Select the method or formula of your choice.

The BLUP are the predicted values of the random terms in the model. Recall the general form of the mixed model:

The vector that produces the BLUP estimates is:

where

For further details on the notation, go to the Methods section.

The estimated standard errors are the square roots of the diagonals of this matrix:

where

For further details on the notation, go to the Methods section.

The degrees of freedom for the test of the BLUP component are:

where

Term | Description |
---|---|

a vector with value 1 at the row and 0 elsewhere with dimension | |

W | the asymptotic variance-covariance matrix of the variance component estimates |

For further details on the notation, go to the Methods section.

The 100 × (1 – *α*)% confidence limits for the conditional expectation of the component of *μ* given response values have the following form:

Term | Description |
---|---|

the BLUP | |

the percentile from the t distribution with the given degrees of freedom | |

1 − confidence level | |

df | the degrees of freedom for the BLUP |

The two-sided p-value for the null hypothesis that a Best Linear Unbiased Predictor (BLUP) equals 0 is:

Term | Description |
---|---|

The probability that under the null hypothesis T is less than the absolute value of the calculated . Here, T follows a t-distribution with df degrees of freedom. | |

The t value for the BLUP. |