Compare exploratory groups across settings and clustering methods

Compare existing external-feature clustering results without refitting. Review how group membership changes when the selected features, number of groups, feature weights, or clustering method changes, including paired comparisons across the same imputations.

Usage

mfrm_cluster_compare(analyses)

# S3 method for class 'mfrm_cluster_comparison'
print(x, ...)

# S3 method for class 'mfrm_cluster_comparison'
summary(object, ...)

Arguments

analyses: A named list of at least two results from mfrm_cluster_pam() and/or mfrm_cluster_hierarchical() or mfrm_cluster_kmeans(), or a named list of results from mfrm_cluster_imputed(). Do not mix the two result types. Names must be unique and nonblank. All results must use the same entity IDs and included entities. Selected features may differ; features with the same name must retain their original values and types. Row and feature order may differ. IDs must refer to the same entities, not, for example, persons and raters that happen to share ID labels. For imputed results, shared completed features must also match by imputation number. When feature selections differ, all results must retain the same mids object, including its data and settings; each retained completion is checked against it using the optional mice package. Reuse one fitted imputation model.
x, object: An object returned by mfrm_cluster_compare().
...: Reserved for method compatibility.

Value

An mfrm_cluster_comparison object containing:

analysis_summary: method, distance, fitted space, scaling, retained component count, linkage (unavailable for PAM and k-means), group count, selected feature count (Features), included/excluded entity counts, smallest/largest group sizes, and mean silhouette for each analysis and imputation. Imputation is NA for ordinary clustering results.
weights: selected features and their supplied weights for each analysis. Unselected features have no row; they are not zero-weight inputs.
comparisons: all pairs of analyses, with one row per imputation. Pairs counts unordered pairs of included entities, excluding self-pairs. SplitPairs were together in First and apart in Second; JoinedPairs were apart in First and together in Second. ChangedFraction is their sum divided by Pairs. AdjustedRand is the adjusted Rand index.
comparison_summary: number of compared partitions, mean/minimum/ maximum changed fraction, and mean adjusted Rand index for each analysis pair. summary() returns this table.
analyses: the original results, including omitted IDs and all imputation-specific partitions, profiles, and settings.

Details

Comparisons align entities by ID and do not compare numeric group labels directly. Zero changed fraction and an adjusted Rand index of one indicate identical partitions, allowing arbitrary renumbering of groups. The changed fraction can be small when many pairs are separated in both partitions. The adjusted Rand index corrects agreement against random partitions with fixed group sizes; it can be negative. Neither measure identifies the correct group count or establishes group validity.

Mean silhouette and group sizes help describe each partition. Silhouette values calculated with different features or weights use different distances; their maximum is not an automatic criterion for selecting features or weights. Review group profiles in the retained analyses alongside the comparison.

With multiple imputations, feature selection is applied to the same completed data on both sides, without refitting the imputation model. A feature omitted from clustering can remain an imputation predictor; this comparison does not evaluate its removal from the imputation model. Every imputation is retained. Summary means and ranges describe sensitivity to settings across those imputations; they are not Rubin-pooled estimates, confidence intervals, or sampling stability. Conflicting shared feature values or different inclusion masks cause an error rather than a silent intersection of entities or imputations. No preferred setting, consensus partition, or hypothesis test is returned.

For an executable rater-attribute example that pairs multiple imputations across settings, see vignette("mfrmr-external-features", package = "mfrmr").

References

Hubert, L. and Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193–218. doi:10.1007/BF01908075 .

Examples

if (requireNamespace("cluster", quietly = TRUE)) {
  # Fictional attributes; experience is measured in completed years.
  raters <- data.frame(Rater = paste0("R", 1:8),
    ExperienceYears = c(1, 2, 3, 4, 11, 12, 13, 14),
    Specialty = rep(c("Language", "Science"), 4))
  features <- mfrm_features(raters, "Rater", c("ExperienceYears", "Specialty"))
  fits <- list(
    TwoGroups = mfrm_cluster_pam(features, k = 2),
    ThreeGroups = mfrm_cluster_pam(features, k = 3),
    ExperienceWeighted = mfrm_cluster_pam(features, k = 2,
      weights = c(ExperienceYears = 3, Specialty = 1)))
  comparison <- mfrm_cluster_compare(fits)
  summary(comparison)
  comparison$analysis_summary
  comparison$comparisons
  # Hold the entities and group count fixed while changing the feature set.
  experience <- mfrm_features(raters, "Rater", "ExperienceYears")
  feature_comparison <- mfrm_cluster_compare(list(
    BothFeatures = fits$TwoGroups,
    ExperienceOnly = mfrm_cluster_pam(experience, k = 2)))
  feature_comparison$analysis_summary
  feature_comparison$weights
}
#>         Analysis         Feature Weight
#> 1   BothFeatures ExperienceYears      1
#> 2   BothFeatures       Specialty      1
#> 3 ExperienceOnly ExperienceYears      1