Add or Drop Single Terms to a Constrained Ordination Model

Compute all single terms that can be added to or dropped from a constrained ordination model.

Usage

# S3 method for cca
add1(object, scope, test = c("none", "permutation"),
    permutations = how(nperm=199), ...)
# S3 method for cca
drop1(object, scope, test = c("none", "permutation"), 
    permutations = how(nperm=199), ...)

Arguments

object: A constrained ordination object from cca, rda, dbrda or capscale.
scope: A formula giving the terms to be considered for adding or dropping; see add1 for details.
test: Should a permutation test be added using anova.cca.
permutations: a list of control values for the permutations as returned by the function how, or the number of permutations required, or a permutation matrix where each row gives the permuted indices.
...: Other arguments passed to add1.default, drop1.default, and anova.cca.

Details

With argument test = "none" the functions will only call add1.default or drop1.default. With argument test = "permutation" the functions will add test results from anova.cca. Function drop1.cca will call anova.cca with argument by = "margin". Function add1.cca will implement a test for single term additions that is not directly available in anova.cca.

Functions are used implicitly in step, ordiR2step and ordistep. The deviance.cca and deviance.rda used in step have no firm basis, and setting argument test = "permutation" may help in getting useful insight into validity of model building. Function ordistep calls alternately drop1.cca and add1.cca with argument test = "permutation" and selects variables by their permutation \(P\)-values. Meticulous use of add1.cca and drop1.cca will allow more judicious model building.

The default number of permutations is set to a low value, because permutation tests can take a long time. It should be sufficient to give a impression on the significances of the terms, but higher values of permutations should be used if \(P\) values really are important.

Value

Returns a similar object as add1 and drop1.

Author

Jari Oksanen

Examples

data(dune)
data(dune.env)
## Automatic model building based on AIC but with permutation tests
step(cca(dune ~  1, dune.env), reformulate(names(dune.env)), test="perm")
#> Start:  AIC=87.66
#> dune ~ 1
#> 
#>              Df    AIC      F Pr(>F)   
#> + Moisture    3 86.608 2.2536  0.005 **
#> + Management  3 86.935 2.1307  0.005 **
#> + A1          1 87.411 2.1400  0.040 * 
#> <none>          87.657                 
#> + Manure      4 88.832 1.5251  0.040 * 
#> + Use         2 89.134 1.1431  0.205   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Step:  AIC=86.61
#> dune ~ Moisture
#> 
#>              Df    AIC      F Pr(>F)   
#> <none>          86.608                 
#> + Management  3 86.813 1.4565  0.055 . 
#> + A1          1 86.992 1.2624  0.175   
#> + Use         2 87.259 1.2760  0.075 . 
#> + Manure      4 87.342 1.3143  0.050 * 
#> - Moisture    3 87.657 2.2536  0.005 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> Call: cca(formula = dune ~ Moisture, data = dune.env)
#> 
#>               Inertia Proportion Rank
#> Total          2.1153     1.0000     
#> Constrained    0.6283     0.2970    3
#> Unconstrained  1.4870     0.7030   16
#> Inertia is scaled Chi-square 
#> 
#> Eigenvalues for constrained axes:
#>   CCA1   CCA2   CCA3 
#> 0.4187 0.1330 0.0766 
#> 
#> Eigenvalues for unconstrained axes:
#>    CA1    CA2    CA3    CA4    CA5    CA6    CA7    CA8    CA9   CA10   CA11 
#> 0.4098 0.2259 0.1761 0.1234 0.1082 0.0908 0.0859 0.0609 0.0566 0.0467 0.0419 
#>   CA12   CA13   CA14   CA15   CA16 
#> 0.0201 0.0143 0.0099 0.0085 0.0080 
#> 
## see ?ordistep to do the same, but based on permutation P-values
if (FALSE) {
ordistep(cca(dune ~  1, dune.env), reformulate(names(dune.env)))
}
## Manual model building
## -- define the maximal model for scope
mbig <- rda(dune ~  ., dune.env)
## -- define an empty model to start with
m0 <- rda(dune ~ 1, dune.env)
## -- manual selection and updating
add1(m0, scope=formula(mbig), test="perm")
#>            Df    AIC      F Pr(>F)   
#> <none>        89.620                 
#> A1          1 89.591 1.9217  0.020 * 
#> Moisture    3 87.707 2.5883  0.005 **
#> Management  3 87.082 2.8400  0.005 **
#> Use         2 91.032 1.1741  0.215   
#> Manure      4 89.232 1.9539  0.005 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
m0 <- update(m0, . ~ . + Management)
add1(m0, scope=formula(mbig), test="perm")
#>          Df    AIC      F Pr(>F)  
#> <none>      87.082                
#> A1        1 87.424 1.2965  0.180  
#> Moisture  3 85.567 1.9764  0.015 *
#> Use       2 88.284 1.0510  0.400  
#> Manure    3 87.517 1.3902  0.100 .
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
m0 <- update(m0, . ~ . + Moisture)
## -- included variables still significant?
drop1(m0, test="perm")
#>            Df    AIC      F Pr(>F)   
#> <none>        85.567                 
#> Management  3 87.707 2.1769   0.01 **
#> Moisture    3 87.082 1.9764   0.01 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
add1(m0, scope=formula(mbig), test="perm")
#>        Df    AIC      F Pr(>F)
#> <none>    85.567              
#> A1      1 86.220 0.8359  0.635
#> Use     2 86.842 0.8027  0.790
#> Manure  3 85.762 1.1225  0.375