# Nested Analysis of Variance via Distance-based Redundancy Analysis or Non-parametric Multivariate Analysis of Variance

### Description

The functions provide nested analysis of variance for a two-level hierarchical model. The functions are implemented by estimating the correct F-ratio for the main and nested factors (assuming the nested factor is random) and using the recommended permutation procedures to test the significance of these F-ratios. F-ratios are estimated from variance estimates that are provided by distance-based redundancy analysis (`capscale`

) or non-parametric multivariate analysis of variance (`adonis`

).

### Usage

1 2 3 |

### Arguments

`formula` |
Formula with a community data frame (with sites as rows, species as columns and species abundance as cell values) or (for |

`data` |
Environmental data set. |

`method` |
Method for calculating ecological distance with function |

`add` |
Should a constant be added to the off-diagonal elements of the distance-matrix (TRUE) or not. |

`permutations` |
The number of permutations for significance testing. |

`warnings` |
Should warnings be suppressed (TRUE) or not. |

### Details

The functions provide two alternative procedures for multivariate analysis of variance on the basis of any distance measure. Function `nested.anova.dbrda`

proceeds via `capscale`

, whereas `nested.npmanova`

proceeds via `adonis`

. Both methods are complementary to each other as `nested.npmanova`

always provides correct F-ratios and estimations of significance, whereas `nested.anova.dbrda`

does not provide correct F-ratios and estimations of significance when negative eigenvalues are encountered or constants are added to the distance matrix, but always provides an ordination diagram.

The F-ratio for the main factor is estimated as the mean square of the main factor divided by the mean square of the nested factor. The significance of the F-ratio of the main factor is tested by permuting entire blocks belonging to levels of the nested factor. The significance of the F-ratio of the nested factor is tested by permuting sample units within strata defined by levels of the main factor.

### Value

The functions provide an ANOVA table.

### Author(s)

Roeland Kindt (World Agroforestry Centre)

### References

Legendre, P. & Anderson, M. J. (1999). Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs 69, 1-24.

Anderson, M.J. (2001). A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26: 32-46.

McArdle, B.H. and M.J. Anderson. (2001). Fitting multivariate models to community data: A comment on distance-based redundancy analysis. Ecology, 82: 290-297.

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
## Not run:
library(vegan)
data(warcom)
data(warenv)
# use larger number of permutations for real studies
nested.npmanova(warcom~rift.valley+popshort, data=warenv, method="jac",
permutations=5)
nested.anova.dbrda(warcom~rift.valley+popshort, data=warenv, method="jac",
permutations=5)
## End(Not run)
``` |