Dataframe of correlated scales from different dataframes of scale items
Source:R/correlateScales.R
correlateScales.RdcorrelateScales() creates a dataframe of
scale items representing correlated constructs,
as one might find in a completed questionnaire.
Value
Returns a dataframe whose columns are taken from the starter dataframes and whose summated values are correlated according to a user-specified correlation matrix
Details
Correlated rating-scale items generally are summed or
averaged to create a measure of an "unobservable", or "latent", construct.
correlateScales() takes several such dataframes of rating-scale
items and rearranges their rows so that the scales are correlated according
to a predefined correlation matrix. Univariate statistics for each dataframe
of rating-scale items do not change,
but their correlations with rating-scale items in other dataframes do.
Examples
## three attitudes and a behavioural intention
n <- 32
lower <- 1
upper <- 5
### attitude #1
cor_1 <- makeCorrAlpha(items = 4, alpha = 0.90)
#> reached max iterations (1600) - best mean difference: 2.2e-05
means_1 <- c(2.5, 2.5, 3.0, 3.5)
sds_1 <- c(0.9, 1.0, 0.9, 1.0)
Att_1 <- makeScales(
n = n, means = means_1, sds = sds_1,
lowerbound = rep(lower, 4), upperbound = rep(upper, 4),
items = 4,
cormatrix = cor_1
)
#> Variable 1 : item01 -
#> reached maximum of 1024 iterations
#> Variable 2 : item02 -
#> best solution in 667 iterations
#> Variable 3 : item03 -
#> reached maximum of 1024 iterations
#> Variable 4 : item04 -
#> reached maximum of 1024 iterations
#>
#> Arranging data to match correlations
#>
#> Successfully generated correlated variables
#>
### attitude #2
cor_2 <- makeCorrAlpha(items = 5, alpha = 0.85)
#> reached max iterations (2500) - best mean difference: 8.1e-05
#> Correlation matrix is not yet positive definite
#> Working on it
#>
#> improved at swap - 1 (min eigenvalue: -0.017242)
#> improved at swap - 3 (min eigenvalue: -0.008469)
#> improved at swap - 4 (min eigenvalue: 0.025501)
#> positive definite at swap - 4
means_2 <- c(2.5, 2.5, 3.0, 3.0, 3.5)
sds_2 <- c(1.0, 1.0, 0.9, 1.0, 1.5)
Att_2 <- makeScales(
n = n, means = means_2, sds = sds_2,
lowerbound = rep(lower, 5), upperbound = rep(upper, 5),
items = 5,
cormatrix = cor_2
)
#> Variable 1 : item01 -
#> reached maximum of 1024 iterations
#> Variable 2 : item02 -
#> reached maximum of 1024 iterations
#> Variable 3 : item03 -
#> best solution in 808 iterations
#> Variable 4 : item04 -
#> reached maximum of 1024 iterations
#> Variable 5 : item05 -
#> reached maximum of 1024 iterations
#>
#> Arranging data to match correlations
#>
#> Successfully generated correlated variables
#>
### attitude #3
cor_3 <- makeCorrAlpha(items = 6, alpha = 0.75)
#> correlation values consistent with desired alpha in 72 iterations
means_3 <- c(2.5, 2.5, 3.0, 3.0, 3.5, 3.5)
sds_3 <- c(1.0, 1.5, 1.0, 1.5, 1.0, 1.5)
Att_3 <- makeScales(
n = n, means = means_3, sds = sds_3,
lowerbound = rep(lower, 6), upperbound = rep(upper, 6),
items = 6,
cormatrix = cor_3
)
#> Variable 1 : item01 -
#> reached maximum of 1024 iterations
#> Variable 2 : item02 -
#> reached maximum of 1024 iterations
#> Variable 3 : item03 -
#> reached maximum of 1024 iterations
#> Variable 4 : item04 -
#> reached maximum of 1024 iterations
#> Variable 5 : item05 -
#> reached maximum of 1024 iterations
#> Variable 6 : item06 -
#> reached maximum of 1024 iterations
#>
#> Arranging data to match correlations
#>
#> Successfully generated correlated variables
#>
### behavioural intention
intent <- lfast(n, mean = 3.0, sd = 3, lowerbound = 0, upperbound = 10) |>
data.frame()
#> reached maximum of 1024 iterations
names(intent) <- "int"
### target scale correlation matrix
scale_cors <- matrix(
c(
1.0, 0.6, 0.5, 0.3,
0.6, 1.0, 0.4, 0.2,
0.5, 0.4, 1.0, 0.1,
0.3, 0.2, 0.1, 1.0
),
nrow = 4
)
data_frames <- list("A1" = Att_1, "A2" = Att_2, "A3" = Att_3, "Int" = intent)
### apply the function
my_correlated_scales <- correlateScales(
dataframes = data_frames,
scalecors = scale_cors
)
#> scalecors is positive-definite
#>
#> New dataframe successfully created
head(my_correlated_scales)
#> A1_1 A1_2 A1_3 A1_4 A2_1 A2_2 A2_3 A2_4 A2_5 A3_1 A3_2 A3_3
#> 1 2.25 1.50 1.75 2.00 1.0 1.6 1.2 1.8 1.0 1.166667 1.000000 1.666667
#> 2 4.25 4.00 4.50 4.75 4.4 3.2 3.8 4.4 5.0 2.833333 2.666667 4.500000
#> 3 1.75 3.00 3.00 4.25 2.4 1.8 2.0 2.8 2.6 3.500000 1.166667 3.833333
#> 4 1.75 2.00 3.00 3.25 2.2 2.6 2.8 1.6 3.2 2.666667 4.166667 3.166667
#> 5 1.25 1.75 2.00 2.00 1.4 1.2 1.6 2.6 1.8 2.333333 3.000000 2.166667
#> 6 1.25 2.25 2.75 4.25 2.0 2.4 2.2 2.6 4.4 3.000000 4.666667 3.166667
#> A3_4 A3_5 A3_6 Int_1
#> 1 1.000000 2.333333 1.333333 1
#> 2 5.000000 3.666667 5.000000 4
#> 3 4.666667 1.833333 5.000000 8
#> 4 5.000000 5.000000 3.666667 2
#> 5 3.000000 2.500000 1.000000 2
#> 6 2.166667 3.833333 3.166667 9