| gremlin-package {gremlin} | R Documentation |
Mixed-Effects REML Incorporating Generalized Inverses
Description
Fit linear mixed-effects models using restricted (or residual) maximum likelihood (REML) and with generalized inverse matrices to specify covariance structures for random effects. In particular, the package is suited to fit quantitative genetic mixed models, often referred to as 'animal models' (Henderson 1973). Implements the average information algorithm (Johnson & Thompson 1995; Gilmour et al. 1995; Meyer & Smith 1996) as the main tool to maximize the restricted log-likelihood, but with other algorithms available.
Details
The average information algorithm combined with sparse matrix techniques can potentially make model fitting very efficient.
Author(s)
Maintainer: Matthew Wolak matthewwolak@gmail.com (ORCID)
References
Henderson, C.R. 1973. Sire evaluation and genetic trends. Journal of Animal Science 1973:10-41.
Johnson, D.L. and R. Thompson. 1995. Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information. Journal of Dairy Science 78:449-456.
Gilmour, A.R., R. Thompson, and B.R. Cullis. 1995. Average information REML: An efficient algorithm for variance parameter estimation in linear mixed models. Biometrics 51:1440-1450.
Meyer, K. and S.P. Smith. 1996. Restricted maximum likelihood estimation for animal models using derivatives of the likelihood. Genetics, Selection, and Evolution 28:23-49.
Mrode, R.A. 2005. Linear Models for the Prediction of Animal Breeding Values, 2nd ed. CABI Publishing, Cambridge, MA, USA.
See Also
Useful links:
Examples
## Not run:
# Following the example from Mrode 2005, chapter 11.
library(nadiv) #<-- to construct inverse of the numerator relatedness matrix
Ainv <- makeAinv(Mrode11[, 1:3])$Ainv
gr11lmm <- gremlin(WWG11 ~ sex - 1,
random = ~ calf,
data = Mrode11,
ginverse = list(calf = Ainv),
Gstart = matrix(0.2), Rstart = matrix(0.4), #<-- specify starting values
maxit = 15, #<-- maximum iterations
v = 2, vit = 1, #<-- moderate screen output (`v`) every iteration (`vit`)
algit = "AI") #<-- only use Average Information algorithm iterations
summary(gr11lmm)
# Compare the model to a Linear Model with no random effects
## Use `update()` to update the model
gr11lm <- update(gr11lmm, random = ~ 1) #<-- `~1`=drop all random effects
summary(gr11lm)
# Do analysis of variance between the two models
## See AIC or evaluate likelihood ratio against a Chi-squared distribution
anova(gr11lm, gr11lmm)
## End(Not run)