Methods and formulas for random effect predictions in Fit Mixed Effects Model

Select the method or formula of your choice.

Best linear unbiased predictors (BLUP)

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.