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Simulate a transformed linear model

Source: R/helper_funs.R
simulate_tlm.Rd

Generate training data (X, y) and testing data (X_test, y_test) for a transformed linear model. The covariates are correlated Gaussian variables. A user-specified proportion (prop_sig) of the regression coefficients are nonozero (= 1) and the rest are zero. There are multiple options for the transformation, which define the support of the data (see below).

Usage

simulate_tlm(
  n,
  p,
  g_type = "beta",
  n_test = 1000,
  heterosked = FALSE,
  lambda = 1,
  prop_sig = 0.5
)

Arguments

n

number of observations in the training data

p

number of covariates

g_type

type of transformation; must be one of beta, step, or box-cox

n_test

number of observations in the testing data

heterosked

logical; if TRUE, simulate the latent data with heteroskedasticity

lambda

Box-Cox parameter (only applies for g_type = 'box-cox')

prop_sig

proportion of signals (nonzero coefficients)

Value

a list with the following elements:

  • y: the response variable in the training data

  • X: the covariates in the training data

  • y_test: the response variable in the testing data

  • X_test: the covariates in the testing data

  • beta_true: the true regression coefficients

  • g_true: the true transformation, evaluated at y

Details

The transformations vary in complexity and support for the observed data, and include the following options: beta yields marginally Beta(0.1, 0.5) data supported on [0,1]; step generates a locally-linear inverse transformation and produces positive data; and box-cox refers to the signed Box-Cox family indexed by lambda, which generates real-valued data with examples including identity, square-root, and log transformations.

Note

The design matrices X and X_test do not include an intercept and there is no intercept parameter in beta_true. The location/scale of the data are not identified in general transformed regression models, so recovering them is not a goal.

Examples

# Simulate data:
dat = simulate_tlm(n = 100, p = 5, g_type = 'beta')
names(dat) # what is returned
#> [1] "y"         "X"         "y_test"    "X_test"    "beta_true" "g_true"   
hist(dat$y, breaks = 25) # marginal distribution