anova.mlm {stats} | R Documentation |

## Comparisons between Multivariate Linear Models

### Description

Compute a (generalized) analysis of variance table for one or more multivariate linear models.

### Usage

```
## S3 method for class 'mlm'
anova(object, ...,
test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy",
"Spherical"),
Sigma = diag(nrow = p), T = Thin.row(Proj(M) - Proj(X)),
M = diag(nrow = p), X = ~0,
idata = data.frame(index = seq_len(p)), tol = 1e-7)
```

### Arguments

`object` |
an object of class |

`...` |
further objects of class |

`test` |
choice of test statistic (see below). Can be abbreviated. |

`Sigma` |
(only relevant if |

`T` |
transformation matrix. By default computed from |

`M` |
formula or matrix describing the outer projection (see below). |

`X` |
formula or matrix describing the inner projection (see below). |

`idata` |
data frame describing intra-block design. |

`tol` |
tolerance to be used in deciding if the residuals are
rank-deficient: see |

### Details

The `anova.mlm`

method uses either a multivariate test statistic for
the summary table, or a test based on sphericity assumptions (i.e.
that the covariance is proportional to a given matrix).

For the multivariate test, \IWilks' statistic is most popular in the
literature, but the default \IPillai–\IBartlett statistic is
recommended by Hand and Taylor (1987). See
`summary.manova`

for further details.

For the `"Spherical"`

test, proportionality is usually with the
identity matrix but a different matrix can be specified using `Sigma`

.
Corrections for asphericity known as the \IGreenhouse–\IGeisser,
respectively \IHuynh–\IFeldt, epsilons are given and adjusted `F`

tests are
performed.

It is common to transform the observations prior to testing. This
typically involves
transformation to intra-block differences, but more complicated
within-block designs can be encountered,
making more elaborate transformations necessary. A
transformation matrix `T`

can be given directly or specified as
the difference between two projections onto the spaces spanned by
`M`

and `X`

, which in turn can be given as matrices or as
model formulas with respect to `idata`

(the tests will be
invariant to parametrization of the quotient space `M/X`

).

As with `anova.lm`

, all test statistics use the SSD matrix from
the largest model considered as the (generalized) denominator.

Contrary to other `anova`

methods, the intercept is not excluded
from the display in the single-model case. When contrast
transformations are involved, it often makes good sense to test for a
zero intercept.

### Value

An object of class `"anova"`

inheriting from class `"data.frame"`

### Note

The \IHuynh–\IFeldt epsilon differs from that calculated by SAS (as of
v. 8.2) except when the DF is equal to the number of observations
minus one. This is believed to be a bug in SAS, not in **R**.

### References

Hand, D. J. and Taylor, C. C. (1987)
*Multivariate Analysis of Variance and Repeated Measures.*
Chapman and Hall.

### See Also

### Examples

```
require(graphics)
utils::example(SSD) # Brings in the mlmfit and reacttime objects
mlmfit0 <- update(mlmfit, ~0)
### Traditional tests of intrasubj. contrasts
## Using MANOVA techniques on contrasts:
anova(mlmfit, mlmfit0, X = ~1)
## Assuming sphericity
anova(mlmfit, mlmfit0, X = ~1, test = "Spherical")
### tests using intra-subject 3x2 design
idata <- data.frame(deg = gl(3, 1, 6, labels = c(0, 4, 8)),
noise = gl(2, 3, 6, labels = c("A", "P")))
anova(mlmfit, mlmfit0, X = ~ deg + noise,
idata = idata, test = "Spherical")
anova(mlmfit, mlmfit0, M = ~ deg + noise, X = ~ noise,
idata = idata, test = "Spherical" )
anova(mlmfit, mlmfit0, M = ~ deg + noise, X = ~ deg,
idata = idata, test = "Spherical" )
f <- factor(rep(1:2, 5)) # bogus, just for illustration
mlmfit2 <- update(mlmfit, ~f)
anova(mlmfit2, mlmfit, mlmfit0, X = ~1, test = "Spherical")
anova(mlmfit2, X = ~1, test = "Spherical")
# one-model form, eqiv. to previous
### There seems to be a strong interaction in these data
plot(colMeans(reacttime))
```

*stats*version 4.4.0 Index]