# ranblock

##### 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

```
randomizedBlock(formula, random, weights=NULL, fixed.estimates=TRUE, data=list(), subset=NULL, contrasts=NULL)
randomizedBlockFit(y,X,Z,w=NULL,fixed.estimates=TRUE)
```

##### Arguments

- formula
- formula specifying the fixed model.
- random
- vector or factor specifying the blocks corresponding to random effects.
- weights
- optional vector of prior weights.
- fixed.estimates
- should the fixed effect coefficients be returned?
- 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`

of`model.matrix.default`

. - y
- response vector.
- X
- design matrix for fixed model.
- Z
- 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.
This function is essentially equivalent to `lme(fixed=formula,random=~1|random)`

but is more accurate and is much faster for small to moderate size data sets.
Missing values in the data are not allowed.

##### Value

- A list with the components.
If
`fixed.estimates=TRUE`

then the components from`"lm.fit"`

are also returned. sigmasquared vector of length two containing the residual and block components of variance. se.sigmasquared standard errors for the components of variance.

##### See Also

##### Examples

```
# Compare with first data example from Venable and Ripley (2002), Chapter 10, "Linear Models"
library(MASS)
data(petrol)
out <- randomizedBlock(Y~SG+VP+V10+EP, random=No, data=petrol)
cbind(sigmasquared=out$sigmasquared,se=out$se.sigmasquared)
```

*Documentation reproduced from package statmod, version 0.6, License: GPL version 2 or newer*