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Simulate data from an (inflated) ordered probit or logit process

Source: R/simulate.R
riop.Rd

Draws a data frame from the data-generating process of oprobit(), ologit(), iop(), or iol(): an ordered latent equation \(y^* = x'\beta + \epsilon\) cut at tau, and, when inflate is given, a split equation \(s^* = z'\gamma + u\) that sends units with \(s^* \le 0\) to the inflated category. Errors are standard normal (link = "probit") or standard logistic ("logit"); with rho != 0 (probit only) \((u, \epsilon)\) are bivariate normal with that correlation.

Usage

riop(
  n,
  beta,
  tau,
  gamma = NULL,
  inflate = NULL,
  rho = 0,
  link = c("probit", "logit"),
  X = NULL,
  Z = NULL,
  labels = NULL
)

Arguments

n

Number of observations (ignored when X is supplied).

beta

Outcome coefficients (length p).

tau

Cutpoints, strictly increasing (length J - 1).

gamma

Inflation coefficients, intercept first (length 1 + q); NULL for an uninflated process. A matrix with 1 + q rows and J - 1 columns gives every non-inflated category its own split equation (one column per non-inflated category, in category order): the generalised (category-specific split) process of Brown, Harris and Spencer (2020) fitted by split = "category".

inflate

The inflated category: "bottom", "middle", "top", or a 0-based category index; NULL for an uninflated process.

rho

Error correlation (probit with inflation only); a vector of length J - 1 (one per split equation) when gamma is a matrix.

"probit" or "logit".

X, Z

Optional covariate matrices (without intercept for X; without intercept for Z, the intercept is added).

labels

Optional category labels (length J); default 0:(J-1).

Value

A data frame with the response y (an ordered factor when labels is given, otherwise an integer 0..J-1), the covariates, and two attributes: "regime" (the latent \(s\) indicator; 1 = ordered regime) and "truth" (the parameter list).

Details

Covariates are drawn as: x1, ..., x<p> standard normal, z1, ..., z<q> standard normal (the inflation equation also gets an intercept, the first element of gamma), unless X / Z matrices are supplied.

See also

iop(), iol(), simulate.iord(); riord() is the low-level response sampler given linear predictors (the d/p/q/r family), whereas riop() draws whole data sets including the covariates.

Other simulation and diagnostics: iord-distribution, residuals.iord(), simulate.iord()

Examples

d <- riop(500, beta = c(1, -0.5), tau = c(-0.5, 0.8), gamma = c(0.3, 1), inflate = "bottom")
table(d$y)
#> 
#>   0   1   2 
#> 323 100  77 
mean(attr(d, "regime") == 0)         # share of inflated-regime units
#> [1] 0.434
## a middle-inflated logit process with labelled categories
d2 <- riop(500, beta = c(0.8, -0.5), tau = c(-0.8, 0.8), gamma = c(0.2, 1),
           inflate = "middle", link = "logit", labels = c("disagree", "neutral", "agree"))
table(d2$y)
#> 
#> disagree  neutral    agree 
#>       97      315       88