Simulate a gaussian data set — gen.gaussian.data • glmtlp

Simulate a data set with gaussian response following the linear regression model.

Usage

gen.gaussian.data(
  n,
  p,
  rho = 0,
  kappa = 5,
  beta.type = 1,
  snr = 1,
  seed = 2021
)

Arguments

n: Sample size.
p: Number of covariates.
rho: The parameter defining the AR(1) correlation matrix.
kappa: The number of nonzero coefficients.
beta.type: Numeric indicator for choosing the beta type. For beta.type = 1, the true coefficient vector has kappa components being 1, roughly equally distributed between 1 to p. For beta.type = 2, the first kappa values are 1, and the rest are 0. For beta.type = 3, the first kappa values are equally-spaced values from 10 to 0.5, and the rest are 0. For beta.type = 4, the first kappa values are the first kappa values in c(-10, -6, -2, 2, 6, 10), and the rest are 0. For beta.type = 5, the first kappa values are 1, and the rest decay exponentially to 0 with base 0.5.
snr: Signal-to-noise ratio. Default is 1.
seed: The seed for reproducibility. Default is 2021.

Value

A list containing the simulated data.

X: the covariate matrix, of dimension n x p.
y: the response, of length n.
beta: the true coefficients, of length p.
sigma: the standard error of the noise.

Examples

gau_data <- gen.gaussian.data(n = 200, p = 20, seed = 2021)
head(gau_data$X)
#>              V1         V2         V3         V4         V5          V6
#> [1,] -0.1224600  0.2701953 -0.6745562  0.1492579  0.5534009  0.80959540
#> [2,]  0.5524566 -1.3432502  0.2381266 -0.3123636 -1.1167970  0.09941633
#> [3,]  0.3486495 -0.8488889  0.5450859 -1.2595894  0.5740307 -2.34302131
#> [4,]  0.3596322 -0.4076079 -0.4488515  0.0519813  1.2043346  0.67652598
#> [5,]  0.8980537 -0.6661505  0.9712467  0.2044272  0.7274956 -3.61147374
#> [6,] -1.9225695 -0.1032374 -1.5471639  1.3869823 -0.7023848 -0.16416799
#>               V7         V8         V9        V10        V11        V12
#> [1,] -0.89020680 -1.1028167  1.3645402  0.4982807  0.3147181 -0.6066470
#> [2,]  0.96022096  0.4343786  0.4568313  0.9032203  1.2000068  1.0565220
#> [3,]  1.26888856  1.2058157  2.1983623 -0.4181034 -0.8072166  1.3920142
#> [4,]  0.25411730 -1.0206682 -0.6805850  1.4747203 -0.6763614 -1.3792104
#> [5,]  0.03379941  1.8178839 -0.9349661 -2.0133506  0.7913844 -0.1406768
#> [6,]  0.03272896 -0.4072112  0.9655597  1.6591117  0.6367649 -1.1186803
#>             V13        V14         V15         V16         V17       V18
#> [1,] -2.8645250 -0.4444342  0.08738679  0.07521845 -0.28434897 1.0566142
#> [2,] -0.4067150  0.8172733 -1.23844170 -0.76200580 -0.04859536 1.4287991
#> [3,] -0.9921254 -0.7647219  0.60099751 -0.82983377 -1.20895180 1.2845802
#> [4,]  1.5503138 -0.2771623 -2.68766095 -0.75836338  0.48379191 0.1668427
#> [5,] -0.1953912  1.2854050 -0.91182644 -1.55430328  2.42388384 1.2601177
#> [6,]  3.1064929 -0.9233080 -0.77375020 -1.62213762  1.74302228 0.9810522
#>             V19        V20
#> [1,]  0.7012877 -0.8384305
#> [2,]  0.4267106  2.2454396
#> [3,] -1.8019905 -0.1551519
#> [4,]  0.4479343  1.8887326
#> [5,] -1.3472316  1.7914329
#> [6,]  0.3858948  0.2903452
head(gau_data$y)
#> [1]  4.828933343  3.050029776  1.688536187 -0.001211368 -3.060247660
#> [6] -0.697806550
head(gau_data$beta)
#> [1] 1 0 0 0 0 1
gau_data$sigma
#> [1] 2.236068