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Unified r Selection for Mixture Models (MFA/MPCA)

Source: R/r_selection_mixture.R
select_r_mixture.Rd

This function provides a unified interface for selecting the optimal number of factors (r) in mixture models. It supports three modes: "clusterwise" (evaluate r separately per cluster), "global-first" (estimate r from pooled data first), and "hybrid" (combine both approaches).

Usage

select_r_mixture(
  list_of_data,
  K,
  rvec = 1:6,
  mode = c("clusterwise", "global-first", "hybrid"),
  model_type = c("MFA", "MPCA"),
  criteria = c("VAF", "VSS", "smoothness"),
  agg_method = c("max", "mean", "min", "majority", "global"),
  global_model = c("PPCA", "FA"),
  global_criterion = c("CV", "ParallelAnalysis"),
  global_folds = 5,
  global_seed = NULL,
  weights = c(VAF = 0.4, VSS = 0.4, smoothness = 0.2),
  vss_threshold = 0.5,
  vss_method = c("threshold", "ratio"),
  vss_rotate = c("none", "varimax"),
  vss_normalize = c("logr", "max", "r", "r2", "none"),
  max_iter = 50,
  nIterFA = 5,
  nIterPCA = 5,
  tol = 0.001,
  n_init = 1,
  use_kmeans_init = TRUE,
  subject_rdim_for_kmeans = 2,
  mc_cores = 1,
  n_threads = 1,
  verbose = FALSE,
  refit_final = TRUE
)

Arguments

list_of_data

A list of N matrices, each (T_i x M).

K

Number of clusters (fixed).

rvec

Vector of candidate r values to evaluate. Default is 1:6.

mode

Selection mode. Options:

  • "clusterwise" (default): Evaluate r separately for each cluster, then aggregate

  • "global-first": Estimate r using global FA/PPCA on pooled data

  • "hybrid": Use global r as initialization for clusterwise evaluation

model_type

Model type. Options: "MFA" (Mixture Factor Analysis, default), "MPCA" (Mixture Principal Component Analysis).

criteria

Character vector specifying which criteria to use for clusterwise selection. Options: "VAF", "VSS", "smoothness". Default is c("VAF", "VSS", "smoothness"). Only used when mode = "clusterwise" or "hybrid".

agg_method

Method for aggregating cluster-specific r values. Options: "max" (conservative, takes maximum r across clusters), "mean" (average r, rounded), "min" (minimum r across clusters), "majority" (most common r value), "global" (use the global r estimate r_global as the final r; only valid in hybrid mode). Default is "max". In clusterwise mode, only "max", "mean", "min", "majority" are allowed. In hybrid mode, you may additionally use "global" to set r_final = r_global. Ignored when mode = "global-first".

global_model

Model for global r estimation. Options: "PPCA" (default), "FA". Only used when mode = "global-first" or "hybrid".

global_criterion

Criterion for global r selection. Options: "CV" (default), "ParallelAnalysis". Only used when mode = "global-first" or "hybrid".

global_folds

Number of CV folds for global r selection. Default is 5. Only used when mode = "global-first" or "hybrid" with criterion = "CV".

global_seed

Random seed for global r selection. Default is NULL.

weights

Named vector of weights for combining criteria in clusterwise mode. Default is c(VAF=0.4, VSS=0.4, smoothness=0.2).

vss_threshold

Threshold for VSS criterion. Default is 0.5.

vss_method

Method for computing VSS. Options: "threshold", "ratio". Default is "threshold".

vss_rotate

Rotation method for VSS. Options: "none", "varimax". Default is "none".

vss_normalize

Method for normalizing VSS. Options: "logr", "max", "r", "r2", "none". Default is "logr".

max_iter

Maximum EM iterations for model fitting.

nIterFA

Sub-iterations for FA update (MFA only).

nIterPCA

Sub-iterations for PCA update (MPCA only).

tol

Convergence tolerance.

n_init

Number of random initializations for mixture model fitting.

use_kmeans_init

Whether to use k-means initialization.

subject_rdim_for_kmeans

Dimension for k-means features.

mc_cores

Number of cores for parallelization.

n_threads

Number of OpenMP threads.

verbose

Logical. If TRUE, print detailed diagnostic information.

refit_final

Logical. If TRUE, refit the final model with selected r_final. Default is TRUE.

Value

A list with class "mixture_r_selection" containing:

r_final

The final selected r value.

r_global

Global r estimate (if mode = "global-first" or "hybrid").

r_cluster

Named vector of cluster-specific r values (if mode = "clusterwise" or "hybrid").

initial_fit

Initial mixture model fit used for cluster assignments (if applicable).

final_fit

Final mixture model fit with r_final (if refit_final = TRUE).

diagnostics

List containing detailed diagnostic information.

mode

The selection mode used.

model_type

The model type used (MFA or MPCA).

agg_method

The aggregation method used (if applicable).

Details

This function provides a unified interface for r selection in mixture models, integrating three complementary approaches:

Mode: "global-first"

  1. Pool all data and fit a global FA/PPCA model

  2. Select r using cross-validation or parallel analysis

  3. Return r_global as the final estimate

This mode is fast and provides a cluster-independent baseline. It's recommended when you want a simple, stable estimate that doesn't depend on cluster structure.

Mode: "clusterwise"

  1. Fit initial mixture model with median(rvec) to get cluster assignments

  2. For each cluster, evaluate different r values using cluster-specific metrics

  3. Aggregate cluster-specific r values using specified method

This mode is useful when different clusters may require different numbers of factors.

Mode: "hybrid"

  1. Estimate r_global using global FA/PPCA (as in "global-first")

  2. Use r_global as initialization for clusterwise evaluation

  3. Evaluate r values around r_global for each cluster

  4. Aggregate cluster-specific r values

This mode combines the stability of global estimation with the flexibility of cluster-specific evaluation.

Examples

if (FALSE) { # \dontrun{
# Global-first mode (recommended for simplicity)
result <- select_r_mixture(
  list_of_data, K = 3, rvec = 2:6,
  mode = "global-first",
  model_type = "MFA"
)
print(result$r_final)

# Clusterwise mode
result <- select_r_mixture(
  list_of_data, K = 3, rvec = 2:6,
  mode = "clusterwise",
  model_type = "MFA",
  agg_method = "max"
)

# Hybrid mode
result <- select_r_mixture(
  list_of_data, K = 3, rvec = 2:6,
  mode = "hybrid",
  model_type = "MPCA"
)
} # }