Simulated Numerical Data with Latent Variable

A dataset similar to num_data but with the variable Z treated as a latent variable and thus omitted.

Usage

num_data_latent

Format

A data.frame with 1000 rows and 4 variables.

X1

Structural equation: \(X_1 := \sqrt{Z} + \epsilon_1\) with \(\epsilon_1 \sim \mathrm{Unif}[0, 2]\)

X2

Structural equation: \(X_2 := 2 \cdot X_3 - \epsilon_2\) with \(\epsilon_2 \sim N(5, 1)\)

X3

Structural equation: \(X_3 := \epsilon_3\) with \(\epsilon_3 \sim \mathrm{Unif}[5, 10]\)

Z

Structural equation: \(Z := |\epsilon_4|\) with \(\epsilon_4 \sim N(10, 1)\)

Y

Structural equation: \(Y := X_1^2 + X_2 - X_3 - Z + \epsilon_5\) with \(\epsilon_5 \sim N(10, 1)\)

Details

The R code used to generate this dataset is as follows:

data(num_data)
num_data_latent <- num_data[, c("X1", "X2", "X3", "Y")]

See also

num_data

Examples

data(num_data_latent)
head(num_data_latent)
#>         X1        X2       X3        Y
#> 1 3.900715  7.048325 6.964806 15.35505
#> 2 4.736112  6.236746 5.666022 23.36749
#> 3 4.657992 12.169805 9.127046 25.32495
#> 4 5.176469  6.392344 6.101088 26.75643
#> 5 4.535538 10.305236 7.465185 22.67612
#> 6 4.885914 10.018856 7.413312 28.03132