#
#
######## Partial Least Squares Path Model (PLS PM) data generation.
#

# Number of subjects

n <- 1000

# Loadings (set 0 to 1); here loadings = 0.6 to 0.9.

i11.loading <- .9
i12.loading <- .8

i21.loading <- .7
i22.loading <- .6
i23.loading <- .9

i31.loading <- .8
i32.loading <- .7
i33.loading <- .6
i34.loading <- .9
i35.loading <- .8
i36.loading <- .7

i41.loading <- .6
i42.loading <- .9
i43.loading <- .8
i44.loading <- .7

i51.loading <- .6
i52.loading <- .9
i53.loading <- .8
i54.loading <- .7
i55.loading <- .6

# Simulate the common attribute value (latent traits or common factors).

f1 <- rnorm(n)
f2 <- rnorm(n)
f3 <- .8*f1 + .6*f2
f4 <- .8*f2 + .6*f3
f5 <- .8*f3 + .6*f4

# Create Data Array (n = 1000 subjects by 20 items).

v1 <- i11.loading*f1 + rnorm(n, 0, sqrt(1 - i11.loading^2))
v2 <- i12.loading*f1 + rnorm(n, 0, sqrt(1 - i12.loading^2))

v3 <- i21.loading*f2 + rnorm(n, 0, sqrt(1 - i21.loading^2))
v4 <- i22.loading*f2 + rnorm(n, 0, sqrt(1 - i22.loading^2))
v5 <- i23.loading*f2 + rnorm(n, 0, sqrt(1 - i23.loading^2))

v6 <- i31.loading*f3 + rnorm(n, 0, sqrt(1 - i31.loading^2))
v7 <- i32.loading*f3 + rnorm(n, 0, sqrt(1 - i32.loading^2))
v8 <- i33.loading*f3 + rnorm(n, 0, sqrt(1 - i33.loading^2))
v9 <- i34.loading*f3 + rnorm(n, 0, sqrt(1 - i34.loading^2))
v10 <- i35.loading*f3 + rnorm(n, 0, sqrt(1 - i35.loading^2))
v11 <- i36.loading*f3 + rnorm(n, 0, sqrt(1 - i36.loading^2))

v12 <- i41.loading*f4 + rnorm(n, 0, sqrt(1 - i41.loading^2))
v13 <- i42.loading*f4 + rnorm(n, 0, sqrt(1 - i42.loading^2))
v14 <- i43.loading*f4 + rnorm(n, 0, sqrt(1 - i43.loading^2))
v15 <- i44.loading*f4 + rnorm(n, 0, sqrt(1 - i44.loading^2))

v16 <- i51.loading*f5 + rnorm(n, 0, sqrt(1 - i51.loading^2))
v17 <- i52.loading*f5 + rnorm(n, 0, sqrt(1 - i52.loading^2))
v18 <- i53.loading*f5 + rnorm(n, 0, sqrt(1 - i53.loading^2))
v19 <- i54.loading*f5 + rnorm(n, 0, sqrt(1 - i54.loading^2))
v20 <- i55.loading*f5 + rnorm(n, 0, sqrt(1 - i55.loading^2))

rm(i11.loading,i12.loading,i21.loading,i22.loading,f1,
   i23.loading,i31.loading,i32.loading,i33.loading,f2,
   i34.loading,i35.loading,i36.loading,i41.loading,f3,
   i42.loading,i43.loading,i44.loading,i51.loading,f4,
   i52.loading,i53.loading,i54.loading,i55.loading,f5)

# Now change the scaling of each item (makes the data more realistic).

# First, standardize each variable or convert each score into z-score form:
# Z.x=(x-mean(x))/sd(x)

v1 <- (v1 - mean(v1))/sd(v1)
v2 <- (v2 - mean(v2))/sd(v2)

v3 <- (v3 - mean(v3))/sd(v3)
v4 <- (v4 - mean(v4))/sd(v4)
v5 <- (v5 - mean(v5))/sd(v5)

v6 <- (v6 - mean(v6))/sd(v6)
v7 <- (v7 - mean(v7))/sd(v7)
v8 <- (v8 - mean(v8))/sd(v8)
v9 <- (v9 - mean(v9))/sd(v9)
v10 <- (v10 - mean(v10))/sd(v10)
v11 <- (v11 - mean(v11))/sd(v11)

v12 <- (v12 - mean(v12))/sd(v12)
v13 <- (v13 - mean(v13))/sd(v13)
v14 <- (v14 - mean(v14))/sd(v14)
v15 <- (v15 - mean(v15))/sd(v15)

v16 <- (v16 - mean(v16))/sd(v16)
v17 <- (v17 - mean(v17))/sd(v17)
v18 <- (v18 - mean(v18))/sd(v18)
v19 <- (v19 - mean(v19))/sd(v19)
v20 <- (v20 - mean(v20))/sd(v20)

# Second; set the scale to whatever you want; typically the scale of each item
# of a factor will be the same (but not always).
# scaled.x <- (x * standard deviation) + mean

v1 <- (v1 * 15) + 100
v2 <- (v2 * 7.5) + 50

v3 <- (v3 * 3.75) + 25
v4 <- (v4 * 11.25) + 75
v5 <- (v5 * 9) + 60

v6 <- (v6 * 6) + 40
v7 <- (v7 * 5.25) + 35
v8 <- (v8 * 8.25) + 55
v9 <- (v9 * 3) + 20
v10 <- (v10 * 3) + 20
v11 <- (v11 * 6.75) + 45

v12 <- (v12 * 12) + 80
v13 <- (v13 * 7.5) + 50
v14 <- (v14 * 3) + 20
v15 <- (v15 * 3) + 20

v16 <- (v16 * 6.75) + 45
v17 <- (v17 * 12) + 80
v18 <- (v18 * 7.5) + 50
v19 <- (v19 * 3) + 20
v20 <- (v20 * 6.75) + 45

# Misc. demographic and identification variables.

id <- seq(1:n)
sex <- sample(c(1,2), n, replace = TRUE)
age <- round(rnorm(n, 32, 4))

# Convert variable vectors to data.frame

data.1 <- data.frame(id, sex, age, v1, v2, v3, v4, v5, v6, v7, v8, v9,
   v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20)

ls()
rm(id, sex, age, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10,
   v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, n)
ls()

# If desired, write the data out to a working directory (note the data used
# in the PLS tutorial is available on the web and accessed in the tutorial
# script).

write.table(data.1,
  "C:/Users/jds0282/Desktop/Workstuff/Jon_R/Example Data/PLSdata001.txt",
  sep=",", col.names=TRUE, row.names=FALSE, quote=TRUE, na="NA")