The predictions \(\widehat{\mathbf{u}} = \widehat{\mathbf{G}}\mathbf{Z}^{\top}\widehat{\mathbf{V}}^{-1} (\mathbf{y} - \mathbf{X}\widehat{\boldsymbol{\beta}})\) of the random effects of a fitted model, with the standard errors of prediction \(\sqrt{\mathrm{diag}(\mathbf{C}_{22})}\), t tests and prediction limits: the solution for random effects of SAS PROC MIXED.
Arguments
- fit
a result of
vlm_fit().- level
confidence level of the prediction limits (default 0.95).
Value
A list of class c("vlm_blup", "vlm_result", "list") with blup (effect, subject, level,
prediction, standard error of prediction, df, t, p and limits).
Details
For a single random factor with \(n_i\) observations on level \(i\), the prediction reduces to
$$\widehat{s}_i = \frac{n_i\widehat{\sigma}_s^2}{n_i\widehat{\sigma}_s^2 + \widehat{\sigma}^2}
(\bar{y}_{i\cdot} - \widehat{\mu}),$$
a shrinkage of the level mean towards the overall mean (Example 2.4.3.1 of the book). The degrees of freedom are
the residual ones, or Satterthwaite ones (numerical derivatives of the prediction-error variance) with
ddfm = "satterth" or "kr".
References
Duchateau, L., Janssen, P. and Rowlands, G. J. (1998). Linear Mixed Models. An Introduction with Applications in Veterinary Research. International Livestock Research Institute, Nairobi. Section 2.4.3.
Henderson, C. R. (1975). Best linear unbiased estimation and prediction under a selection model. Biometrics, 31, 423-447.
See also
Other VetResearchLMM inference:
emmeans_mixed_model(),
report_mixed_model(),
vlm_estimate(),
vlm_lsmeans()
Author
Muhammad Yaseen (myaseen208@gmail.com)
Examples
# Example 2.4.3.1: PROC MIXED; CLASS sire; MODEL ww = ; RANDOM sire / SOLUTION;
fs <-
vlm_fit(
fixed = Ww ~ 1
, data = ex127
, random = ~ sire
, repeated = NULL
, method = "REML"
, ddfm = "default"
, type = 3
, class = NULL
, bound = TRUE
, control = list()
)
bl <-
vlm_blup(
fit = fs
, level = 0.95
)
bl
#> Best linear unbiased predictions of the random effects
#>
#> Solution for random effects
#> effect level estimate se df t p lower upper
#> sire 1 -2.198 1.101 35 -1.997 0.05364 -4.432 0.03641
#> sire 2 -0.03189 0.8983 35 -0.03550 0.97188 -1.855 1.792
#> sire 3 -1.743 1.101 35 -1.584 0.12216 -3.978 0.4908
#> sire 4 3.159 0.9589 35 3.294 0.00227 1.212 5.106
#> sire 5 0.8692 0.9340 35 0.9306 0.35842 -1.027 2.765
#> sire 6 -0.8628 0.9915 35 -0.8702 0.39013 -2.876 1.150
#> sire 7 1.356 1.036 35 1.309 0.19922 -0.7475 3.459
#> sire 8 -0.5476 0.9589 35 -0.5710 0.57162 -2.494 1.399
#>
#> Sources: Duchateau, Janssen and Rowlands (1998); Henderson (1975). Full
#> references: vlm_cite(x).