LikertMakeR (version 1.3.0)

makeCorrLoadings: 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
)

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

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.

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)