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Heuristic Variable Splitting for NMF-SEM

Source: R/nmf.sem.R
nmf.sem.split.Rd

Infers a heuristic partition of observed variables into exogenous (\(Y_2\)) and endogenous (\(Y_1\)) blocks for use in NMF-SEM. The method is based on positive-SEM logic, causal ordering, and optional sign alignment using the first principal component (PC1).

The procedure:

  • internally standardizes variables (mean 0, sd 1),

  • optionally flips signs so that most variables align positively with PC1,

  • infers a causal ordering by repeatedly regressing each variable on the remaining ones and selecting the variable with the largest minimum standardized coefficient,

  • determines an exogenous block by scanning the ordering from upstream and stopping at the first variable whose strongest parent coefficient exceeds threshold.

If n.exogenous is supplied, it overrides the automatic threshold rule.

Usage

nmf.sem.split(
  x,
  n.exogenous = NULL,
  threshold = 0.1,
  auto.flipped = TRUE,
  verbose = FALSE
)

Arguments

x

A numeric matrix or data frame with rows = samples and columns = observed variables.

n.exogenous

Optional integer specifying the number of exogenous variables (\(Y_2\)). If NULL, the number is inferred automatically by the coefficient cut-off rule.

threshold

Standardized regression-coefficient threshold used in the automatic exogenous–endogenous split. A variable is treated as endogenous once its maximum standardized parent coefficient exceeds this value. (Default: 0.1)

auto.flipped

Logical; if TRUE, applies PC1-based automatic sign flipping after standardization to ensure consistent orientation. (Default: TRUE)

verbose

Logical; if TRUE, prints progress messages and the resulting variable split. (Default: FALSE)

Value

A list with:

endogenous.variables

Character vector of variables selected as endogenous (\(Y_1\)).

exogenous.variables

Character vector of variables selected as exogenous (\(Y_2\)).

ordered.variables

Variables in inferred causal order (from exogenous to endogenous).

is.flipped

Logical vector indicating which variables were sign-flipped during processing.

n.exogenous

Integer giving the number of exogenous variables.

See also

nmf.sem

Examples

# Infer exogenous/endogenous split from iris
sp <- nmf.sem.split(iris[, -5], n.exogenous = 2)
sp$endogenous.variables
#> [1] "Petal.Width"  "Petal.Length"
sp$exogenous.variables
#> [1] "Sepal.Length" "Sepal.Width"