anova.mlm {stats} | R Documentation |

Compute gereralized analysis of variance table for a list of multivariate linear models. At least two models must be given.

## S3 method for class 'mlm' anova.mlm(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(length = p)))

`object` |
An object of class `mlm` |

`...` |
Further objects of class `mlm` |

`test` |
Choice of test statistic (se below) |

`Sigma` |
(Only relevant if `test=="Spherical"` ). Covariance
matrix assumed proportional to `Sigma` |

`T` |
Transformation matrix. By default computed from `M` and
`X` |

`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 |

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, Wilks' statistic is most popular in the literature, but the default Pillai-Bartlett statistic is recommended by Hand and Taylor (1987).

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 Greenhouse-Geisser,
respectively Huynh-Feldt, 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`

).

Similar to `anova.lm`

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

An object of class `"anova"`

inheriting from class `"data.frame"`

The Huynh-Feldt 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.

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

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" ) ### There seems to be a strong interaction in these data plot(colMeans(reacttime))

[Package *stats* version 2.1.0 Index]