
| Compute gainv = inverse of the matrix of multibreed additive genetic covariances |
| Using algorithm to compute gainv directly; Elzo (1990a),JAS 68:1215-1228 |
| gainv | |||||
|---|---|---|---|---|---|
| 0.0648148 | 0.0138889 | 0.0138889 | -0.018519 | -0.027778 | -0.027778 |
| 0.0138889 | 0.0509259 | -0.018519 | 0 | -0.027778 | 0 |
| 0.0138889 | -0.018519 | 0.0509259 | 0 | 0 | -0.027778 |
| -0.018519 | 0 | 0 | 0.037037 | 0 | 0 |
| -0.027778 | -0.027778 | 0 | 0 | 0.0555556 | 0 |
| -0.027778 | 0 | -0.027778 | 0 | 0 | 0.0555556 |
| gainv | |||||
|---|---|---|---|---|---|
| 0.065 | 0.014 | 0.014 | -0.019 | -0.028 | -0.028 |
| 0.014 | 0.051 | -0.019 | 0.000 | -0.028 | 0.000 |
| 0.014 | -0.019 | 0.051 | 0.000 | 0.000 | -0.028 |
| -0.019 | 0.000 | 0.000 | 0.037 | 0.000 | 0.000 |
| -0.028 | -0.028 | 0.000 | 0.000 | 0.056 | 0.000 |
| -0.028 | 0.000 | -0.028 | 0.000 | 0.000 | 0.056 |
| Compute gninv = inverse of the matrix of regression nonadditive genetic covariances |
| Using algorithm to compute gninv directly; Elzo (1990b),JAS 68:4079-4099 |
| gninv | |||||
|---|---|---|---|---|---|
| 0.1458333 | 0.03125 | 0.03125 | -0.041667 | -0.0625 | -0.0625 |
| 0.03125 | 0.1145833 | -0.041667 | 0 | -0.0625 | 0 |
| 0.03125 | -0.041667 | 0.1145833 | 0 | 0 | -0.0625 |
| -0.041667 | 0 | 0 | 0.0833333 | 0 | 0 |
| -0.0625 | -0.0625 | 0 | 0 | 0.125 | 0 |
| -0.0625 | 0 | -0.0625 | 0 | 0 | 0.125 |
| gninv | |||||
|---|---|---|---|---|---|
| 0.146 | 0.031 | 0.031 | -0.042 | -0.063 | -0.063 |
| 0.031 | 0.115 | -0.042 | 0.000 | -0.063 | 0.000 |
| 0.031 | -0.042 | 0.115 | 0.000 | 0.000 | -0.063 |
| -0.042 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 |
| -0.063 | -0.063 | 0.000 | 0.000 | 0.125 | 0.000 |
| -0.063 | 0.000 | -0.063 | 0.000 | 0.000 | 0.125 |
| Compute lhs = left hand side of the MME |
| Add gainv to lhs |
| Add gninv to lhs |
| lhs | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 6 | 3.25 | 2.75 | 3.5 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 2.5 | 2 | 0.5 | 0 | 0 | 0 |
| ROW2 | 3.25 | 2.3125 | 0.9375 | 1.875 | 2.25 | 1 | 1 | 0 | 0.5 | 0.5 | 0.5 | 0.75 | 1.375 | 1 | 0.375 | 0 | 0 | 0 |
| ROW3 | 2.75 | 0.9375 | 1.8125 | 1.625 | 0.75 | 2 | 0 | 1 | 0.5 | 0.5 | 0.5 | 0.25 | 1.125 | 1 | 0.125 | 0 | 0 | 0 |
| ROW4 | 3.5 | 1.875 | 1.625 | 3.25 | 1.5 | 2 | 0 | 0 | 1 | 1 | 1 | 0.5 | 2.25 | 2 | 0.25 | 0 | 0 | 0 |
| ROW5 | 3 | 2.25 | 0.75 | 1.5 | 3 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1.5 | 1 | 0.5 | 0 | 0 | 0 |
| ROW6 | 3 | 1 | 2 | 2 | 0 | 3 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW7 | 1 | 1 | 0 | 0 | 1 | 0 | 4.1759259 | 0.6805556 | 0.6805556 | -0.907407 | -1.361111 | -1.361111 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW8 | 1 | 0 | 1 | 0 | 0 | 1 | 0.6805556 | 3.4953704 | -0.907407 | 0 | -1.361111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW9 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0.6805556 | -0.907407 | 3.4953704 | 0 | 0 | -1.361111 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW10 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | -0.907407 | 0 | 0 | 2.8148148 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW11 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | -1.361111 | -1.361111 | 0 | 0 | 3.7222222 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW12 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | -1.361111 | 0 | -1.361111 | 0 | 0 | 3.7222222 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| ROW13 | 2.5 | 1.375 | 1.125 | 2.25 | 1.5 | 1 | 0 | 0 | 0 | 1 | 1 | 0.5 | 9.3958333 | 2.53125 | 1.78125 | -2.041667 | -3.0625 | -3.0625 |
| ROW14 | 2 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 2.53125 | 7.6145833 | -2.041667 | 0 | -3.0625 | 0 |
| ROW15 | 0.5 | 0.375 | 0.125 | 0.25 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 1.78125 | -2.041667 | 5.8645833 | 0 | 0 | -3.0625 |
| ROW16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2.041667 | 0 | 0 | 4.0833333 | 0 | 0 |
| ROW17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -3.0625 | -3.0625 | 0 | 0 | 6.125 | 0 |
| ROW18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -3.0625 | 0 | -3.0625 | 0 | 0 | 6.125 |
| lhs | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6.000 | 3.250 | 2.750 | 3.500 | 3.000 | 3.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 2.500 | 2.000 | 0.500 | 0.000 | 0.000 | 0.000 |
| 3.250 | 2.313 | 0.938 | 1.875 | 2.250 | 1.000 | 1.000 | 0.000 | 0.500 | 0.500 | 0.500 | 0.750 | 1.375 | 1.000 | 0.375 | 0.000 | 0.000 | 0.000 |
| 2.750 | 0.938 | 1.813 | 1.625 | 0.750 | 2.000 | 0.000 | 1.000 | 0.500 | 0.500 | 0.500 | 0.250 | 1.125 | 1.000 | 0.125 | 0.000 | 0.000 | 0.000 |
| 3.500 | 1.875 | 1.625 | 3.250 | 1.500 | 2.000 | 0.000 | 0.000 | 1.000 | 1.000 | 1.000 | 0.500 | 2.250 | 2.000 | 0.250 | 0.000 | 0.000 | 0.000 |
| 3.000 | 2.250 | 0.750 | 1.500 | 3.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 1.500 | 1.000 | 0.500 | 0.000 | 0.000 | 0.000 |
| 3.000 | 1.000 | 2.000 | 2.000 | 0.000 | 3.000 | 0.000 | 1.000 | 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | 0.000 | 4.176 | 0.681 | 0.681 | -0.907 | -1.361 | -1.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.000 | 1.000 | 0.000 | 0.000 | 1.000 | 0.681 | 3.495 | -0.907 | 0.000 | -1.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 0.000 | 1.000 | 0.681 | -0.907 | 3.495 | 0.000 | 0.000 | -1.361 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 0.000 | 1.000 | -0.907 | 0.000 | 0.000 | 2.815 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 1.000 | 0.000 | -1.361 | -1.361 | 0.000 | 0.000 | 3.722 | 0.000 | 1.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.750 | 0.250 | 0.500 | 1.000 | 0.000 | -1.361 | 0.000 | -1.361 | 0.000 | 0.000 | 3.722 | 0.500 | 0.000 | 0.500 | 0.000 | 0.000 | 0.000 |
| 2.500 | 1.375 | 1.125 | 2.250 | 1.500 | 1.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 0.500 | 9.396 | 2.531 | 1.781 | -2.042 | -3.063 | -3.063 |
| 2.000 | 1.000 | 1.000 | 2.000 | 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | 0.000 | 1.000 | 0.000 | 2.531 | 7.615 | -2.042 | 0.000 | -3.063 | 0.000 |
| 0.500 | 0.375 | 0.125 | 0.250 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.500 | 1.781 | -2.042 | 5.865 | 0.000 | 0.000 | -3.063 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -2.042 | 0.000 | 0.000 | 4.083 | 0.000 | 0.000 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -3.063 | -3.063 | 0.000 | 0.000 | 6.125 | 0.000 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -3.063 | 0.000 | -3.063 | 0.000 | 0.000 | 6.125 |
| Compute rhs = right hand side of the MME |
| rhs |
|---|
| 1629 |
| 908 |
| 721 |
| 952 |
| 867 |
| 762 |
| 289 |
| 245 |
| 256 |
| 261 |
| 292 |
| 286 |
| 696 |
| 548 |
| 143 |
| 0 |
| 0 |
| 0 |
| rhs |
|---|
| 1629.0 |
| 908.00 |
| 721.00 |
| 952.00 |
| 867.00 |
| 762.00 |
| 289.00 |
| 245.00 |
| 256.00 |
| 261.00 |
| 292.00 |
| 286.00 |
| 696.00 |
| 548.00 |
| 143.00 |
| 0.00 |
| 0.00 |
| 0.00 |
| Compute ginvlhs = generalized inverse of the left hand side of the MME |
| ginvlhs | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0.203586 | 0.066550 | 0.137036 | -0.300665 | 0.112509 | 0.091077 | -0.171408 | -0.181700 | -0.109248 | -0.088665 | -0.162315 | -0.168807 | -0.001754 | 0.008083 | -0.005451 | -0.000877 | 0.003164 | -0.003603 |
| ROW2 | 0.066550 | 1.441156 | -1.374605 | -0.393957 | -0.532495 | 0.599045 | -0.338362 | 0.334010 | -0.014227 | -0.256930 | 0.177145 | -0.167590 | 0.111266 | 0.050065 | 0.027934 | 0.055633 | 0.080665 | 0.069600 |
| ROW3 | 0.137036 | -1.374605 | 1.511641 | 0.093293 | 0.645004 | -0.507968 | 0.166954 | -0.515709 | -0.095021 | 0.168266 | -0.339459 | -0.001217 | -0.113020 | -0.041982 | -0.033386 | -0.056510 | -0.077501 | -0.073203 |
| ROW4 | -0.300665 | -0.393957 | 0.093293 | 1.424320 | 0.084507 | -0.385171 | 0.096230 | 0.092544 | -0.098074 | -0.090700 | -0.084186 | -0.011123 | -0.245526 | -0.242003 | -0.124402 | -0.122763 | -0.243764 | -0.184964 |
| ROW5 | 0.112509 | -0.532495 | 0.645004 | 0.084507 | 0.567579 | -0.455070 | -0.144955 | -0.177443 | -0.009044 | 0.055932 | -0.299923 | -0.166898 | -0.087171 | -0.056117 | -0.058025 | -0.043585 | -0.071644 | -0.072598 |
| ROW6 | 0.091077 | 0.599045 | -0.507968 | -0.385171 | -0.455070 | 0.546147 | -0.026453 | -0.004257 | -0.100204 | -0.144596 | 0.137608 | -0.001908 | 0.085417 | 0.064200 | 0.052573 | 0.042708 | 0.074808 | 0.068995 |
| ROW7 | -0.171408 | -0.338362 | 0.166954 | 0.096230 | -0.144955 | -0.026453 | 0.690606 | 0.030907 | 0.081585 | 0.298943 | 0.347576 | 0.412457 | -0.027473 | 0.021615 | 0.019595 | -0.013736 | -0.002929 | -0.003939 |
| ROW8 | -0.181700 | 0.334010 | -0.515709 | 0.092544 | -0.177443 | -0.004257 | 0.030907 | 0.701666 | 0.304473 | 0.064995 | 0.364165 | 0.171932 | 0.029358 | -0.030301 | -0.013736 | 0.014679 | -0.000471 | 0.007811 |
| ROW9 | -0.109248 | -0.014227 | -0.095021 | -0.098074 | -0.009044 | -0.100204 | 0.081585 | 0.304473 | 0.580879 | 0.135104 | 0.211740 | 0.293811 | 0.055888 | -0.047572 | -0.036260 | 0.027944 | 0.004158 | 0.009814 |
| ROW10 | -0.088665 | -0.256930 | 0.168266 | -0.090700 | 0.055932 | -0.144596 | 0.298943 | 0.064995 | 0.135104 | 0.602999 | 0.178560 | 0.223841 | -0.057774 | 0.056259 | 0.030402 | -0.028887 | -0.000758 | -0.013686 |
| ROW11 | -0.162315 | 0.177145 | -0.339459 | -0.084186 | -0.299923 | 0.137608 | 0.347576 | 0.364165 | 0.211740 | 0.178560 | 0.700265 | 0.325563 | 0.002828 | -0.013029 | 0.008787 | 0.001414 | -0.005101 | 0.005808 |
| ROW12 | -0.168807 | -0.167590 | -0.001217 | -0.011123 | -0.166898 | -0.001908 | 0.412457 | 0.171932 | 0.293811 | 0.223841 | 0.325563 | 0.653743 | 0.010437 | 0.004394 | -0.020049 | 0.005218 | 0.007415 | -0.004806 |
| ROW13 | -0.001754 | 0.111266 | -0.113020 | -0.245526 | -0.087171 | 0.085417 | -0.027473 | 0.029358 | 0.055888 | -0.057774 | 0.002828 | 0.010437 | 0.300434 | 0.026934 | 0.012210 | 0.150217 | 0.163684 | 0.156322 |
| ROW14 | 0.008083 | 0.050065 | -0.041982 | -0.242003 | -0.056117 | 0.064200 | 0.021615 | -0.030301 | -0.047572 | 0.056259 | -0.013029 | 0.004394 | 0.026934 | 0.295736 | 0.153659 | 0.013467 | 0.161335 | 0.090296 |
| ROW15 | -0.005451 | 0.027934 | -0.033386 | -0.124402 | -0.058025 | 0.052573 | 0.019595 | -0.013736 | -0.036260 | 0.030402 | 0.008787 | -0.020049 | 0.012210 | 0.153659 | 0.317822 | 0.006105 | 0.082934 | 0.165016 |
| ROW16 | -0.000877 | 0.055633 | -0.056510 | -0.122763 | -0.043585 | 0.042708 | -0.013736 | 0.014679 | 0.027944 | -0.028887 | 0.001414 | 0.005218 | 0.150217 | 0.013467 | 0.006105 | 0.320007 | 0.081842 | 0.078161 |
| ROW17 | 0.003164 | 0.080665 | -0.077501 | -0.243764 | -0.071644 | 0.074808 | -0.002929 | -0.000471 | 0.004158 | -0.000758 | -0.005101 | 0.007415 | 0.163684 | 0.161335 | 0.082934 | 0.081842 | 0.325775 | 0.123309 |
| ROW18 | -0.003603 | 0.069600 | -0.073203 | -0.184964 | -0.072598 | 0.068995 | -0.003939 | 0.007811 | 0.009814 | -0.013686 | 0.005808 | -0.004806 | 0.156322 | 0.090296 | 0.165016 | 0.078161 | 0.123309 | 0.323934 |
| ginvlhs | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.204 | 0.067 | 0.137 | -0.301 | 0.113 | 0.091 | -0.171 | -0.182 | -0.109 | -0.089 | -0.162 | -0.169 | -0.002 | 0.008 | -0.005 | -0.001 | 0.003 | -0.004 |
| 0.067 | 1.441 | -1.375 | -0.394 | -0.532 | 0.599 | -0.338 | 0.334 | -0.014 | -0.257 | 0.177 | -0.168 | 0.111 | 0.050 | 0.028 | 0.056 | 0.081 | 0.070 |
| 0.137 | -1.375 | 1.512 | 0.093 | 0.645 | -0.508 | 0.167 | -0.516 | -0.095 | 0.168 | -0.339 | -0.001 | -0.113 | -0.042 | -0.033 | -0.057 | -0.078 | -0.073 |
| -0.301 | -0.394 | 0.093 | 1.424 | 0.085 | -0.385 | 0.096 | 0.093 | -0.098 | -0.091 | -0.084 | -0.011 | -0.246 | -0.242 | -0.124 | -0.123 | -0.244 | -0.185 |
| 0.113 | -0.532 | 0.645 | 0.085 | 0.568 | -0.455 | -0.145 | -0.177 | -0.009 | 0.056 | -0.300 | -0.167 | -0.087 | -0.056 | -0.058 | -0.044 | -0.072 | -0.073 |
| 0.091 | 0.599 | -0.508 | -0.385 | -0.455 | 0.546 | -0.026 | -0.004 | -0.100 | -0.145 | 0.138 | -0.002 | 0.085 | 0.064 | 0.053 | 0.043 | 0.075 | 0.069 |
| -0.171 | -0.338 | 0.167 | 0.096 | -0.145 | -0.026 | 0.691 | 0.031 | 0.082 | 0.299 | 0.348 | 0.412 | -0.027 | 0.022 | 0.020 | -0.014 | -0.003 | -0.004 |
| -0.182 | 0.334 | -0.516 | 0.093 | -0.177 | -0.004 | 0.031 | 0.702 | 0.304 | 0.065 | 0.364 | 0.172 | 0.029 | -0.030 | -0.014 | 0.015 | -0.000 | 0.008 |
| -0.109 | -0.014 | -0.095 | -0.098 | -0.009 | -0.100 | 0.082 | 0.304 | 0.581 | 0.135 | 0.212 | 0.294 | 0.056 | -0.048 | -0.036 | 0.028 | 0.004 | 0.010 |
| -0.089 | -0.257 | 0.168 | -0.091 | 0.056 | -0.145 | 0.299 | 0.065 | 0.135 | 0.603 | 0.179 | 0.224 | -0.058 | 0.056 | 0.030 | -0.029 | -0.001 | -0.014 |
| -0.162 | 0.177 | -0.339 | -0.084 | -0.300 | 0.138 | 0.348 | 0.364 | 0.212 | 0.179 | 0.700 | 0.326 | 0.003 | -0.013 | 0.009 | 0.001 | -0.005 | 0.006 |
| -0.169 | -0.168 | -0.001 | -0.011 | -0.167 | -0.002 | 0.412 | 0.172 | 0.294 | 0.224 | 0.326 | 0.654 | 0.010 | 0.004 | -0.020 | 0.005 | 0.007 | -0.005 |
| -0.002 | 0.111 | -0.113 | -0.246 | -0.087 | 0.085 | -0.027 | 0.029 | 0.056 | -0.058 | 0.003 | 0.010 | 0.300 | 0.027 | 0.012 | 0.150 | 0.164 | 0.156 |
| 0.008 | 0.050 | -0.042 | -0.242 | -0.056 | 0.064 | 0.022 | -0.030 | -0.048 | 0.056 | -0.013 | 0.004 | 0.027 | 0.296 | 0.154 | 0.013 | 0.161 | 0.090 |
| -0.005 | 0.028 | -0.033 | -0.124 | -0.058 | 0.053 | 0.020 | -0.014 | -0.036 | 0.030 | 0.009 | -0.020 | 0.012 | 0.154 | 0.318 | 0.006 | 0.083 | 0.165 |
| -0.001 | 0.056 | -0.057 | -0.123 | -0.044 | 0.043 | -0.014 | 0.015 | 0.028 | -0.029 | 0.001 | 0.005 | 0.150 | 0.013 | 0.006 | 0.320 | 0.082 | 0.078 |
| 0.003 | 0.081 | -0.078 | -0.244 | -0.072 | 0.075 | -0.003 | -0.000 | 0.004 | -0.001 | -0.005 | 0.007 | 0.164 | 0.161 | 0.083 | 0.082 | 0.326 | 0.123 |
| -0.004 | 0.070 | -0.073 | -0.185 | -0.073 | 0.069 | -0.004 | 0.008 | 0.010 | -0.014 | 0.006 | -0.005 | 0.156 | 0.090 | 0.165 | 0.078 | 0.123 | 0.324 |
| Compute gl = ginvlhs*lhs = matrix of expectations of solutions |
| gl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.500 | 0.250 | 0.250 | -0.000 | 0.250 | 0.250 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.250 | 0.625 | -0.375 | 0.000 | 0.125 | 0.125 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.250 | -0.375 | 0.625 | -0.000 | 0.125 | 0.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.250 | 0.125 | 0.125 | -0.000 | 0.625 | -0.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.250 | 0.125 | 0.125 | 0.000 | -0.375 | 0.625 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 |
| -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 1.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | -0.000 | 0.000 | 0.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 |
| Notice that lg = gl (i.e., lhs*ginvlhs = lhs*ginvlhs) |
| lg | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.500 | 0.250 | 0.250 | 0.000 | 0.250 | 0.250 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.250 | 0.625 | -0.375 | 0.000 | 0.125 | 0.125 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.250 | -0.375 | 0.625 | -0.000 | 0.125 | 0.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| -0.000 | 0.000 | 0.000 | 1.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.250 | 0.125 | 0.125 | -0.000 | 0.625 | -0.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.250 | 0.125 | 0.125 | 0.000 | -0.375 | 0.625 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 |
| 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 |
| 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 1.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 |
| 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 |
| -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 1.000 | -0.000 | 0.000 | 0.000 | -0.000 |
| 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | -0.000 |
| 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 1.000 | -0.000 |
| 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 |
| Verify that lgl = lhs (i.e., lhs*ginvlhs*lhs = lhs => generalized inverse is correct) |
| lgl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6.000 | 3.250 | 2.750 | 3.500 | 3.000 | 3.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 2.500 | 2.000 | 0.500 | 0.000 | 0.000 | -0.000 |
| 3.250 | 2.313 | 0.937 | 1.875 | 2.250 | 1.000 | 1.000 | -0.000 | 0.500 | 0.500 | 0.500 | 0.750 | 1.375 | 1.000 | 0.375 | -0.000 | 0.000 | -0.000 |
| 2.750 | 0.937 | 1.813 | 1.625 | 0.750 | 2.000 | 0.000 | 1.000 | 0.500 | 0.500 | 0.500 | 0.250 | 1.125 | 1.000 | 0.125 | 0.000 | 0.000 | 0.000 |
| 3.500 | 1.875 | 1.625 | 3.250 | 1.500 | 2.000 | -0.000 | -0.000 | 1.000 | 1.000 | 1.000 | 0.500 | 2.250 | 2.000 | 0.250 | 0.000 | 0.000 | -0.000 |
| 3.000 | 2.250 | 0.750 | 1.500 | 3.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 1.500 | 1.000 | 0.500 | 0.000 | 0.000 | 0.000 |
| 3.000 | 1.000 | 2.000 | 2.000 | 0.000 | 3.000 | -0.000 | 1.000 | 1.000 | 1.000 | -0.000 | -0.000 | 1.000 | 1.000 | 0.000 | 0.000 | -0.000 | -0.000 |
| 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | 0.000 | 4.176 | 0.681 | 0.681 | -0.907 | -1.361 | -1.361 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 |
| 1.000 | 0.000 | 1.000 | -0.000 | 0.000 | 1.000 | 0.681 | 3.495 | -0.907 | -0.000 | -1.361 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | -0.000 | 1.000 | 0.681 | -0.907 | 3.495 | 0.000 | 0.000 | -1.361 | 0.000 | 1.000 | 0.000 | -0.000 | 0.000 | -0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | -0.000 | 1.000 | -0.907 | -0.000 | 0.000 | 2.815 | 0.000 | 0.000 | 1.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 1.000 | 0.000 | -1.361 | -1.361 | 0.000 | -0.000 | 3.722 | -0.000 | 1.000 | 1.000 | -0.000 | 0.000 | 0.000 | -0.000 |
| 1.000 | 0.750 | 0.250 | 0.500 | 1.000 | -0.000 | -1.361 | 0.000 | -1.361 | 0.000 | -0.000 | 3.722 | 0.500 | -0.000 | 0.500 | 0.000 | -0.000 | 0.000 |
| 2.500 | 1.375 | 1.125 | 2.250 | 1.500 | 1.000 | -0.000 | -0.000 | 0.000 | 1.000 | 1.000 | 0.500 | 9.396 | 2.531 | 1.781 | -2.042 | -3.063 | -3.062 |
| 2.000 | 1.000 | 1.000 | 2.000 | 1.000 | 1.000 | -0.000 | -0.000 | 1.000 | 0.000 | 1.000 | -0.000 | 2.531 | 7.615 | -2.042 | 0.000 | -3.063 | -0.000 |
| 0.500 | 0.375 | 0.125 | 0.250 | 0.500 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.500 | 1.781 | -2.042 | 5.865 | 0.000 | 0.000 | -3.062 |
| 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -2.042 | -0.000 | 0.000 | 4.083 | -0.000 | -0.000 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -3.062 | -3.063 | 0.000 | -0.000 | 6.125 | -0.000 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -3.062 | 0.000 | -3.063 | -0.000 | -0.000 | 6.125 |
| Compute ranklhs = rank of the MME = trace of ginvlhs*lhs |
| ranklhs |
|---|
| 16 |
| Compute yhat = vector of solutions for the MME |
| yhat |
|---|
| 133.178 |
| 71.652882 |
| 61.525121 |
| 8.1346577 |
| 82.483546 |
| 50.694457 |
| 0.7436074 |
| -0.39758 |
| -1.314201 |
| 0.9681743 |
| 0.5190404 |
| -0.977351 |
| 0.3534048 |
| -0.199615 |
| -0.330492 |
| 0.1767024 |
| 0.0768949 |
| 0.0114563 |
| yhat |
|---|
| 133.18 |
| 71.65 |
| 61.53 |
| 8.13 |
| 82.48 |
| 50.69 |
| 0.74 |
| -0.40 |
| -1.31 |
| 0.97 |
| 0.52 |
| -0.98 |
| 0.35 |
| -0.20 |
| -0.33 |
| 0.18 |
| 0.08 |
| 0.01 |
| Compute sesol = standard error of solutions |
| sesol |
|---|
| 3.16 |
| 8.40 |
| 8.61 |
| 8.35 |
| 5.27 |
| 5.17 |
| 5.82 |
| 5.86 |
| 5.34 |
| 5.44 |
| 5.86 |
| 5.66 |
| 3.84 |
| 3.81 |
| 3.95 |
| 3.96 |
| 4.00 |
| 3.98 |
| Computation of Additive, Nonadditive, and Total Genetic Predictions |
| Using matrix computations |
| Define ka = coefficient matrix of additive genetic predictions |
| ka | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0 | 1 | -1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 0 | 0.5 | -0.5 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW4 | 0 | 0.5 | -0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 0 | 0.5 | -0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW6 | 0 | 0.75 | -0.75 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| ka | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 1.00 | -1.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.75 | -0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Compute kagl = ka*ginvlhs*lhs to check if functions in matrix ka are estimable |
| (kagl = ka if functions in ka are estimable) |
| kagl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 1.00 | -1.00 | 0.00 | 0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.75 | -0.75 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| difkaglka | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| Compute uaka = vector of multibreed additive genetic predictions |
| uaka |
|---|
| 10.87 |
| -0.40 |
| 3.75 |
| 6.03 |
| 5.58 |
| 6.62 |
| Compute vepuaka = matrix of variance of errors of additive genetic predictions |
| vepuaka | |||||
|---|---|---|---|---|---|
| 263.72 | 43.15 | 135.28 | 121.13 | 169.66 | 203.04 |
| 43.15 | 34.38 | 35.74 | 24.00 | 38.66 | 39.65 |
| 135.28 | 35.74 | 102.27 | 68.03 | 94.86 | 118.06 |
| 121.13 | 24.00 | 68.03 | 78.56 | 80.84 | 96.04 |
| 169.66 | 38.66 | 94.86 | 80.84 | 129.48 | 135.64 |
| 203.04 | 39.65 | 118.06 | 96.04 | 135.64 | 176.97 |
| Compute sepuaka = vector of standard errors of additive genetic predictions |
| sepuaka |
|---|
| 16.24 |
| 5.86 |
| 10.11 |
| 8.86 |
| 11.38 |
| 13.30 |
| Define kn = coefficient matrix of nonadditive genetic predictions |
| Assume that males will be mated to (1/2A 1/2B) females and viceversa |
| kn | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 |
| ROW3 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 |
| ROW4 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 |
| ROW5 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 |
| ROW6 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 |
| kn | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 |
| Compute kngl = kn*ginvlhs*lhs to check if functions in matrix kn are estimable |
| (kngl = kn if functions in kn are estimable) |
| kngl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | -0.00 | 0.00 | 0.50 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | 0.50 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | 0.50 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | 0.50 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | 0.50 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| -0.00 | -0.00 | 0.00 | 0.50 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 |
| difknglkn | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Compute uakn = vector of multibreed nonadditive genetic predictions |
| uakn |
|---|
| 4.24 |
| 3.97 |
| 3.90 |
| 4.16 |
| 4.11 |
| 4.07 |
| Compute vepuaks = matrix of variance of errors of nonadditive genetic predictions |
| vepuakn | |||||
|---|---|---|---|---|---|
| 15.11 | 11.81 | 13.07 | 14.78 | 13.46 | 14.09 |
| 11.81 | 15.14 | 14.84 | 13.14 | 13.47 | 13.32 |
| 13.07 | 14.84 | 18.29 | 14.49 | 13.95 | 15.68 |
| 14.78 | 13.14 | 14.49 | 18.36 | 13.96 | 14.64 |
| 13.46 | 13.47 | 13.95 | 13.96 | 15.47 | 13.71 |
| 14.09 | 13.32 | 15.68 | 14.64 | 13.71 | 16.88 |
| Compute sepuakn = vector of standard errors of nonadditive genetic predictions |
| sepuakn |
|---|
| 3.89 |
| 3.89 |
| 4.28 |
| 4.28 |
| 3.93 |
| 4.11 |
| Define kt = coefficient matrix of total genetic predictions |
| Assume that males will be mated to (1/2A 1/2B) females and viceversa |
| kt | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0 | 1 | -1 | 0.5 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 |
| ROW3 | 0 | 0.5 | -0.5 | 0.5 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 |
| ROW4 | 0 | 0.5 | -0.5 | 0.5 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 |
| ROW5 | 0 | 0.5 | -0.5 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 |
| ROW6 | 0 | 0.75 | -0.75 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 |
| kt | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 1.00 | -1.00 | 0.50 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| 0.00 | 0.75 | -0.75 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 |
| Compute ktgl = kt*ginvlhs*lhs to check if functions in matrix kt are estimable |
| (ktgl = kt if functions in kt are estimable) |
| ktgl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 1.00 | -1.00 | 0.50 | 0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.50 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.50 | 0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.50 | 0.00 | -0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.50 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.50 | -0.00 | -0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.50 | -0.00 |
| 0.00 | 0.75 | -0.75 | 0.50 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 1.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.50 |
| difktglkt | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| Compute uakt = vector of multibreed total genetic predictions |
| uakt |
|---|
| 15.12 |
| 3.57 |
| 7.65 |
| 10.19 |
| 9.69 |
| 10.69 |
| Compute vepuaks = matrix of variance of errors of total genetic predictions |
| vepuakt | |||||
|---|---|---|---|---|---|
| 269.31 | 51.15 | 136.49 | 121.88 | 172.13 | 206.10 |
| 51.15 | 52.57 | 44.10 | 34.09 | 47.17 | 48.01 |
| 136.49 | 44.10 | 103.55 | 69.52 | 95.42 | 118.77 |
| 121.88 | 34.09 | 69.52 | 81.87 | 81.90 | 96.86 |
| 172.13 | 47.17 | 95.42 | 81.90 | 132.50 | 137.07 |
| 206.10 | 48.01 | 118.77 | 96.86 | 137.07 | 180.41 |
| Compute sepuakt = vector of standard errors of total genetic predictions |
| sepuakt |
|---|
| 16.41 |
| 7.25 |
| 10.18 |
| 9.05 |
| 11.51 |
| 13.43 |