Generate Inter-Item Correlation Matrix from Factor Loadings
Source:R/makeCorrLoadings.R
makeCorrLoadings.RdConstructs an inter-item correlation matrix based on a user-supplied matrix of standardized factor loadings and (optionally) a factor correlation matrix.
Usage
makeCorrLoadings(
loadings,
factorCor = NULL,
uniquenesses = NULL,
nearPD = FALSE,
diagnostics = FALSE
)Arguments
- loadings
Numeric matrix. A k × f matrix of standardized factor loadings (items × factors). Row names and column names are used for diagnostics if present.
- factorCor
Optional f × f matrix of factor correlations (Φ). 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: data.frame of communalities, uniquenesses, and primary factor
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)
#> Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
#> Q1 1.000 0.638 0.683 0.537 0.477 0.484 0.552 0.521
#> Q2 0.638 1.000 0.735 0.503 0.434 0.436 0.557 0.531
#> Q3 0.683 0.735 1.000 0.569 0.499 0.503 0.601 0.570
#> Q4 0.537 0.503 0.569 1.000 0.799 0.839 0.751 0.676
#> Q5 0.477 0.434 0.499 0.799 1.000 0.805 0.670 0.599
#> Q6 0.484 0.436 0.503 0.839 0.805 1.000 0.709 0.633
#> Q7 0.552 0.557 0.601 0.751 0.670 0.709 1.000 0.790
#> Q8 0.521 0.531 0.570 0.676 0.599 0.633 0.790 1.000
# --------------------------------------------------------
# Example 2: Diagnostics with factor correlations (Adjusted Omega)
# --------------------------------------------------------
result_adj <- makeCorrLoadings(
loadings = factorLoadings,
factorCor = factorCor,
diagnostics = TRUE
)
#> Diagnostics returned with Adjusted Omega (accounting for factor correlations).
# View outputs
round(result_adj$R, 3) # correlation matrix
#> Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
#> Q1 1.000 0.638 0.683 0.537 0.477 0.484 0.552 0.521
#> Q2 0.638 1.000 0.735 0.503 0.434 0.436 0.557 0.531
#> Q3 0.683 0.735 1.000 0.569 0.499 0.503 0.601 0.570
#> Q4 0.537 0.503 0.569 1.000 0.799 0.839 0.751 0.676
#> Q5 0.477 0.434 0.499 0.799 1.000 0.805 0.670 0.599
#> Q6 0.484 0.436 0.503 0.839 0.805 1.000 0.709 0.633
#> Q7 0.552 0.557 0.601 0.751 0.670 0.709 1.000 0.790
#> Q8 0.521 0.531 0.570 0.676 0.599 0.633 0.790 1.000
round(result_adj$Omega, 3) # adjusted Omega
#> Factor1 Factor2 Factor3
#> 0.691 0.683 0.638
round(result_adj$OmegaTotal, 3) # total Omega
#> [1] 0.768
print(result_adj$Diagnostics) # communality and uniqueness per item
#> Item Communality Uniqueness PrimaryFactor
#> Q1 Q1 0.5325 0.4675 Factor3
#> Q2 Q2 0.6525 0.3475 Factor3
#> Q3 Q3 0.7475 0.2525 Factor3
#> Q4 Q4 0.7850 0.2150 Factor2
#> Q5 Q5 0.7350 0.2650 Factor2
#> Q6 Q6 0.8225 0.1775 Factor2
#> Q7 Q7 0.8350 0.1650 Factor1
#> Q8 Q8 0.6600 0.3400 Factor1
# --------------------------------------------------------
# Example 3: Diagnostics assuming orthogonal factors (Per-Factor Omega)
# --------------------------------------------------------
result_orth <- makeCorrLoadings(
loadings = factorLoadings,
diagnostics = TRUE
)
#> Diagnostics returned with Per-Factor Omega (assuming orthogonal factors).
round(result_orth$Omega, 3) # per-factor Omega
#> Factor1 Factor2 Factor3
#> 0.405 0.513 0.460
round(result_orth$OmegaTotal, 3) # total Omega
#> [1] 0.721
print(result_orth$Diagnostics)
#> Item Communality Uniqueness PrimaryFactor
#> Q1 Q1 0.5325 0.4675 Factor3
#> Q2 Q2 0.6525 0.3475 Factor3
#> Q3 Q3 0.7475 0.2525 Factor3
#> Q4 Q4 0.7850 0.2150 Factor2
#> Q5 Q5 0.7350 0.2650 Factor2
#> Q6 Q6 0.8225 0.1775 Factor2
#> Q7 Q7 0.8350 0.1650 Factor1
#> Q8 Q8 0.6600 0.3400 Factor1