Estimate the number of components and loading reliability (shared helpers)

These helpers provide a common interface for component retention and loading reliability across bada, mfa, penalized_mfa, and related models. They are intentionally modular so alternative criteria (e.g., AIC, permutations) can be added later without changing call sites.

Usage

estimate_components(
  fit,
  method = c("rmt", "variance"),
  sdev = NULL,
  V_list = NULL,
  n = NULL,
  tail_q = 0.2,
  alpha = 0.05
)

loading_reliability(
  fit,
  method = c("bootstrap"),
  boot_loadings = NULL,
  alpha = 0.05,
  V_ref = NULL
)

Arguments

fit

A fitted object (e.g., bada, mfa, penalized_mfa, penalized_mfa_clusterwise).

method

Component or reliability method. For estimate_components, one of "rmt" (Marchenko–Pastur edge) or "variance" (keep all non-zero). For loading_reliability, currently "bootstrap".

sdev

Optional singular values; if NULL, taken from fit$sdev when available.

V_list

Optional list of loading matrices; if NULL, the helper attempts to extract from fit (using attr(fit, "V_list") or splitting fit$v by block_indices when present).

n

Optional number of observations (rows); defaults to nrow of scores if available.

tail_q

Numeric; fraction of smallest eigenvalues used to estimate noise variance for the RMT test (default 0.2). Only used in estimate_components when method = "rmt".

alpha

Confidence level for hypothesis tests or bootstrap intervals.

boot_loadings

For loading_reliability: a list of loading matrices from bootstrap refits (all same dimensions as the reference loadings).

V_ref

For loading_reliability: optional reference loading matrix. If NULL, extracted from fit using the same logic as V_list.

Value

estimate_components

A list with keep, criterion, and method_used.

loading_reliability

A list with matrices mean, sd, lower, upper, and sign_consistency.