makeCorrLoadings: Generate Inter-Item Correlation Matrix from Factor Loadings

In LikertMakeR: Synthesise and Correlate Likert Scale and Rating-Scale Data Based on Summary Statistics

Generate Inter-Item Correlation Matrix from Factor Loadings

Description

Constructs an inter-item correlation matrix based on a user-supplied matrix of standardised factor loadings and (optionally) a factor correlation matrix. The makeCorrLoadings() function does a surprisingly good job of reproducing a target correlation matrix when all item-factor loadings are present, as shown in the makeCorrLoadings() validation article.

Usage

makeCorrLoadings(
  loadings,
  factorCor = NULL,
  uniquenesses = NULL,
  nearPD = FALSE,
  diagnostics = FALSE
)

Arguments

loadings	Numeric matrix. A k \times f matrix of standardized factor loadings items \times factors. Row names and column names are used for diagnostics if present.
factorCor	Optional f \times f matrix of factor correlations (\Phi). If NULL, assumes orthogonal factors.
uniquenesses	Optional vector of length k. If NULL, calculated as 1 - rowSums(loadings^2).
nearPD	Logical. If TRUE, attempts to coerce non–positive-definite matrices using Matrix::nearPD().
diagnostics	Logical. If TRUE, returns diagnostics including McDonald's Omega and item-level summaries.

Value

If diagnostics = FALSE, returns a correlation matrix (class: matrix). If diagnostics = TRUE, returns a list with: - R: correlation matrix - Omega: per-factor Omega or adjusted Omega - OmegaTotal: total Omega across all factors - Diagnostics: dataframe of communalities, uniquenesses, and primary factor

See Also

• makeCorrLoadings() validation article: https://winzarh.github.io/LikertMakeR/articles/makeCorrLoadings_validate.html

• Package website: https://winzarh.github.io/LikertMakeR/

Examples

# --------------------------------------------------------
# Example 1: Basic use without diagnostics
# --------------------------------------------------------

factorLoadings <- matrix(
  c(
    0.05, 0.20, 0.70,
    0.10, 0.05, 0.80,
    0.05, 0.15, 0.85,
    0.20, 0.85, 0.15,
    0.05, 0.85, 0.10,
    0.10, 0.90, 0.05,
    0.90, 0.15, 0.05,
    0.80, 0.10, 0.10
  ),
  nrow = 8, ncol = 3, byrow = TRUE
)

rownames(factorLoadings) <- paste0("Q", 1:8)
colnames(factorLoadings) <- c("Factor1", "Factor2", "Factor3")

factorCor <- matrix(
  c(
    1.0,  0.7, 0.6,
    0.7,  1.0, 0.4,
    0.6,  0.4, 1.0
  ),
  nrow = 3, byrow = TRUE
)

itemCor <- makeCorrLoadings(factorLoadings, factorCor)
round(itemCor, 3)

# --------------------------------------------------------
# Example 2: Diagnostics with factor correlations (Adjusted Omega)
# --------------------------------------------------------

result_adj <- makeCorrLoadings(
  loadings = factorLoadings,
  factorCor = factorCor,
  diagnostics = TRUE
)

# View outputs
round(result_adj$R, 3) # correlation matrix
round(result_adj$Omega, 3) # adjusted Omega
round(result_adj$OmegaTotal, 3) # total Omega
print(result_adj$Diagnostics) # communality and uniqueness per item

# --------------------------------------------------------
# Example 3: Diagnostics assuming orthogonal factors (Per-Factor Omega)
# --------------------------------------------------------

result_orth <- makeCorrLoadings(
  loadings = factorLoadings,
  diagnostics = TRUE
)

round(result_orth$Omega, 3) # per-factor Omega
round(result_orth$OmegaTotal, 3) # total Omega
print(result_orth$Diagnostics)

LikertMakeR documentation built on March 23, 2026, 9:07 a.m.