Redundancy-Guided Short Form of a Unidimensional Scale

Builds a short form of an (essentially) unidimensional scale by iteratively removing the most locally-dependent item. At each step a one-factor model is fitted, the pair of items with the largest residual correlation is located, and the item of that pair with the lower loading is dropped (keeping the stronger indicator). Pruning stops when the target length k is reached or when no residual correlation exceeds threshold. This addresses the common situation where a scale is unidimensional but the one-factor model misfits because of near-duplicate items (local dependence).

Usage

redundancy_short_form(
  data,
  items,
  k = NULL,
  groups = NULL,
  min_per_group = 3,
  threshold = 0.15,
  min_omega = NULL,
  estimator = "WLSMV",
  ordered = TRUE
)

Arguments

data

Data frame with the item responses.

items

Character vector with the candidate item names.

k

Target number of items. If NULL, prunes until the largest residual correlation drops below threshold. Default NULL.

groups

Optional named list mapping content groups to items (e.g. theoretical dimensions), used only to preserve at least min_per_group items per group during pruning. Default NULL (no constraint).

min_per_group

Minimum items kept per group in groups. Default 3.

threshold

Residual-correlation stopping threshold when k = NULL. Default 0.15.

min_omega

Reliability floor. When set (e.g. 0.80), an item is only dropped if the resulting form keeps McDonald's omega at or above this value, so the short form cannot buy fit at the cost of internal consistency. A scale that already sits below the floor is not frozen: for it the effective bar is its current omega, so removals that do not reduce reliability are still allowed. NULL (default) disables the check.

estimator

Estimator passed to lavaan::cfa. Default "WLSMV".

ordered

Logical; treat items as ordered. Default TRUE.

Value

A list with items (retained items), trajectory (data frame with n_items, cfi, tli, rmsea, srmr, omega and the item dropped at each step), fit (final one-factor lavaan object), loadings (standardized), omega (McDonald's omega of the final form) and stop_reason ("target_k", "threshold", "min_items", "min_per_group" or "min_omega").

Details

Removing redundant items is preferred over piling up residual covariances, which capitalizes on chance (MacCallum, Roznowski & Necowitz, 1992). The resulting short form should be cross-validated on an independent sample (see cross_validate_cfa).

References

MacCallum, R. C., Roznowski, M., & Necowitz, L. B. (1992). Model modifications in covariance structure analysis: The problem of capitalization on chance. Psychological Bulletin, 111(3), 490–504.

See also

cross_validate_cfa

Examples

data(Data_Expectativas)
sf <- redundancy_short_form(Data_Expectativas, paste0("EAF", 1:10), k = 6,
        groups = list(A = paste0("EAF", 1:5), B = paste0("EAF", 6:10)))
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.160079e-16) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 2.580688e-18) 
#>    is close to zero. This may be a symptom that the model is not identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= 2.873136e-18) 
#>    is close to zero. This may be a symptom that the model is not identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.241411e-17) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -7.291260e-18) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -7.291260e-18) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.
sf$trajectory; sf$items; sf$omega
#>   n_items   cfi   tli rmsea  srmr omega dropped
#> 1      10 0.934 0.916 0.182 0.095 0.938       -
#> 2       9 0.961 0.948 0.156 0.067 0.940    EAF6
#> 3       8 0.991 0.988 0.082 0.044 0.937    EAF5
#> 4       7 0.996 0.994 0.060 0.037 0.931    EAF2
#> 5       6 1.000 1.004 0.000 0.026 0.920   EAF10
#> [1] "EAF1" "EAF3" "EAF4" "EAF7" "EAF8" "EAF9"
#> [1] 0.92