Performs clustering analysis with selection of variables.

## Usage

clustering(
.data,
...,
by = NULL,
scale = FALSE,
selvar = FALSE,
verbose = TRUE,
distmethod = "euclidean",
clustmethod = "average",
nclust = NA
)

## Arguments

.data

The data to be analyzed. It can be a data frame, possible with grouped data passed from dplyr::group_by().

...

The variables in .data to compute the distances. Set to NULL, i.e., all the numeric variables in .data are used.

by

One variable (factor) to compute the function by. It is a shortcut to dplyr::group_by(). To compute the statistics by more than one grouping variable use that function.

scale

Should the data be scaled before computing the distances? Set to FALSE. If TRUE, then, each observation will be divided by the standard deviation of the variable $$Z_{ij} = X_{ij} / sd_j$$

selvar

Logical argument, set to FALSE. If TRUE, then an algorithm for selecting variables is implemented. See the section Details for additional information.

verbose

Logical argument. If TRUE (default) then the results for variable selection are shown in the console.

distmethod

The distance measure to be used. This must be one of 'euclidean', 'maximum', 'manhattan', 'canberra', 'binary', 'minkowski', 'pearson', 'spearman', or 'kendall'. The last three are correlation-based distance.

clustmethod

The agglomeration method to be used. This should be one of 'ward.D', 'ward.D2', 'single', 'complete', 'average' (= UPGMA), 'mcquitty' (= WPGMA), 'median' (= WPGMC) or 'centroid' (= UPGMC).

nclust

The number of clusters to be formed. Set to NA

## Value

• data The data that was used to compute the distances.

• cutpoint The cutpoint of the dendrogram according to Mojena (1977).

• distance The matrix with the distances.

• de The distances in an object of class dist.

• hc The hierarchical clustering.

• Sqt The total sum of squares.

• tab A table with the clusters and similarity.

• clusters The sum of square and the mean of the clusters for each variable.

• cofgrap If selectvar = TRUE, then, cofpgrap is a ggplot2-based graphic showing the cophenetic correlation for each model (with different number of variables). Else, will be a NULL object.

• statistics If selectvar = TRUE, then, statistics shows the summary of the models fitted with different number of variables, including cophenetic correlation, Mantel's correlation with the original distances (all variables) and the p-value associated with the Mantel's test. Else, will be a NULL object.

## Details

When selvar = TRUE a variable selection algorithm is executed. The objective is to select a group of variables that most contribute to explain the variability of the original data. The selection of the variables is based on eigenvalue/eigenvectors solution based on the following steps.

1. compute the distance matrix and the cophenetic correlation with the original variables (all numeric variables in dataset);

2. compute the eigenvalues and eigenvectors of the correlation matrix between the variables;

3. Delete the variable with the largest weight (highest eigenvector in the lowest eigenvalue);

4. Compute the distance matrix and cophenetic correlation with the remaining variables;

5. Compute the Mantel's correlation between the obtained distances matrix and the original distance matrix;

6. Iterate steps 2 to 5 p - 2 times, where p is the number of original variables.

At the end of the p - 2 iterations, a summary of the models is returned. The distance is calculated with the variables that generated the model with the largest cophenetic correlation. I suggest a careful evaluation aiming at choosing a parsimonious model, i.e., the one with the fewer number of variables, that presents acceptable cophenetic correlation and high similarity with the original distances.

## References

Mojena, R. 2015. Hierarchical grouping methods and stopping rules: an evaluation. Comput. J. 20:359-363. doi:10.1093/comjnl/20.4.359

## Author

Tiago Olivoto tiagoolivoto@gmail.com

## Examples

# \donttest{
library(metan)

# All rows and all numeric variables from data
d1 <- clustering(data_ge2)

# Based on the mean for each genotype
mean_gen <-
data_ge2 %>%
means_by(GEN) %>%
column_to_rownames("GEN")

d2 <- clustering(mean_gen)

# Select variables for compute the distances
d3 <- clustering(mean_gen, selvar = TRUE)
#> EH excluded in this step |===                                             | 7%
EP excluded in this step |=======                                         | 14%
CDED excluded in this step |==========                                    | 21%
PH excluded in this step |==============                                  | 29%
CL excluded in this step |=================                               | 36%
NR excluded in this step |=====================                           | 43%
PERK excluded in this step |=======================                       | 50%
EL excluded in this step |===========================                     | 57%
CD excluded in this step |===============================                 | 64%
ED excluded in this step |==================================              | 71%
KW excluded in this step |======================================          | 79%
CW excluded in this step |=========================================       | 86%
NKR excluded in this step |============================================   | 93%
TKW excluded in this step |===============================================| 100%

#> --------------------------------------------------------------------------
#>
#> Summary of the adjusted models
#> --------------------------------------------------------------------------
#>     Model excluded cophenetic remaining cormantel    pvmantel
#>   Model 1        -  0.8656190        15 1.0000000 0.000999001
#>   Model 2       EH  0.8656191        14 1.0000000 0.000999001
#>   Model 3       EP  0.8656191        13 1.0000000 0.000999001
#>   Model 4     CDED  0.8656191        12 1.0000000 0.000999001
#>   Model 5       PH  0.8656189        11 1.0000000 0.000999001
#>   Model 6       CL  0.8655939        10 0.9999996 0.000999001
#>   Model 7       NR  0.8656719         9 0.9999982 0.000999001
#>   Model 8     PERK  0.8657259         8 0.9999977 0.000999001
#>   Model 9       EL  0.8657904         7 0.9999972 0.000999001
#>  Model 10       CD  0.8658997         6 0.9999964 0.000999001
#>  Model 11       ED  0.8658274         5 0.9999931 0.000999001
#>  Model 12       KW  0.8643556         4 0.9929266 0.000999001
#>  Model 13       CW  0.8640355         3 0.9927593 0.000999001
#>  Model 14      NKR  0.8648384         2 0.9925396 0.000999001
#> --------------------------------------------------------------------------
#> Suggested variables to be used in the analysis
#> --------------------------------------------------------------------------
#> The clustering was calculated with the  Model 10
#> The variables included in this model were...
#>  ED CW KW NKR TKW NKE
#> --------------------------------------------------------------------------
#>

# Compute the distances with standardized data
# Define 4 clusters
d4 <- clustering(data_ge,
by = ENV,
scale = TRUE,
nclust = 4)

# }