LBG - FS2024 – Exercise 5

Problem 1: Sire Model

As already shown during the lecture for the small data set at

https://charlotte-ngs.github.io/lbgfs2024/data/small_beef_data.csv

a sire model is to be used for the following dataset, already used in Exercise 4. The data set is available from

https://charlotte-ngs.github.io/lbgfs2024/data/beef_data_bc.csv

The ration ${\lambda }_s$ between the residual variance and the sire variance can be assumed to be

$${\lambda }_s=\frac{{\sigma }_e^2}{{\sigma }_s^2}=1$$

Solution

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# read the data

s_beef <- 'https://charlotte-ngs.github.io/lbgfs2024/data/beef_data_bc.csv'

tbl_beef <- readr::read_delim(s_beef, delim = ",")

_webr_editor_1 = Object {code: null, options: Object, indicator: Ke}

• Design matrix $X$

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# design matrix X

_webr_editor_2 = Object {code: null, options: Object, indicator: Ke}

• Design matrix $Z$

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# design matrix Z

_webr_editor_3 = Object {code: null, options: Object, indicator: Ke}

• Coefficient matrix of mixed model equations

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# coefficient matrix

_webr_editor_4 = Object {code: null, options: Object, indicator: Ke}

• Right-hand side of mixed model equations

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# right-hand side

_webr_editor_5 = Object {code: null, options: Object, indicator: Ke}

• Solve mixed model equations

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# solve mme

_webr_editor_6 = Object {code: null, options: Object, indicator: Ke}

• Identify estimates of fixed effects and predictions of sire effects

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# fixed effects estimates

# predictions of sire effects

_webr_editor_7 = Object {code: null, options: Object, indicator: Ke}

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