# Sib-pair Command: blup

 Class Analysis and data manipulation command Name blup Arguments (

) | ( [ | ( [(>|>=|<|<=|==|^= ]))).

Calculates BLUPs (best linear unbiased predictions of the breeding value) for a quantitative trait assuming the given heritability.

If a marker locus is specified, the BLUEs (best linear unbiased estimates) of the marker allele frequencies are calculated, following McPeek et al [2004]:

ai = (1' A-1 1)-1 1' A-1 zi ,

where,

A is the numerator relationship matrix
zi is a score representing the count for the ith allele in each individual (0, 0.5, 1).

If a second binary or thresholded quantitative trait is also specified, the BLUEs for the marker allele frequencies for individuals matching the criterion is printed.

McPeek et al [2007] note that the BLUEs are occasionally negative.

Increasing the plevel to 1 gives the BLUE ASEs.

Example:

```>> inc schrott.in
>> blup logChol 0.5

--------------------------------------------
BLUPs for "logChol" with H2 = 50.0%
--------------------------------------------
Pedigree     Individual Observed    BLUP    FamMean   Residual
------------ ---------- --------- --------- --------- ---------
1            101            x        0.3080    5.4186    0.0000
1            102           5.3132    0.1013    5.4186   -0.2067
1            202           5.6904    0.2714    5.4186    0.0004
1            204           5.5452    0.0431    5.4186    0.0836
1            206           5.6560    0.0338    5.4186    0.2036
[...]
1            414           5.2149   -0.1231    5.4186   -0.0805

Overall intercept       =      5.4186
Mean Square Error (VE)  =      0.0308
```

```>> blu D14S52

------------------------------------------------
BLUE allele frequencies for locus "D14S52"
------------------------------------------------
Allele  Frequency   Count  Histogram
57     0.0067        0  *
69     0.0461        2  *
81     0.0213        1  *
83     0.5020       21  **********
85     0.1514        6  ***
87     0.2177        9  ****
93     0.0550        2  *

Number of alleles    =    7
Heterozygosity (Hu)  =    0.6885
Poly. Inf. Content   =    0.6308
4 Neff mu (SSMM)     =    3.60518644
Number persons typed =     21 ( 27.3%)

>> fre D14S52

------------------------------------------------
Allele frequencies for locus "D14S52"
------------------------------------------------
Allele  Frequency   Count  Histogram
57     0.0238        1  *
69     0.0238        1  *
81     0.0476        2  *
83     0.4286       18  *********
85     0.1905        8  ****
87     0.2381       10  *****
93     0.0476        2  *

Number of alleles    =    7
Heterozygosity (Hu)  =    0.7352
Poly. Inf. Content   =    0.6763
4 Neff mu (SSMM)     =    4.88968079
Number persons typed =     21 ( 27.3%)

>> mcf D14S52

------------------------------------------------
MCEM allele frequencies for locus "D14S52"
------------------------------------------------
Allele  Frequency   Count  Histogram
57     0.0418        2  *
69     0.0432        2  *
81     0.0441        2  *
83     0.4944       19  **********
85     0.0854        3  **
87     0.2491        9  *****
93     0.0419        2  *

Number of alleles    =    7
Heterozygosity (Hu)  =    0.6972
Poly. Inf. Content   =    0.6394
4 Neff mu (SSMM)     =    3.67040887
Number of founders   =     19 (  2.6% typed)
#
# Compare to MLEs from MENDEL and BLUEs from MQLS
#
# Allele  MLE (ASE)         BLUE (SE)
# ------  ---------------   ---------------
# 57      0.0431 (0.0422)   0.0067 (0.0185)
# 69      0.0431 (0.0422)   0.0461 (0.0476)
# 81      0.0431 (0.0422)   0.0213 (0.0328)
# 83      0.4950 (0.1072)   0.5020 (0.1136)
# 85      0.0822 (0.0639)   0.1514 (0.0814)
# 87      0.2505 (0.0915)   0.2177 (0.0938)
# 93      0.0431 (0.0422)   0.0550 (0.0518)
#
```