numbers 14 and 15 respectively because we deleted row #8 which is devoid of
species.
Jaccard’s similarity index has the following formula for two objects x 1 and x 2 :
S (x1,x2) ¼ a/(a + b + c)
where a is the number of double 1’s, and b and c are the numbers of 0–1 and
1–0 combinations.
After the computation, convert the similarity value to a dissimilarity using the
formulas used in vegan and ade4 (not the same formula).
---–
For the aficionados: display the code used in the ade4 function dist.binary
(just type dist.binary). Look how the quantities a, b, c and d are computed in
just four lines for whole data frames. A fine example of programming elegance by
Daniel Chessel and Stéphane Dray.
3.3.3 Q Mode: Quantitative Data (Excluding Species
Abundances)
For quantitative variables with a clear interpretation of double zeros, the queen of the
symmetrical distance measures is the Euclidean distance D 1 . “It is computed using
Pythagora’s formula, from site-points positioned in a p-dimensional space called a
metric or Euclidean space” (Legendre and Legendre 2012, p. 299).
The Euclidean distance has no upper limit and its value is strongly influenced by
the scale of each descriptor. For instance, changing the scale of a set of measurements from g/L to mg/L multiplies the contribution of that descriptor to the Euclidean distance by 1000. Therefore, the use of the Euclidean distance on raw data is
restricted to datasets that are dimensionally homogeneous, e.g. geographic coordinates expressed in km. Otherwise, D 1 is computed on standardized variables (zscores). Standardization is also applied to situations where one wishes to give the
same weight to all variables in a set of dimensionally homogeneous descriptors.
Here you could compute a matrix of Euclidean distances on the (standardized)
environmental variables of our env dataset. We shall remove one variable, dfs
(distance from the source), since it is a spatial rather than an environmental descriptor. The results will be displayed using coldiss() (Fig. 3.2).
46
3 Association Measures and Matrices
species.
Jaccard’s similarity index has the following formula for two objects x 1 and x 2 :
S (x1,x2) ¼ a/(a + b + c)
where a is the number of double 1’s, and b and c are the numbers of 0–1 and
1–0 combinations.
After the computation, convert the similarity value to a dissimilarity using the
formulas used in vegan and ade4 (not the same formula).
---–
For the aficionados: display the code used in the ade4 function dist.binary
(just type dist.binary). Look how the quantities a, b, c and d are computed in
just four lines for whole data frames. A fine example of programming elegance by
Daniel Chessel and Stéphane Dray.
3.3.3 Q Mode: Quantitative Data (Excluding Species
Abundances)
For quantitative variables with a clear interpretation of double zeros, the queen of the
symmetrical distance measures is the Euclidean distance D 1 . “It is computed using
Pythagora’s formula, from site-points positioned in a p-dimensional space called a
metric or Euclidean space” (Legendre and Legendre 2012, p. 299).
The Euclidean distance has no upper limit and its value is strongly influenced by
the scale of each descriptor. For instance, changing the scale of a set of measurements from g/L to mg/L multiplies the contribution of that descriptor to the Euclidean distance by 1000. Therefore, the use of the Euclidean distance on raw data is
restricted to datasets that are dimensionally homogeneous, e.g. geographic coordinates expressed in km. Otherwise, D 1 is computed on standardized variables (zscores). Standardization is also applied to situations where one wishes to give the
same weight to all variables in a set of dimensionally homogeneous descriptors.
Here you could compute a matrix of Euclidean distances on the (standardized)
environmental variables of our env dataset. We shall remove one variable, dfs
(distance from the source), since it is a spatial rather than an environmental descriptor. The results will be displayed using coldiss() (Fig. 3.2).
46
3 Association Measures and Matrices