Description Usage Arguments Details Value Author(s) References See Also Examples

`gowdis`

measures the Gower (1971) dissimilarity for mixed variables, including asymmetric binary variables. Variable weights can be specified. `gowdis`

implements Podani's (1999) extension to ordinal variables.

1 |

`x` |
matrix or data frame containing the variables. Variables can be |

`w` |
vector listing the weights for the variables in |

`asym.bin` |
vector listing the asymmetric binary variables in |

`ord` |
character string specifying the method to be used for ordinal variables (i.e. |

`gowdis`

computes the Gower (1971) similarity coefficient exactly as described by Podani (1999), then converts it to a dissimilarity coefficient by using *D = 1 - S*. It integrates variable weights as described by Legendre and Legendre (1998).

Let *X = {Xij}* be a matrix containing *n* objects (rows) and *m* columns (variables). The similarity *Gjk* between objects *j* and *k* is computed as

*
Gjk = sum(Wijk * Sijk) / sum(Wijk)*

,

where *Wijk* is the weight of variable *i* for the *j*-*k* pair, and *Sijk* is the partial similarity of variable *i* for the *j*-*k* pair,

and where *Wijk = 0* if objects *j* and *k* cannot be compared because *Xij* or *Xik* is unknown (i.e. `NA`

).

For binary variables, *Sijk = 0* if *Xij is not equal to Xik*, and *Sijk = 1* if *Xij = Xik = 1* or if *Xij = Xik = 0*.

For asymmetric binary variables, same as above except that *Wijk = 0* if *Xij = Xik = 0*.

For nominal variables, *Sijk = 0* if *Xij is not equal to Xik* and *Sijk = 1* if *Xij = Xik*.

For continuous variables,

*
Sijk = 1 - [ |Xij - Xik| / (Xi.max - Xi.min) ]*

where *Xi.max* and *Xi.min* are the maximum and minimum values of variable *i*, respectively.

For ordinal variables, when `ord = "podani"`

or `ord = "metric"`

, all *Xij* are replaced by their ranks *Rij* determined over all objects (such that ties are also considered), and then

if `ord = "podani"`

*Sijk = 1* if *Rij = Rik*, otherwise

*
Sijk = 1 - [ |Rij - Rik| - (Tij - 1) / 2 - (Tik - 1) / 2 / Ri.max - Ri.min - (Ti.max - 1) / 2 - (Ti.min - 1) / 2 ]*

where *Tij* is the number of objects which have the same rank score for variable *i* as object *j* (including *j* itself), *Tik* is the number of objects which have the same rank score for variable *i* as object *k* (including *k* itself), *Ri.max* and *Ri.min* are the maximum and minimum ranks for variable *i*, respectively, *Ti.max* is the number of objects with the maximum rank, and *Ti.min* is the number of objects with the minimum rank.

if `ord = "metric"`

*
Sijk = 1 - [ |Rij - Rik| / (Ri.max - Ri.min) ]*

When `ord = "classic"`

, ordinal variables are simply treated as continuous variables.

an object of class `dist`

with the following attributes: `Labels`

, `Types`

(the variable types, where 'C' is continuous/numeric, 'O' is ordinal, 'B' is symmetric binary, 'A' is asymmetric binary, and 'N' is nominal), `Size`

, `Metric`

.

Etienne Laliberté etiennelaliberte@gmail.com http://www.elaliberte.info, with some help from Philippe Casgrain for the C interface.

Gower, J. C. (1971) A general coefficient of similarity and some of its properties. *Biometrics* **27**:857-871.

Legendre, P. and L. Legendre (1998) *Numerical Ecology*. 2nd English edition. Amsterdam: Elsevier.

Podani, J. (1999) Extending Gower's general coefficient of similarity to ordinal characters. *Taxon* **48**:331-340.

`daisy`

is similar but less flexible, since it does not include variable weights and does not treat ordinal variables as described by Podani (1999). Using `ord = "classic"`

reproduces the behaviour of `daisy`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
ex1 <- gowdis(dummy$trait)
ex1
# check attributes
attributes(ex1)
# to include weights
w <- c(4,3,5,1,2,8,3,6)
ex2 <- gowdis(dummy$trait, w)
ex2
# variable 7 as asymmetric binary
ex3 <- gowdis(dummy$trait, asym.bin = 7)
ex3
# example with trait data from New Zealand vascular plant species
ex4 <- gowdis(tussock$trait)
``` |

```
Loading required package: ade4
Loading required package: ape
Loading required package: geometry
Loading required package: magic
Loading required package: abind
Loading required package: vegan
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-4
sp1 sp2 sp3 sp4 sp5 sp6 sp7
sp2 0.2181884
sp3 0.5240052 0.6678082
sp4 0.6737443 0.5610028 0.8225701
sp5 0.5291113 0.8145699 0.4862253 0.4843264
sp6 0.6100161 0.5932587 0.2784736 0.7073925 0.6067323
sp7 0.4484235 0.6863374 0.4848663 0.5575126 0.3023416 0.6187844
sp8 0.4072834 0.2039443 0.5958904 0.2390962 0.5585525 0.4470207 0.7030186
$Labels
[1] "sp1" "sp2" "sp3" "sp4" "sp5" "sp6" "sp7" "sp8"
$Size
[1] 8
$Metric
[1] "Gower"
$Types
[1] "C" "C" "N" "N" "O" "O" "B" "B"
$class
[1] "dist"
sp1 sp2 sp3 sp4 sp5 sp6 sp7
sp2 0.1190154
sp3 0.4156230 0.5584826
sp4 0.7157249 0.7541962 0.7478800
sp5 0.6538987 0.8231658 0.3994155 0.3880160
sp6 0.5074762 0.4422926 0.2767123 0.7753720 0.6317876
sp7 0.5006495 0.6116622 0.4934116 0.4642192 0.3773199 0.5997205
sp8 0.2813567 0.2730468 0.3359142 0.3658275 0.4977458 0.3645410 0.6129055
sp1 sp2 sp3 sp4 sp5 sp6 sp7
sp2 0.2545531
sp3 0.5240052 0.6678082
sp4 0.7699935 0.6545032 0.8225701
sp5 0.5291113 0.8145699 0.4862253 0.4843264
sp6 0.6100161 0.5932587 0.2784736 0.7073925 0.6067323
sp7 0.4484235 0.6863374 0.4848663 0.5575126 0.3023416 0.6187844
sp8 0.4751640 0.2447331 0.5958904 0.2789456 0.5585525 0.4470207 0.7030186
```

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