Hierarchical grouping of external features

For new code use mfrm_cluster(..., method = "hierarchical"). The former method-specific entry is no longer exported. This guide retains its statistical details and saved-result plotting methods.

Usage

# S3 method for class 'mfrm_hierarchical_clusters'
plot(
  x,
  type = c("dendrogram", "silhouette", "profile"),
  feature = NULL,
  labels = NULL,
  draw = TRUE,
  preset = "standard",
  ...
)

Arguments

x: For clustering, a table reviewed with mfrm_features(). For plotting, an mfrm_hierarchical_clusters result.
type: "dendrogram" (default), "silhouette", or "profile".
feature: A single selected feature name, required for type = "profile". Numeric features show means and medians in their original units; categorical features show within-group proportions in the original level order (including unused factor levels).
labels: Whether to display entity IDs on dendrograms and silhouettes. The default labels at most 50 included entities. Hiding labels does not remove entities. Profile plots always label groups and levels.
draw: Draw the plot when TRUE; FALSE only returns plotted values.
preset: Plot style: "standard", "publication", "compact", or "monochrome".
...: Reserved for future use; additional arguments are rejected.

Value

An mfrm_hierarchical_clusters object inheriting from mfrm_clusters. It retains the hclust object in tree, ID-aligned membership (ID, Cluster, Silhouette), cluster_summary, profiles, feature_data, and settings including the linkage. Hierarchical clustering does not select medoids; medoids is NULL and membership has no Medoid column. summary() returns the size/silhouette table. plot() invisibly returns a ggplot object; plot_data() extracts the tree, leaf order, memberships, group count, and excluded IDs.

Details

Build an agglomerative hierarchy from weighted Gower dissimilarities, cut it into a chosen number of groups, and inspect the retained dendrogram.

Call mfrm_cluster(x, k, method = "hierarchical", linkage = "average"). The k, weights and missing controls follow mfrm_cluster(). linkage is "average" (default, UPGMA) or "complete". Average linkage uses the mean dissimilarity over all cross-group pairs; complete linkage uses their maximum. Neither is selected automatically from the data.

Uses stats::hclust() followed by stats::cutree() at the requested k. Feature types, scaling, weights, missingness handling, silhouette definition, and the 5,000-included-entity limit follow mfrm_cluster(). No distance transformation or automatic sampling is performed. This limit is not a memory or speed guarantee.

Only average and complete linkage are supported. Ward's minimum-variance criterion requires an appropriate Euclidean geometry; this mixed-feature Gower interface does not define a Euclidean conversion or a Ward analysis. Clustering MFRM bias estimates is a separate methodological question from grouping the external attributes accepted here. Measurement uncertainty is not propagated.

The tree is fitted independently of PAM. Its merge heights describe the selected linkage on Gower dissimilarities, not significance or branch support. Tied distances can produce alternative hierarchies and input order can affect their resolution. A cut at k uses merge order even when heights tie, so a horizontal height threshold need not uniquely identify that cut.

The default plot draws this stored tree, with boxes marking the stored k groups. Labels are shown for at most 50 included entities by default; hiding labels does not sample or remove entities. Excluded entities have no leaves but remain in the result and plot data. Silhouette and feature-profile views reuse plot.mfrm_clusters(). Plots do not refit or choose groups. as_ggplot() converts the stored dendrogram without refitting. The default and component = "tree" retain the full tree and group boxes. Leaf order, heights, label settings and excluded IDs are preserved. Dashed boxes differ from the solid tree branches even in monochrome. Box widths and physical text sizes can differ from base graphics. Tied heights retain the merge-order partition; boxes do not imply a unique horizontal height cut. Use ggplot2::labs(title = NULL, subtitle = NULL, caption = NULL) to remove headings and annotations, and plot_data() to inspect the retained source evidence. Silhouette/profile conversions use the same dedicated summary renderers as plot.mfrm_clusters().

Use mfrm_cluster_compare() to compare this partition with PAM or another linkage on the same data. For multiple imputations, use mfrm_cluster_imputed(..., method = "hierarchical", linkage = "average"). Each completion retains its own tree; no pooled tree or branch support is estimated. See online feature-analysis guide.

Session plot defaults

See mfrmr_visual_diagnostics for options(mfrmr.plot_preset), argument precedence, and appearance when saving or reusing a plot.

Reading clustering metrics

For entity i, a(i) is its mean dissimilarity to other members of its own group; b(i) is the smallest mean dissimilarity to any other group. Silhouette = (b - a) / max(a, b), between -1 and 1. Values near 1 indicate compact, separated placement in this fitted geometry; near zero indicates a boundary; negative values indicate closer average proximity to another group. A singleton receives 0 by convention; zero does not establish overlap. A zero denominator also receives 0. Overall means weight entities equally; cluster means use that cluster's included entities. Excluded IDs have NA. A silhouette is neither a membership probability nor evidence of stability.

Gower distance is unitless in [0, 1] here: numeric absolute differences divided by included-sample ranges, nominal/binary mismatches, and ordinal rank differences are combined using the specified feature weights. The PAM medoid is an actual included entity minimizing within-group total dissimilarity; it is not a feature-wise mean. Profile Mean/Median/SD retain original units; categorical Proportion uses included group size as denominator. A large group or a high silhouette is not a better-performing group. Compare partitions under a fixed feature/distance definition; changing the sample, weights or scaling changes what these numbers measure. See cluster::silhouette() and Rousseeuw (1987), doi:10.1016/0377-0427(87)90125-7 , for the silhouette definition.

References

Murtagh, F. and Legendre, P. (2014). Ward's Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward's Criterion? Journal of Classification, 31, 274–295. doi:10.1007/s00357-014-9161-z .

Examples

if (requireNamespace("cluster", quietly = TRUE)) {
  # Fictional rater backgrounds; R7 has unrecorded experience.
  raters <- data.frame(Rater = paste0("R", 1:7),
    ExperienceYears = c(1, 2, 3, 12, 13, 14, NA),
    Specialty = factor(c(rep("Language", 3), rep("Science", 4))))
  features <- mfrm_features(raters, "Rater", c("ExperienceYears", "Specialty"))
  hierarchy <- mfrm_cluster(method = "hierarchical", features, k = 2, missing = "omit")
  plot(hierarchy)
  plot(hierarchy, type = "silhouette")
  plot(hierarchy, type = "profile", feature = "ExperienceYears")
  comparison <- mfrm_cluster_compare(list(
    PAM = mfrm_cluster(method = "pam", features, k = 2, missing = "omit"),
    Average = hierarchy,
    Complete = mfrm_cluster(method = "hierarchical", features, k = 2,
      linkage = "complete", missing = "omit")))
  comparison$analysis_summary
  summary(comparison)
}



#>     First   Second Partitions Included Pairs MeanChangedFraction
#> 1     PAM  Average          1        6    15                   0
#> 2     PAM Complete          1        6    15                   0
#> 3 Average Complete          1        6    15                   0
#>   MinChangedFraction MaxChangedFraction MeanAdjustedRand
#> 1                  0                  0                1
#> 2                  0                  0                1
#> 3                  0                  0                1