dataGenerationFn: A dataset simulation function
In syhyunpark/csim: Constrained single index models (CSIM)

Description Usage Arguments Value

dataGenerationFn generates an example dataset under a model that contains a main effect component, a treatment-by-covariates interaction effect component, and a random noise component.

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dataGenerationFn(n = 200, p = 50, w = 1, delta = 1,
  true.alpha = NULL, true.eta = NULL, sigma = 0.4,
  correlationX = 0, sigmaX = 1, sim.seed = NULL, obs = FALSE)

`n`	sample size.
`p`	dimension of the pretreatment covariates.
`w`	controls the nonliarity of the treatment-specific link function that defines the interaction effect component. `w=1` linear `w=2` almost linear `w=3` highly nonlinear
`delta`	controls the intensity of the main effect. `delta=1` moderate main effect `delta=2` big main effect
`true.alpha`	a vector of the true single index coefficients (associated with the interaction effect component); if `NULL`, then `true.alpha` is set to be `(1, 0.5, 0.25, 0.125, 0,...0)`' (only the first 4 elements are nonzero).
`true.eta`	a vector of the true main effect coefficients; if `NULL`, then `true.eta` is randomly generated in a way that only the first 10 elements are nonzero.
`sigma`	standard deviation of the random noise term.
`correlationX`	correlation among the pretreatment covariates.
`sigmaX`	standard deviation of the pretreatment covariates.
`sim.seed`	a seed number for random data generation
`obs`	if `TRUE`, use an observational study setting (X and Tr are correlated)

`y`	a n x 1 vector of treatment outcomes.
`Tr`	a n x 1 vector of treatment indicators.
`X`	a n x p matrix of pretreatment covariates.
`SNR`	the "signal" (interaction effects) to "nuisance" (main effects + noise) variance ratio (SNR) of the dataset.
`true.alpha`	the true single index coefficients.
`true.eta`	the true main effect coefficients.
`optTr`	a n x 1 vector of treatments indicating the optimal treatment selections.
`value.opt`	the "Value" of the optimal treatment selection rule, `optTr`.