Simulate Model Matrix and Response Vector

Generates synthetic covariates and response vector from a specified distribution for simulation studies or method validation.

Usage

simulXy(
  n,
  p,
  interc = 0,
  beta,
  family = gaussian(),
  prop = 0.1,
  lim.b = c(-3, 3),
  sigma = 1,
  size = 1,
  rho = 0,
  scale.data = TRUE,
  seed = NULL,
  X = NULL,
  dispersion = 0.1
)

Arguments

n: Integer. Number of observations.
p: Integer. Total number of covariates in the model matrix.
interc: Numeric. Intercept to include in the linear predictor. Default is 0.
beta: Numeric vector of length p. Regression coefficients in the linear predictor.
family: Distribution and link function. Allowed: gaussian(), binomial(), poisson() and , Gamma(). Can be a string, function, or family object.
prop: Numeric in [0,1]. Used only if beta is missing; proportion of non-zero coefficients in p. Default is 0.1.
lim.b: Numeric vector of length 2. Range for coefficients if beta is missing. Default: c(-3, 3).
sigma: Standard deviation of Gaussian response. Default is 1.
size: Integer. Number of trials for binomial response. Default is 1.
rho: Numeric. Correlation coefficient for generating covariates. Used to create AR(1)-type covariance: rho^|i-j|. Default is 0.
scale.data: Logical. Whether to scale columns of the model matrix. Default is TRUE.
seed: Optional. Integer seed for reproducibility.
X: Optional. Custom model matrix. If supplied, it overrides the internally generated X.
dispersion: Dispersion parameter of Gamma response. Default is 0.1.

Value

A list with components:

X: Model matrix of dimension n x p
y: Simulated response vector
beta: True regression coefficients used
eta: Linear predictor

Examples

n <- 100; p <- 100
beta <- c(runif(10, -3, 3), rep(0, p - 10))
sim <- simulXy(n = n, p = p, beta = beta, seed = 1234)
o <- islasso(y ~ ., data = sim$data, family = gaussian())
summary(o, pval = 0.05)
#> 
#> Call:
#> islasso(formula = y ~ ., family = gaussian(), data = sim$data)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -1.9777 -0.5928 -0.0602  0.5340  2.2449 
#> 
#>             Estimate Std. Error      Df z value Pr(>|z|)    
#> (Intercept)  -0.1159     0.1258   1.000  -0.921  0.35708    
#> X1            0.3477     0.1402   0.976   2.480  0.01315 *  
#> X2           -2.3120     0.1492   1.000 -15.497  < 2e-16 ***
#> X3           -0.4404     0.1437   0.995  -3.064  0.00218 ** 
#> X4            1.3065     0.1457   1.000   8.967  < 2e-16 ***
#> X5           -2.0609     0.1443   1.000 -14.280  < 2e-16 ***
#> X6           -0.5635     0.1448   1.000  -3.892 9.96e-05 ***
#> X7            1.2906     0.1399   1.000   9.225  < 2e-16 ***
#> X8            1.8948     0.1490   1.000  12.719  < 2e-16 ***
#> X9           -1.0072     0.1515   1.000  -6.649 2.96e-11 ***
#> X10          -2.1626     0.1500   1.000 -14.418  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Dispersion parameter for gaussian family taken to be 1.583274)
#> 
#>     Null deviance: 2492.536  on 99.00  degrees of freedom
#> Residual deviance:   92.352  on 58.33  degrees of freedom
#> AIC: 175.69
#> Lambda: 11.472
#> 
#> Number of Newton-Raphson iterations: 102
#>