Heuristic Specification Search for CFA Models (deprecated)

[Deprecated] This fit-only search has been superseded by specification_search_theory, which adds a theory-congruence term to the loss and avoids drifting toward models that fit well but break the intended factor structure. specification_search() is kept for backward compatibility and emits a deprecation warning on every call; new code should use specification_search_theory() (set theory_weight = 0 there to reproduce the fit-only behaviour).

Performs a heuristic specification search over CFA models in the spirit of MacCallum (1986). For each seed configuration (with a fixed number of factors), the algorithm runs a hill-climbing loop that evaluates three local operations at each step: move an item between factors, drop an item, and cov (add a residual covariance suggested by modification indices). Optionally, a bifactor variant is fitted for every seed with k >= 2. The function returns every configuration evaluated, the subset that meets the user-supplied fit targets, and the best model under a composite loss.

Usage

specification_search(
  data,
  items,
  seeds = NULL,
  max_factors = 4,
  min_items_factor = 2,
  cfi_target = 0.95,
  rmsea_target = 0.08,
  srmr_target = 0.08,
  max_iter_per_config = 40,
  max_covs = 5,
  max_items_removed = 6,
  try_bifactor = TRUE,
  operations = c("move", "drop", "cov"),
  estimator = "WLSMV",
  ordered = TRUE,
  std.lv = TRUE,
  mi_min = 10,
  mi_top = 3,
  loss_weights = c(rmsea = 0.5, cfi = 0.3, srmr = 0.2),
  patience = 8,
  early_stop_after_meet = 3,
  n_cores = 1,
  verbose = TRUE
)

Arguments

data

Data frame with the observed item responses.

items

Character vector with the names of the items to be searched over.

seeds

Named list of initial configurations. Names are the number of factors as character (e.g. "3"). Each element is a list of seeds, where every seed is a named list list(F1 = c("it1","it2"), ...). If NULL, default block-partition seeds are generated for k = 1 to max_factors.

max_factors

Maximum number of factors when seeds = NULL.

min_items_factor

Minimum items per factor preserved during move/drop.

cfi_target, rmsea_target, srmr_target

Fit thresholds. A model is flagged as successful if CFI >= cfi_target and RMSEA <= rmsea_target.

max_iter_per_config

Maximum hill-climbing iterations per seed.

max_covs

Maximum residual covariances added per configuration.

max_items_removed

Maximum items removed across all factors per configuration.

try_bifactor

If TRUE, fit bifactor variant for every k >= 2 seed.

operations

Subset of c("move","drop","cov") controlling enabled ops.

estimator

Estimator passed to lavaan::cfa.

ordered

If TRUE, items are treated as ordered.

std.lv

If TRUE, latent variances are fixed to one.

mi_min

Minimum modification-index value considered for covariances.

mi_top

Maximum number of top-MI candidates examined at each step.

loss_weights

Named numeric vector with weights for the composite loss.

patience

Iterations without improvement that stop the hill climb.

early_stop_after_meet

Extra iterations allowed after targets are met.

n_cores

Number of CPU cores for parallel evaluation of the candidate models within each greedy iteration (they are independent). Default 1 (sequential). Values > 1 use a PSOCK cluster (works on Windows, where fork is unavailable); results are identical to the sequential run, only faster. A practical choice is parallel::detectCores() - 1.

verbose

Print progress and the MacCallum warning.

Details

Warning (MacCallum, 1986). Specification search capitalizes on chance: the more configurations explored, the more likely the resulting model is sample-specific. If you publish results obtained with this function you should (a) report the procedure transparently as exploratory, (b) cross-validate the chosen model with an independent sample or via bootstrap, and (c) justify each accepted modification on substantive theoretical grounds. The function prints this warning on every call unless verbose = FALSE.

Value

An object of class specification_search, a list with:

• table: data frame, one row per configuration, ordered by loss.

• successful: subset of table that meets the targets.

• best: the best result (fit, syntax, factors, covs, indices, bifactor, meets, loss).

• results: every configuration evaluated.

• call: the matched call.

References

MacCallum, R. C. (1986). Specification searches in covariance structure modeling. Psychological Bulletin, 100(1), 107–120.

Saris, W. E., Satorra, A., & van der Veld, W. M. (2009). Testing structural equation models or detection of misspecifications? Structural Equation Modeling, 16(4), 561–582.

See also

specification_search_theory (recommended replacement), cfa_boosting

Examples

# \donttest{
data(Data_Expectativas)
items <- paste0("EAF", 1:10)

res <- specification_search(
  data                = Data_Expectativas,
  items               = items,
  max_factors         = 2,
  max_iter_per_config = 5,
  estimator           = "MLR",
  ordered             = FALSE,
  try_bifactor        = FALSE,
  verbose             = TRUE
)
#> Warning: specification_search() is deprecated: use specification_search_theory(), which adds a theory-congruence penalty to the loss (theory_weight = 0 reproduces the fit-only search).
#> 
#> ========================================================================
#>  Specification Search (MacCallum, 1986)
#> ========================================================================
#>  WARNING: specification search capitalizes on chance. Use this
#>  function only as an EXPLORATORY device. Recommended practice:
#>    (1) Report the procedure transparently as exploratory.
#>    (2) Cross-validate the chosen model with an independent
#>        sample or via bootstrap.
#>    (3) Justify each accepted modification on theoretical grounds.
#> ========================================================================
#> 
#>  Items: 10 | Max factors: 2 | Operations: move/drop/cov | Bifactor: FALSE 
#>  Targets: CFI >= 0.95  | RMSEA <= 0.08  | SRMR <= 0.08 
#> 
#> --- k = 1 factor(s) ---
#>   Config: k1_s1 (standard)
#>     [k1_s1] iter 1: DROP EAF6 from G -> CFI=0.9061 RMSEA=0.0972 SRMR=0.0672 loss=0.7245
#>     [k1_s1] iter 2: DROP EAF5 from G -> CFI=0.9752 RMSEA=0.0550 SRMR=0.0453 loss=0.0000
#> --- k = 2 factor(s) ---
#>   Config: k2_s1 (standard)
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#>     [k2_s1] iter 1: DROP EAF6 from F2 -> CFI=0.9136 RMSEA=0.0950 SRMR=0.0647 loss=0.6131
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#>     [k2_s1] iter 2: DROP EAF5 from F1 -> CFI=0.9713 RMSEA=0.0608 SRMR=0.0448 loss=0.0000
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> Warning: lavaan->lav_object_post_check():  
#>    covariance matrix of latent variables is not positive definite ; use 
#>    lavInspect(fit, "cov.lv") to investigate.
#> 
#> Models evaluated: 2 

print(res, top = 5)
#> Specification search: 2 configurations evaluated
#> Successful (meets CFI/RMSEA targets): 2 
#> 
#> Top 2 by composite loss:
#>  config n_factors bifactor n_items n_covs    cfi    tli  rmsea   srmr chisq df
#>   k1_s1         1    FALSE       8      0 0.9752 0.9653 0.0550 0.0453 26.06 20
#>   k2_s1         2    FALSE       8      0 0.9713 0.9577 0.0608 0.0448 26.02 19
#>  loss meets
#>     0  TRUE
#>     0  TRUE
#> 
#> Best model (k1_s1):
#>   CFI=0.9752 | RMSEA=0.0550 | SRMR=0.0453 | loss=0.0000 | meets=TRUE
#>   Factor assignment:
#>     G: EAF1, EAF2, EAF3, EAF4, EAF7, EAF8, EAF9, EAF10
res$successful
#>   config n_factors bifactor n_items n_covs    cfi    tli  rmsea   srmr chisq df
#> 1  k1_s1         1    FALSE       8      0 0.9752 0.9653 0.0550 0.0453 26.06 20
#> 2  k2_s1         2    FALSE       8      0 0.9713 0.9577 0.0608 0.0448 26.02 19
#>   loss meets
#> 1    0  TRUE
#> 2    0  TRUE
# }