missalpha (version 0.2.0)

cronbachs_alpha: Compute Lower and Upper Bound of Cronbach's Alpha

Description

This function computes the lower and upper bound of Cronbach's alpha using various methods such as enumeration, random sampling, or optimization algorithms. The function also supports rough approximations and allows integer-only or floating-point scores during sampling.

Usage

cronbachs_alpha(
  scores_mat,
  score_max,
  tol = 0.001,
  num_random = 1000,
  enum_all = FALSE,
  rough = FALSE,
  num_opt = 1,
  int_only = TRUE,
  method = "GA",
  ...
)

Value

A list containing:

alpha_min_opt

The smallest possible Cronbach's alpha computed by the optimization algorithm (if used).

alpha_max_opt

The largest possible Cronbach's alpha computed by the optimization algorithm (if used).

alpha_min_enum

The smallest possible Cronbach's alpha obtained by enumerating all possible scores (if used).

alpha_max_enum

The largest possible Cronbach's alpha obtained by enumerating all possible scores (if used).

alpha_min_rough

The smallest possible Cronbach's alpha obtained by rough approximation (if used).

alpha_max_rough

The largest possible Cronbach's alpha obtained by rough approximation (if used).

method

The optimization method used.

runtime

The total computation time in seconds.

Arguments

scores_mat

A matrix where rows represent persons and columns represent tests (or items), providing the performance of a person on a test. NA should be used for missing values.

score_max

An integer indicating the largest possible score of the test.

tol

A numeric value representing the desired accuracy in computing the lower and upper bound of Cronbach's alpha.

num_random

An integer specifying the number of random samples used in estimating the lower and upper bound. Default is 1000.

enum_all

A logical value indicating whether to enumerate all possible scores for Cronbach's alpha. Default is FALSE.

rough

A logical value indicating whether to compute a rough approximation of Cronbach's alpha bounds. Default is FALSE.

num_opt

An integer specifying the number of times to run the optimization algorithm. Default is 1.

int_only

A logical value indicating whether the random sampling should be restricted to integer-only scores. Default is TRUE.

method

A character string specifying the optimization method to be used ('GA', 'DEoptim', 'nloptr'). Default is 'GA'.

...

Additional parameters passed to the optimization algorithm.

See Also

compute_alpha_min, compute_alpha_max, cronbach_alpha_enum, cronbach_alpha_rough, generate_scores_mat_bernoulli, qp_solver

Examples

# \donttest{
# Example 1: Run `cronbachs_alpha` with a sample matrix
scores_mat <- matrix(c(
  NaN, 1, 0, 0, 0, 0, 0, 0, NaN, 0, 0, 0,
  2, 0, 0, 1, NaN, 0, 0, 0, 0, 0, 0, 0,
  1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1
), nrow = 10, ncol = 4, byrow = TRUE)

result <- cronbachs_alpha(scores_mat, score_max = 4, enum_all = FALSE)
print(result$alpha_min_opt)
print(result$alpha_max_opt)

# Example 2: Generate a Bernoulli matrix and compute Cronbach's alpha
score_max <- 2
scores_mat_bernoulli <- generate_scores_mat_bernoulli(50, 10, 20, score_max)
result <- cronbachs_alpha(scores_mat_bernoulli, score_max, enum_all = FALSE)
print(result$alpha_min_opt)
print(result$alpha_max_opt)

# Example 3: Using a predefined dataset from missalpha
scores_df <- missalpha::sample
scores_mat <- as.matrix(scores_df)
result <- cronbachs_alpha(scores_mat, score_max = 4, enum_all = FALSE)
print(result$alpha_min_opt)
print(result$alpha_max_opt)
# }