Estimate scale reliability for Likert and rating-scale data

Computes internal consistency reliability estimates for a single-factor scale, including Cronbach’s alpha, McDonald’s omega (total), and optional ordinal (polychoric-based) variants. Confidence intervals may be obtained via nonparametric bootstrap.

Usage

reliability(
  data,
  include = "none",
  ci = FALSE,
  ci_level = 0.95,
  n_boot = 1000,
  na_method = c("pairwise", "listwise"),
  min_count = 2,
  digits = 3,
  verbose = TRUE
)

Arguments

data

A data frame or matrix containing item responses. Each column represents one item; rows represent respondents.

include

Character vector specifying which additional estimates to compute. Possible values are:

• "none" (default): Pearson-based alpha and omega only.

• "lambda6": Include Guttman’s lambda-6 (requires package psych).

• "polychoric": Include ordinal (polychoric-based) alpha and omega.

Multiple options may be supplied.

ci

Logical; if TRUE, confidence intervals are computed using nonparametric bootstrap. Default is FALSE.

ci_level

Confidence level for bootstrap intervals. Default is 0.95.

n_boot

Number of bootstrap resamples used when ci = TRUE. Default is 1000.

na_method

Method for handling missing values. Either "pairwise" (default) or "listwise".

min_count

Minimum observed frequency per response category required to attempt polychoric correlations. Ordinal reliability estimates are skipped if this condition is violated. Default is 2.

digits

Number of decimal places used when printing estimates. Default is 3.

verbose

Logical; if TRUE, warnings and progress indicators are displayed. Default is TRUE.

Value

A tibble with one row per reliability coefficient and columns:

• coef_name: Name of the reliability coefficient.

• estimate: Point estimate.

• ci_lower, ci_upper: Confidence interval bounds (only present when ci = TRUE).

• notes: Methodological notes describing how the estimate was obtained.

The returned object has class "likert_reliability" and includes additional attributes containing diagnostics and bootstrap information.

Details

The function is designed for Likert-type and rating-scale data and prioritises transparent diagnostics when ordinal reliability estimates are not feasible due to sparse response categories.

Cronbach’s alpha and McDonald’s omega are computed from Pearson correlations. When include = "polychoric", ordinal reliability estimates are computed using polychoric correlations and correspond to Zumbo’s alpha and ordinal omega.

Ordinal reliability estimates are skipped if response categories are sparse or if polychoric estimation fails. Diagnostics explaining these decisions are stored in the returned object and may be inspected using ordinal_diagnostics.

This function assumes a single common factor and is not intended for multidimensional or structural equation modelling contexts.

See also

ordinal_diagnostics

Examples

## create dataset
my_cor <- LikertMakeR::makeCorrAlpha(
  items = 4,
  alpha = 0.80
)
#> reached max iterations (1600) - best mean difference: 1.1e-05

my_data <- LikertMakeR::makeScales(
  n = 64,
  means = c(2.75, 3.00, 3.25, 3.50),
  sds = c(1.25, 1.50, 1.30, 1.25),
  lowerbound = rep(1, 4),
  upperbound = rep(5, 4),
  cormatrix = my_cor
)
#> Variable  1 :  item01  - 
#> reached maximum of 4096 iterations
#> Variable  2 :  item02  - 
#> best solution in 2657 iterations
#> Variable  3 :  item03  - 
#> reached maximum of 4096 iterations
#> Variable  4 :  item04  - 
#> reached maximum of 4096 iterations
#> 
#> Arranging data to match correlations
#> 
#> Successfully generated correlated variables
#> 

## run function
reliability(my_data)
#>    coef_name estimate n_items n_obs                notes
#>        alpha    0.801       4    64 Pearson correlations
#>  omega_total    0.871       4    64 1-factor eigen omega

reliability(
  my_data,
  include = c("lambda6", "polychoric")
)
#>            coef_name estimate n_items n_obs
#>                alpha    0.801       4    64
#>          omega_total    0.871       4    64
#>              lambda6    0.795       4    64
#>        ordinal_alpha    0.760       4    64
#>  ordinal_omega_total    0.848       4    64
#>                                                notes
#>                                 Pearson correlations
#>                                 1-factor eigen omega
#>                                       psych::alpha()
#>                              Polychoric correlations
#>  Polychoric correlations | Ordinal CIs not requested

# \donttest{
## slower (not run on CRAN checks)
reliability(
  my_data,
  include = "polychoric",
  ci = TRUE,
  n_boot = 200
)
#>            coef_name estimate ci_lower ci_upper n_items n_obs
#>                alpha    0.801    0.700    0.864       4    64
#>          omega_total    0.871    0.819    0.908       4    64
#>        ordinal_alpha    0.760    0.640    0.813       4    64
#>  ordinal_omega_total    0.848    0.788    0.878       4    64
#>                                                notes
#>                                 Pearson correlations
#>                                 1-factor eigen omega
#>                              Polychoric correlations
#>  Polychoric correlations | Ordinal CIs via bootstrap
# }