LikertMakeR (version 1.0.0)

makeItems: Synthesise rating-scale data with given first and second moments and a predefined correlation matrix

Description

makeItems() generates a dataframe of random discrete values so the data replicate a rating scale, and are correlated close to a predefined correlation matrix.

makeItems() is wrapper function for:

• lfast(), generates a dataframe that best fits the desired moments, and

• lcor(), which rearranges values in each column of the dataframe so they closely match the desired correlation matrix.

Usage

makeItems(n, means, sds, lowerbound, upperbound, cormatrix)

Value

a dataframe of rating-scale values

Arguments

n

(positive, int) sample-size - number of observations

means

(real) target means: a vector of length k of mean values for each scale item

sds

(positive, real) target standard deviations: a vector of length k of standard deviation values for each scale item

lowerbound

(positive, int) a vector of length k (same as rows & columns of correlation matrix) of values for lower bound of each scale item (e.g. '1' for a 1-5 rating scale)

upperbound

(positive, int) a vector of length k (same as rows & columns of correlation matrix) of values for upper bound of each scale item (e.g. '5' for a 1-5 rating scale)

cormatrix

(real, matrix) the target correlation matrix: a square symmetric positive-semi-definite matrix of values ranging between -1 and +1, and '1' in the diagonal.

Examples

## define parameters

n <- 16
dfMeans <- c(2.5, 3.0, 3.0, 3.5)
dfSds <- c(1.0, 1.0, 1.5, 0.75)
lowerbound <- rep(1, 4)
upperbound <- rep(5, 4)

corMat <- matrix(
  c(
    1.00, 0.30, 0.40, 0.60,
    0.30, 1.00, 0.50, 0.70,
    0.40, 0.50, 1.00, 0.80,
    0.60, 0.70, 0.80, 1.00
  ),
  nrow = 4, ncol = 4
)

item_names <- c("Q1", "Q2", "Q3", "Q4")
rownames(corMat) <- item_names
colnames(corMat) <- item_names

## apply function

df <- makeItems(
  n = n, means = dfMeans, sds = dfSds,
  lowerbound = lowerbound, upperbound = upperbound, cormatrix = corMat
)

## test function

str(df)

# means
apply(df, 2, mean) |> round(3)

# standard deviations
apply(df, 2, sd) |> round(3)

# correlations
cor(df) |> round(3)