Check Feasibility of Target Reliability

Screens whether a given target reliability is attainable in the generated finite Monte Carlo design for a particular test design (number of items, model, latent distribution, item source) by computing the range of empirical reliabilities across a range of scaling factors.

This function is useful for determining whether a planned simulation study is feasible before running the (potentially expensive) calibration algorithms.

Usage

check_feasibility(
  n_items,
  model = c("rasch", "2pl", "3pl"),
  latent_shape = "normal",
  item_source = "parametric",
  c_bounds = c(0.1, 10),
  M = 10000L,
  seed = NULL,
  latent_params = list(),
  item_params = list(),
  target_rho = NULL,
  verbose = TRUE
)

# S3 method for class 'feasibility_check'
print(x, digits = 4, ...)

Arguments

n_items: Integer. Number of items in the test form.
model: Character. Measurement model: "rasch", "2pl", or "3pl". For 3PL, supply lower-asymptote generation controls in item_params; discrimination alone is varied under D = 1.
latent_shape: Character. Shape argument passed to sim_latentG().
item_source: Character. Source argument passed to sim_item_params().
c_bounds: Numeric length-2 vector. Range of scaling factors to evaluate. Default: c(0.1, 10).
M: Integer. Monte Carlo sample size for theta. Default: 10000.
seed: Optional integer for reproducibility.
latent_params: List. Additional arguments passed to sim_latentG().
item_params: List. Additional arguments passed to sim_item_params().
target_rho: Optional numeric scalar in (0, 1). If supplied, the result includes status fields indicating whether the target is below, inside, or above the achievable range for each metric.
verbose: Logical. If TRUE, print results.
x: An object of class "feasibility_check".
digits: Integer. Number of decimal places for printing.
...: Additional arguments (ignored).

Value

An object of class "feasibility_check" (a list) with:

rho_range_info: Numeric length-2 vector: empirical range of average-information reliability (\(\tilde{\rho}\)) computed by the configured finite scan; provisional when topology is unresolved.
rho_range_msem: Numeric length-2 vector: empirical range of MSEM-based reliability (\(\bar{w}\)) computed by the configured finite scan; provisional when topology is unresolved.
rho_bounds_info: Endpoint reliabilities for average-information reliability.
rho_bounds_msem: Endpoint reliabilities for MSEM-based reliability.
rho_info_max_c: Scaling factor at the maximum information reliability detected by the configured scan within c_bounds; provisional when topology is unresolved.
rho_msem_max_c: Scaling factor at the maximum MSEM reliability detected by the configured scan within c_bounds; provisional when topology is unresolved.
target_status_info: If target_rho is supplied, one of "below_lower", "boundary_lower", "feasible", "boundary_upper", or "above_upper" for \(\tilde{\rho}\).
target_status_msem: Analogous status for \(\bar{w}\).
topology_info, topology_msem: Complete configured log-grid scans, polished extrema, detected roots, monotone branches, evaluation counts, and resolution status for each metric.
target_status_info_canonical, target_status_msem_canonical: Canonical feasibility status: "feasible", "infeasible_below_range", "infeasible_above_range", or "uncertain".
root_count_info, root_count_msem, admissible_root_count_info, admissible_root_count_msem: Detected roots and roots on increasing crossing/boundary branches.
best_achievable_info, best_achievable_msem: Closest detected point to target_rho, including scale, reliability, residual, absolute error, and location type.
n_items: Number of items.
model: Model used.
latent_shape: Latent distribution shape.
c_bounds: Scaling factor bounds evaluated.
M: Monte Carlo sample size.
theta_var: Estimated latent variance.

The input object, invisibly.

Details

Either reliability metric can be non-monotone over a sufficiently broad finite empirical integration interval. Both metrics therefore use the same adaptive log-scale topology scan as the calibrators. Endpoint values remain available in rho_bounds_*, while rho_range_* includes all resolved interior extrema within the user-supplied bounds.

These ranges and target classifications are conditional on the generated finite theta sample. In particular, for the built-in latent_shape = "heavy_tail", the population MSEM functional can be non-integrable even though a finite Monte Carlo sample yields a numeric rho_range_msem. Treat that MSEM range as finite-grid sensitivity evidence, not as a population feasibility guarantee.

Examples

# Check feasibility for 25-item Rasch test
feas <- check_feasibility(n_items = 25, model = "rasch",
                          target_rho = 0.90, seed = 42,
                          M = 5000, verbose = FALSE)
print(feas)
#> 
#> =======================================================
#>   Feasibility Check: Achievable Reliability Range
#> =======================================================
#> 
#>   Number of items  : 25
#>   Model            : RASCH
#>   Latent shape     : normal
#>   Latent variance  : 1.0099
#>   c range          : [0.10, 10.00]
#>   Monte Carlo M    : 5000
#> 
#> Achievable Reliability Ranges:
#>   rho_tilde (info) : [0.0591, 0.9872]
#>   rho_bar   (msem) : [0.0002, 0.9146]
#> 
#> Target rho*        : 0.9000
#>   info status      : feasible
#>   msem status      : feasible
#> 
#> Note: rho_tilde >= rho_bar on the same information grid (Jensen's inequality).
#>   rho_tilde range screens EQC targets; root policy must still admit a root.
#>   rho_bar range screens SAC targets; stable interior-branch preflight is also required.
#> 

# Metric-specific target status
feas$target_status_info
#> [1] "feasible"
feas$target_status_msem
#> [1] "feasible"

Usage

Arguments

Value

Details

See also

Examples