Compute Reliability as a Function of Scaling Factor

Computes and optionally plots the reliability curve \(\rho(c)\) across a grid of scaling factor values. This visualization helps understand how reliability varies with the discrimination scaling factor and aids in selecting appropriate target reliability values.

Usage

rho_curve(
  c_values = seq(0.1, 5, length.out = 50),
  n_items,
  model = c("rasch", "2pl", "3pl"),
  latent_shape = "normal",
  item_source = "parametric",
  metric = c("both", "info", "msem"),
  M = 5000L,
  seed = NULL,
  latent_params = list(),
  item_params = list(),
  plot = TRUE
)

# S3 method for class 'rho_curve'
print(x, ...)

Arguments

c_values: Numeric vector. Grid of scaling factor values to evaluate. Default: seq(0.1, 5, length.out = 50).
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().
metric: Character. Which reliability metric(s) to compute: "both", "info", or "msem".
M: Integer. Monte Carlo sample size. Default: 5000.
seed: Optional integer for reproducibility.
latent_params: List. Additional arguments passed to sim_latentG().
item_params: List. Additional arguments passed to sim_item_params().
plot: Logical. If TRUE (default), create a plot of the curve.
x: An object of class "rho_curve".
...: Additional arguments (ignored).

Value

A data frame of class "rho_curve" with columns:

c: Scaling factor values.
rho_tilde: Average-information reliability (if metric includes "info").
rho_bar: MSEM-based reliability (if metric includes "msem").

The input object, invisibly.

Details

The function generates a single set of theta and item parameters, then evaluates the reliability at each value of c_values. When metric = "both", it uses compute_rho_both for efficiency. For a curve with detected interior extrema or unresolved regions, an independently scanned topology_info and/or topology_msem attribute is attached. Topology is never inferred from the display grid alone.

Values are conditional on the generated finite theta sample. For the built-in latent_shape = "heavy_tail", a numeric MSEM curve is a finite-grid sensitivity result; the corresponding population MSEM functional can be non-integrable and is not certified by this function.

Examples

# Basic usage: compute reliability curve for 25-item Rasch test
curve_data <- rho_curve(n_items = 25, model = "rasch", seed = 42,
                        M = 3000, plot = FALSE)
head(curve_data)
#> Reliability Curve
#> =================
#>   Items: 25 | Model: RASCH | Metric: both
#>   c range: [0.10, 0.60] (6 points)
#>   rho_tilde range: [0.0592, 0.6645]
#>   rho_bar range  : [0.0592, 0.6622]
#> 
#>     c  rho_tilde    rho_bar
#> 1 0.1 0.05922061 0.05921989
#> 2 0.2 0.19896249 0.19893104
#> 3 0.3 0.35354114 0.35333047
#> 4 0.4 0.48588780 0.48523096
#> 5 0.5 0.58813434 0.58675218
#> 6 0.6 0.66450137 0.66217929