mixedModel2

Fit Mixed Linear Model with 2 Error Components

Fits a mixed linear model by REML. The linear model contains one random factor apart from the unit errors.

Usage

mixedModel2(formula, random, weights=NULL, only.varcomp=FALSE, data=list(),
            subset=NULL, contrasts=NULL, tol=1e-6, maxit=50, trace=FALSE)
mixedModel2Fit(y, X, Z, w=NULL, only.varcomp=FALSE, tol=1e-6, maxit=50, trace=FALSE)
randomizedBlock(formula, random, weights=NULL, only.varcomp=FALSE, data=list(),
            subset=NULL, contrasts=NULL, tol=1e-6, maxit=50, trace=FALSE)
randomizedBlockFit(y, X, Z, w=NULL, only.varcomp=FALSE, tol=1e-6, maxit=50, trace=FALSE)

Details

Note that randomizedBlock and mixedModel2 are alternative names for the same function.

This function fits the model \(y=Xb+Zu+e\) where \(b\) is a vector of fixed coefficients and \(u\) is a vector of random effects. Write \(n\) for the length of \(y\) and \(q\) for the length of \(u\). The random effect vector \(u\) is assumed to be normal, mean zero, with covariance matrix \(\sigma^2_uI_q\) while \(e\) is normal, mean zero, with covariance matrix \(\sigma^2I_n\). If \(Z\) is an indicator matrix, then this model corresponds to a randomized block experiment. The model is fitted using an eigenvalue decomposition that transforms the problem into a Gamma generalized linear model. To the knowledge of the author, this is an original and unpublished approach to the problem of fitting mixed models.

Note that the block variance component varcomp[2] is not constrained to be non-negative. It may take negative values corresponding to negative intra-block correlations. However the correlation varcomp[2]/sum(varcomp) must lie between -1 and 1.

Missing values in the data are not allowed.

This function is in principle equivalent to lme(fixed=formula,random=~1|random) except that the block variance component is not constrained to be non-negative. If the block variance component is non-negative, then this function is faster and more accurate than lme for small to moderate size data sets but slower than lme when the number of observations is large.

This function tends to be fast and reliable, compared to competitor functions that fit randomized block models, when then number of observations is small, say no more than 200. However it becomes quadratically slow as the number of observations increases because of the need to compute two singular value decompositions of order nearly equal to the number of observations, although this can be limited to only one decomposition if only.varcomp = TRUE). For these reasons, this function is a good choice when fitting large numbers of mixed models to small datasets but is not optimal as currently implemented for fitting mixed models to very large data sets.

References

Venables, W., and Ripley, B. (2002). Modern Applied Statistics with S-Plus, Springer.

See Also

glmgam.fit, lme, lm, lm.fit

Aliases

• mixedModel2
• mixedModel2Fit
• randomizedBlock
• randomizedBlockFit

Examples

# NOT RUN {
#  Compare with first data example from Venable and Ripley (2002),
#  Chapter 10, "Linear Models"
library(MASS)
data(petrol)
out <- mixedModel2(Y~SG+VP+V10+EP, random=No, data=petrol)
cbind(varcomp=out$varcomp,se=out$se.varcomp)
# }