Data preparation with RENUMF90

Yutaka Masuda

August 2026

Multiple-trait models

Model

When renumbering a multiple-trait model, we still need an instruction file very similar to that for the single-trait model. The only differences are: (1) the need to specify the model for each trait and (2) the use of a covariance matrix instead of a scalar value.

We will consider a two-trait model with equal design matrices, which means all traits have the same model. The mathematical model is \[ \begin{aligned} y_{ijk:1} &= A_{i:1} + S_{j:1} + \beta_{1} x_{ijk:1} + u_{k:1} + e_{ijk:1}\\ y_{ijk:2} &= A_{i:2} + S_{j:2} + \beta_{2} x_{ijk:2} + u_{k:2} + e_{ijk:2} \end{aligned} \] where \(y_{ijk:t}\) is an observation for trait \(t\), \(A_{i:t}\) is the fixed effect for trait \(t\), \(S_{j:t}\) is also the fixed effect for trait \(t\), \(\beta_{t}\) is the fixed regression coefficient for trait \(t\), \(x_{ijk:t}\) is a covariate for trait \(t\), \(u_{k:t}\) is the additive genetic effect for trait \(t\), and \(e_{ijk:t}\) is the random residual effect. The genetic (\(\mathbf{G}_0\)) and residual (\(\mathbf{R}_0\)) covariance matrices are \[ \mathbf{G}_{0} = \left[ \begin{array}{rr} 0.50&-0.25\\ -0.25&1.00 \end{array} \right] \quad \text{and} \quad \mathbf{R}_{0} = \left[ \begin{array}{rr} 2.0&1.0\\ 1.0&1.5 \end{array} \right] \]

Required files

The raw data file is identical to the previous single-trait data, except for the additional column for trait 2. The data file should contain all required effects and observations for all traits.

  ID006  A  1  1.0  3.0  4.5
  ID009  A  2  1.0  2.0  7.5
  ID012  A  1  2.0  4.0  3.5
  ID007  B  2  2.0  6.0 -0.5
  ID010  B  1  1.0  3.0  5.5
  ID013  B  2  2.0  6.0  1.5
  ID008  C  1  2.0  6.0 -1.5
  ID011  C  2  1.0  6.0  2.5
  ID014  C  1  1.0  8.0  0.5
  ID015  C  2  2.0  4.0  4.5

The pedigree file is also the same as the one used previously.

ID001        0         0
ID002        0         0
ID003        0         0
ID004        0         0
ID005        0         0
ID006        0         0
ID007    ID002     ID005
ID008    ID001     ID004
ID009    ID002     ID003
ID010    ID007     ID006
ID011    ID007     ID004
ID012    ID011     ID008
ID013    ID011     ID010
ID014    ID009     ID013
ID015    ID011     ID010

The instruction file for this two-trait model is as follows.

DATAFILE
rawdata5.txt
TRAITS          # two-trait model: put 2 positions
5 6
FIELDS_PASSED TO OUTPUT

WEIGHT(S)

RESIDUAL_VARIANCE
2.0 1.0
1.0 1.5
EFFECT           # 1st effect fixed
2 2 cross alpha
EFFECT           # 2nd effect fixed
3 3 cross alpha
EFFECT           # 3rd effect fixed
4 4 cov
EFFECT           # 4th effect
1 1 cross alpha
RANDOM           ## treated as a random effect
animal
FILE             ## pedigree file
rawpedigree5.txt
FILE_POS         ## animal, sire and dam IDs, and two 0s
1 2 3 0 0
(CO)VARIANCES    ## its variance component
 0.50 -0.25
-0.25  1.00

For a multiple-trait model, you should check the following points in an instruction file. An incorrect description in these statements will cause RENUMF90 to stop abruptly.

TRAITS: Enumerate the positions of observations in the data file. If you have 2 traits, you should put 2 numbers (positions) here.
RESIDUAL_VARIANCE: Put a residual covariance matrix here. The whole matrix is needed (all upper, lower, and diagonal elements).
EFFECT: Enumerate the positions of effects for each trait in the data file; then specify the effect type (and data type). For example, with a two-trait model, first put 2 numbers (the positions of the effects for traits 1 and 2), 1 keyword (cross or cov), and, if needed, a data type (numer or alpha) when the effect type is cross.
(CO)VARIANCES: Put a covariance matrix here. The whole matrix is needed.

Run RENUMF90 with the above files to obtain a parameter file configured for the two-trait model.

Missing observations

You can include missing observations in the data file. RENUMF90 does not distinguish between real and missing observations; the program simply reads the raw data and passes the observations to the renumbered file. Although RENUMF90 does not process missing observations specially, BLUPF90 interprets the values. Therefore, the generated parameter file (renf90.par) should include an option defining the missing code. You can write the following option in the instruction file, and RENUMF90 will pass it to renf90.par.

OPTION missing -999

This example treats an observation with the value -999 as missing. The default is 0 (that is, if you do not define a missing code, the program assumes that 0 is missing).

Note that RENUMF90 still recognizes 0 as a missing observation when computing basic statistics (for example, the average and standard deviation) for informational purposes. In this case, the statistics may be inaccurate, but all the files are correctly renumbered.

Different models across traits (Unequal design matrices)

Now we consider a multiple-trait model with different mathematical models across traits. It is typically called a model with unequal design matrices. Let us examine the following two-trait model. \[ \begin{aligned} y_{ijk:1} &= A_{i:1} + \phantom{S_{j:1} + } \beta_1 x_{ijk:1} + u_{k:1} + e_{ijk:1}\\ y_{ijk:2} &= A_{i:2} + S_{j:2} + \beta_{2} x_{ijk:2} + u_{k:2} + e_{ijk:2} \end{aligned} \] In this model, \(S_{j:1}\) is missing for trait 1. To support this model with RENUMF90, you can simply change a line in the previous instruction file.

EFFECT                  # 2nd effect fixed
0 3 cross alpha

A position of 0 means that this effect will not be included in the model for this trait.

We further consider the following two-trait model. \[ \begin{aligned} y_{ijk:1} &= A_{i:1} \phantom{+ S_{j:1} } + \beta_1 x_{ijk:1} + u_{k:1} + e_{ijk:1}\\ y_{ijk:2} &= \phantom{A_{i:2} + } S_{j:2} + \beta_{2} x_{ijk:2} + u_{k:2} + e_{ijk:2} \end{aligned} \] In this case, \(S_{j:1}\) is missing for trait 1 and \(A_{i:2}\) is missing for trait 2. Applying the above principle, you can derive the following instruction (only part of the instruction file is shown).

EFFECT                  # 1st effect fixed
2 0 cross alpha
EFFECT                  # 2nd effect fixed
0 3 cross alpha

The above statements make it easy to identify which effects are missing for a particular trait.

There is another way to handle such a model. You can combine the above two EFFECT lines into one as follows.

EFFECT                  # 1st and 2nd effects fixed
2 3 cross alpha

This statement may be useful when different effects are considered to be the same type of effect. For example, in dairy cattle, a contemporary group effect (such as HYS: herd-year-season) is commonly included in the model for production traits, but its definition should differ across parities. HYS in the 1st lactation and HYS in the 2nd lactation are different but are considered similar effects. With this compact definition, memory requirements would be reduced. If you are confused by this notation, you do not have to use the compact statement.

Summary

RENUMF90 supports multiple-trait models.
Carefully describe TRAITS, RESIDUAL_VARIANCE, EFFECT, and (CO)VARIANCES in an instruction file.
TRAITS has the same number of entries as the number of traits.
The covariance matrix should be fully specified.
EFFECT describes the position of the effect for each trait.
Missing observations are passed to renf90.dat. You can add OPTION missing to the instruction file to change the missing code.
RENUMF90 supports a multiple-trait model with unequal design matrices.

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