Generate scale items from a summated scale, with desired Cronbach's Alpha

makeItemsScale() generates a random dataframe of scale items based on a predefined summated scale (such as created by the lfast() function), and a desired Cronbach's Alpha.

Usage

makeItemsScale(
  scale,
  lowerbound,
  upperbound,
  items,
  alpha = 0.8,
  summated = TRUE,
  progress = TRUE
)

Arguments

scale

(int) a vector or dataframe of the summated rating scale. Should range from \(lowerbound \times items\) to \(upperbound \times items\)

lowerbound

(int) lower bound of the scale item (example: '1' in a '1' to '5' rating)

upperbound

(int) upper bound of the scale item (example: '5' in a '1' to '5' rating)

items

(positive, int) k, or number of columns to generate

alpha

(posiitve, real) desired Cronbach's Alpha for the new dataframe of items. Default = '0.8'.

summated

logical. If TRUE (default), scale is assumed to be a summated scale. If FALSE, the input is treated as a mean scale and will be multiplied by items internally.

progress

logical. If TRUE (default is interactive()), a progress bar is displayed during optimisation. Set to FALSE for slightly faster execution.

Value

a dataframe with 'items' columns and 'length(scale)' rows

Details

simulated annealing

Simulated annealing is used in makeItemsScale() to search for item configurations that satisfy several competing objectives simultaneously. These include achieving a target Cronbach’s alpha, maintaining similar item means, and preserving constant row sums. Because improving one objective can worsen another, a simple greedy search often becomes trapped in suboptimal solutions.

Simulated annealing addresses this by allowing occasional acceptance of worse solutions early in the search, promoting exploration of the solution space. As the algorithm progresses, a cooling schedule reduces this randomness, increasingly favouring improvements across all criteria. This process enables the function to converge on a balanced solution that jointly satisfies the desired scale properties, rather than optimizing any single objective at the expense of others.

Examples

summatedScale <- c(16, 11, 14, 7, 10, 13, 16, 13, 12, 14, 8, 11, 8, 18, 8, 13)

newItems <- makeItemsScale(
  scale = summatedScale,
  lowerbound = 1,
  upperbound = 5,
  items = 4,
  alpha = 0.8
)
#> generate 16 rows
#> rearrange 4 values within each of 16 rows
#> 
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#> reached maximum of 512 iterations
#> Complete!
#> desired Cronbach's alpha = 0.8 (achieved alpha = 0.7961)