# Synthesise rating-scale data with given first and second moments and a predefined correlation matrix `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. ```r makeItems(n, means, sds, lowerbound, upperbound, cormatrix) ``` ## 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. ## Returns a dataframe of rating-scale values ## Examples ```r ## 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) ```

makeItems function