Fit MCA followed by Mclust for nominal categorical data — CreateClusterModel_MCA

Use this pipeline for many nominal categorical variables when a lower-dimensional category space is useful before mixture clustering.

Usage

CreateClusterModel_MCA_MClust(
  data,
  variables,
  method = c("exploratory", "finalize"),
  k_range = 2:10,
  models = c(1L, 2L, 3L),
  final_k = NULL,
  final_model = NULL,
  ClusterVariableName = "Cluster",
  seed = 93421L,
  mca_variance_threshold = 75,
  stability_resamples = 0L,
  stability_seed = seed + 1L,
  stability_progress = FALSE
)

Arguments

data: Data frame containing numeric clustering variables.
variables: Variables used for clustering.
method: Either "exploratory" or "finalize".
k_range: Candidate cluster counts in exploratory mode.
models: Numeric Mclust model IDs: 1 = EEI, 2 = VVI, 3 = EEE.
final_k, final_model: Finalized cluster count and numeric model ID.
ClusterVariableName: Output cluster column name.
seed: Random seed retained for reproducibility.
mca_variance_threshold: Cumulative MCA inertia percentage retained.
stability_resamples: Number of 80% participant subsample refits used to estimate candidate reproducibility. Subsamples are drawn without replacement. Use 0 to disable stability analysis.
stability_seed: Seed controlling participant subsampling.
stability_progress: Whether to print subsample progress messages.

Value

A fitted MCA plus Mclust model containing the frozen MCA object, mixture-model fit and subsample stability metrics, and posterior probabilities. ModelInfo$plots leads with the reduction layer's scree and loadings, followed by the mixture-model structure figures in MCA score space and categorical_composition restated on the original items. BIC/ICL/AIC, entropy, and uncertainty use the same interpretation as Mclust.

Stability output

Stability assesses internal reproducibility by full-pipeline 80% participant subsampling without replacement. For each replicate, 80% of complete participants are selected once, all preprocessing and any reduction (PCA, MCA, or SOM) are refit, the selected clustering method is refit, and the original complete training participants are projected into that subsample fit for comparison with the original fitted partition. It is an internal sensitivity analysis, not independent-cohort validation.

Stability$settings records the analysis provenance:

resamples: requested number of 80% subsample refits.
seed: seed used to select subsamples.
refit_scope: always "full_pipeline", meaning preprocessing, reduction where applicable, and clustering were all refit.
resample_type: "subsample_without_replacement" for the primary stability analysis.
resample_fraction: the retained participant fraction, 0.80.
coassignment_limit: maximum number of complete training participants (2,000) for which the full pairwise co-assignment matrix is calculated.
noise_policy: whether the method has noise labels. For ordinary methods it is "all clusters included"; HDBSCAN variants retain noise in global partition metrics but exclude it from per-cluster inclusion and co-assignment summaries.

Stability$replicates has one row per requested refit. Model and Classes identify the selected candidate (for HDBSCAN, Classes is the data-derived extracted count); Replicate is its sequence number; Status is "success" or a failure status; and Error contains the error message for an unsuccessful refit. Successful rows contain these partition metrics:

ARI: adjusted Rand index, agreement corrected for chance; higher is better and can be negative when agreement is worse than chance.
VI: variation of information, the information lost or gained when changing partitions; lower is better and zero is identical.
NMI: normalized mutual information; higher is better and one is identical.
FowlkesMallows: pairwise clustering agreement; higher is better and one is identical.

Stability$cluster_recovery has one row for each reference Cluster in each successful Replicate. Jaccard is the recovery of that reference cluster after matching it to the subsample cluster with the largest Jaccard overlap; higher is better and one is exact recovery. Model and Classes again identify the fitted candidate.

Stability$summary combines successful subsample refits: StabilitySuccessRate is successful refits divided by requested refits, an operational reliability measure that does not enter the reproducibility score. StabilityARI_Mean and StabilityARI_P05 are the mean and fifth percentile of ARI. StabilityJaccard_Mean and StabilityJaccard_Min are respectively the mean and minimum label-matched Jaccard recovery. ReproducibilityScore is the mean of the finite StabilityARI_Mean and StabilityJaccard_Mean values only; it does not include success rate, VI, NMI, or Fowlkes–Mallows.

Stability$failures repeats the replicate columns for unsuccessful refits, making fit failures auditable without mixing them with successful metrics.

Stability$participant_inclusion is one row per complete reference participant. RowIndex identifies its original row position, Cluster its reference assignment, SuccessfulRefits the number of usable refits, and InclusionProbability the proportion of those refits in which the participant returned to that cluster's label-matched subsample cluster. Model and Classes identify the candidate. Higher inclusion is better.

Stability$cluster_inclusion summarizes inclusion within each reference Cluster: MeanInclusion, P05Inclusion, and MinInclusion are the mean, fifth percentile, and minimum participant inclusion probabilities; Model and Classes identify the candidate. Higher values indicate that all, not only the average, of a cluster is recovered consistently.

Stability$coassignment is available only when the complete training cohort has at most coassignment_limit participants. Each candidate entry has a status of "available", "skipped", or "not_available"; reason explains a non-available result; matrix is the pairwise probability that two complete reference participants are assigned together across successful subsample refits; and row_ids maps matrix rows and columns to original training-row positions. Higher matrix values mean more consistent pairwise co-membership. Where more than one candidate is summarized, entries are named by its Model_Classes key. The matrix is diagnostic only and is never used for selection.

Stability$plots contains cluster_recovery (per-cluster Jaccard), partition_metrics (ARI, VI, NMI, and Fowlkes–Mallows distributions), and cluster_inclusion; it also contains a co-assignment heatmap when the matrix is available. These diagnostics complement rather than replace ARI and Jaccard: none can turn a poorly reproducible cluster into a stable phenotype.

Metric sources: Hubert and Arabie (1985) define ARI; Jaccard (1901) defines the overlap coefficient; Meila (2005) defines VI; Strehl and Ghosh (2002) describe NMI for partition comparison; Fowlkes and Mallows (1983) define their pairwise index; and Monti et al. (2003) describe resampling-based consensus co-assignment.

References

Greenacre M. Correspondence Analysis in Practice. 3rd ed. Chapman and Hall/CRC; 2017. Scrucca L et al. mclust 5. J Stat Softw. 2016;71(11):1-29.

Examples

# \donttest{
data("SimulatedPhenotypeData")
df_Training <- dplyr::filter(SimulatedPhenotypeData, .data$Cohort == "Training")
df_Projection <- dplyr::filter(SimulatedPhenotypeData, .data$Cohort == "Projection")
vars_Categorical <- paste0("CatVar", 1:3)
review <- CreateClusterModel_MCA_MClust(
  df_Training, vars_Categorical, k_range = 2:4, models = 1,
  stability_resamples = 2
)
review$ModelInfo$fit_table
#> # A tibble: 3 × 27
#>   Model ModelName Classes    BIC    ICL   AIC Entropy MinClusterN SizeBalance
#>   <int> <chr>       <int>  <dbl>  <dbl> <dbl>   <dbl>       <int>       <dbl>
#> 1     1 EEI             4   173.   173. -241.   1.000          80       1    
#> 2     1 EEI             3 -1113. -1113. 1060.   1.000          80       0.5  
#> 3     1 EEI             2 -2486. -2487. 2448.   0.991          80       0.333
#> # ℹ 18 more variables: MaxUncertainty <dbl>, BIC_scaled <dbl>,
#> #   ICL_scaled <dbl>, Entropy_scaled <dbl>, MinClusterN_scaled <dbl>,
#> #   SizeBalance_scaled <dbl>, MaxUncertainty_scaled <dbl>, ahp_index <dbl>,
#> #   Recommended <lgl>, StabilitySuccessRate <dbl>, StabilityARI_Mean <dbl>,
#> #   StabilityARI_P05 <dbl>, StabilityJaccard_Mean <dbl>,
#> #   StabilityJaccard_Min <dbl>, NoiseSensitivity <dbl>, NoiseSpecificity <dbl>,
#> #   ReproducibilityScore <dbl>, ReproducibilityScore_scaled <dbl>
review$ModelInfo$AHP$recommendation
#> [1] "AHP-style review recommends MCA plus Gaussian-mixture model (Model = 1, Classes = 4). Review this advisory choice alongside the candidate plots."
review$fit_plot

review$ModelInfo$plots$scree

model <- CreateClusterModel_MCA_MClust(
  df_Training, vars_Categorical, method = "finalize", final_k = 4,
  final_model = 1, stability_resamples = 2
)
model$ModelInfo$plots$loadings

model$ModelInfo$plots$categorical_composition

projected <- ProjectCluster(model, df_Projection)
projected$ProjectionFit$plots$projection_fit_class_bar

# }