possumDiv | R Documentation |

## Possum Diversity Data

### Description

Possum diversity data: As issued from a study of the diversity of possum (arboreal marsupials) in the Montane ash forest (Australia), this dataset was collected in view of the management of hardwood forest to take conservation and recreation values, as well as wood production, into account.

The study is fully described in the two references.
The number of different species of arboreal marsupials (possum) was
observed on 151 different 3ha sites with uniform vegetation. For each
site the nine variable measures (see below) were recorded.
The problem is to model the relationship between `diversity`

and these
other variables.

### Usage

`data(possumDiv, package="robustbase")`

### Format

Two different representations of the same data are available:

`possumDiv`

is a data frame of 151 observations
of 9 variables, where the last two are factors, `eucalyptus`

with
3 levels and `aspect`

with 4 levels.

`possum.mat`

is a numeric (integer) matrix of 151 rows
(observations) and 14 columns (variables) where the last seven ones
are 0-1 dummy variables, three (`E.*`

) are coding for the kind of
`eucalyptus`

and the last four are 0-1 coding for the
`aspect`

factor.

The variables have the following meaning:

- Diversity
main variable of interest is the number of different species of arboreal marsupial (possum) observed, with values in 0:5.

- Shrubs
the number of shrubs.

- Stumps
the number of cut stumps from past logging operations.

- Stags
the number of stags (hollow-bearing trees).

- Bark
bark index (integer) vector reflecting the quantity of decorticating bark.

- Habitat
an integer score indicating the suitability of nesting and foraging habitat for Leadbeater's possum.

- BAcacia
a numeric vector giving the basal area of acacia species.

- eucalyptus
a 3-level

`factor`

specifying the species of eucalypt with the greatest stand basal area. This has the same information as the following three variables- E.regnans
0-1 indicator for Eucalyptus regnans

- E.delegatensis
0-1 indicator for Eucalyptus deleg.

- E.nitens
0-1 indicator for Eucalyptus nitens

- aspect
a 4-level

`factor`

specifying the aspect of the site. It is the same information as the following four variables.- NW-NE
0-1 indicator

- NW-SE
0-1 indicator

- SE-SW
0-1 indicator

- SW-NW
0-1 indicator

### Source

Eva Cantoni (2004)
Analysis of Robust Quasi-deviances for Generalized Linear Models.
*Journal of Statistical Software* **10**, 04,
https://www.jstatsoft.org/article/view/v010i04

### References

Lindenmayer, D. B., Cunningham, R. B., Tanton, M. T., Nix, H. A. and
Smith, A. P. (1991)
The conservation of arboreal marsupials in the montane ash forests of
the central highlands of victoria, south-east australia: III. The habitat
requirements of leadbeater's possum *gymnobelideus leadbeateri* and
models of the diversity and abundance of arboreal marsupials.
*Biological Conservation* **56**, 295–315.

Lindenmayer, D. B., Cunningham, R. B., Tanton, M. T., Smith, A. P. and
Nix, H. A. (1990)
The conservation of arboreal marsupials in the montane ash forests of
the victoria, south-east australia, I. Factors influencing the occupancy of
trees with hollows, *Biological Conservation* **54**, 111–131.

See also the references in `glmrob`

.

### Examples

```
data(possumDiv)
head(possum.mat)
str(possumDiv)
## summarize all variables as multilevel factors:
summary(as.data.frame(lapply(possumDiv, function(v)
if(is.integer(v)) factor(v) else v)))
## Following Cantoni & Ronchetti (2001), JASA, p.1026 f.:% cf. ../tests/poisson-ex.R
pdFit <- glmrob(Diversity ~ . , data = possumDiv,
family=poisson, tcc = 1.6, weights.on.x = "hat", acc = 1e-15)
summary(pdFit)
summary(pdF2 <- update(pdFit, ~ . -Shrubs))
summary(pdF3 <- update(pdF2, ~ . -eucalyptus))
summary(pdF4 <- update(pdF3, ~ . -Stumps))
summary(pdF5 <- update(pdF4, ~ . -BAcacia))
summary(pdF6 <- update(pdF5, ~ . -aspect))# too much ..
anova(pdFit, pdF3, pdF4, pdF5, pdF6, test = "QD") # indeed,
## indeed, the last simplification is too much
possumD.2 <- within(possumDiv, levels(aspect)[1:3] <- rep("other", 3))
## and use this binary 'aspect' instead of the 4-level one:
summary(pdF5.1 <- update(pdF5, data = possumD.2))
if(FALSE) # not ok, as formually not nested.
anova(pdF5, pdF5.1)
summarizeRobWeights(weights(pdF5.1, type="rob"), eps = 0.73)
##-> "outliers" (1, 59, 110)
wrob <- setNames(weights(pdF5.1, type="rob"), rownames(possumDiv))
head(sort(wrob))
```