# mixedmodel

0th

Percentile

##### Randomized Block Mixed Linear Model

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

Keywords
regression
##### 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)
##### Arguments
formula
formula specifying the fixed model.
random
vector or factor specifying the blocks corresponding to random effects.
weights
optional vector of prior weights.
only.varcomp
logical value, if TRUE computation of standard errors and fixed effect coefficients will be skipped
data
an optional data frame containing the variables in the model.
subset
an optional vector specifying a subset of observations to be used in the fitting process.
contrasts
an optional list. See the contrasts.arg argument of model.matrix.default.
tol
small positive numeric tolerance, passed to glmgam.fit
maxit
maximum number of iterations permitted, passed to glmgam.fit
trace
logical value, passed to glmgam.fit. If TRUE then working estimates will be printed at each iteration.
y
numeric response vector
X
numeric design matrix for fixed model
Z
numeric design matrix for random effects
w
optional vector of prior weights
##### Details

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 which transforms the problem into a Gamma generalized linear model. 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 equivalent to lme(fixed=formula,random=~1|random), except that the block variance component is not constrained to be non-negative, but is faster and more accurate for small to moderate size data sets. It is slower than lme when the number of observations is large. This function tends to be fast and reliable, compared to competitor functions which 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 do two eigenvalue decompositions of order nearly equal to the number of observations. So it is a good choice when fitting large numbers of small data sets, but not a good choice for fitting large data sets.

##### Value

• A list with the components:
• varcompvector of length two containing the residual and block components of variance.
• se.varcompstandard errors for the components of variance.
• reml.residualsstandardized residuals in the null space of the design matrix.
• If fixed.estimates=TRUE then the components from the diagonalized weighted least squares fit are also returned.

##### References

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

glmgam.fit, lme, lm, lm.fit

##### Aliases
• mixedModel2
• mixedModel2Fit
##### Examples
#  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)
Documentation reproduced from package statmod, version 1.2.3, License: LGPL version 2 or newer

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