id_sim_gen: Simulate IRT ideal point data

In idealstan: Robust Measurement with 'Stan'

Simulate IRT ideal point data

Description

A function designed to simulate IRT ideal point data.

Usage

id_sim_gen(
  num_person = 20,
  num_items = 50,
  cov_effect = NULL,
  person_cov = NULL,
  person_cov_effect = NULL,
  item_cov = NULL,
  item_discrim_cov_effect = NULL,
  item_miss_cov = NULL,
  item_miss_discrim_cov_effect = NULL,
  model_type = "binary",
  latent_space = FALSE,
  absence_discrim_sd = 3,
  absence_diff_mean = 0,
  discrim_reg_upb = 1,
  discrim_reg_lb = -1,
  discrim_miss_upb = 1,
  discrim_miss_lb = -1,
  discrim_reg_scale = 2,
  discrim_reg_shape = 2,
  discrim_miss_scale = 2,
  discrim_miss_shape = 2,
  diff_sd = 3,
  time_points = 1,
  time_process = "random",
  time_sd = 0.1,
  ideal_pts_sd = 3,
  prior_type = "gaussian",
  ordinal_outcomes = 3,
  inflate = FALSE,
  sigma_sd = 1,
  spline_knots = NULL,
  spline_degree = 2,
  spline_intercept_sd = 0.5,
  spline_basis_sd = 0.5,
  phi = 1,
  gp_rho = 0.5,
  gp_alpha = 0.5,
  gp_nugget = 0.1
)

Arguments

num_person	The number of persons/persons
num_items	The number of items (bills in the canonical ideal point model)
cov_effect	The effect of a hierarchical/external covariate on the person ideal points. The covariate will be a uniformly-distributed random variable on the [0,1] scale, so covariate effects in the [-2,2] approximate range would result in noticeable effects on the ideal point scale. This is a legacy parameter; prefer using person_cov and person_cov_effect for more control.
person_cov	Either NULL (no covariate), "continuous" to generate a uniform random covariate, "binary" to generate a binary (0/1) covariate, or a numeric matrix with num_person rows where each column is a covariate. If cov_effect is provided and person_cov is NULL, defaults to "continuous" for backward compatibility.
person_cov_effect	A numeric vector of regression coefficients for person covariates. Length must match the number of columns in person_cov matrix. If person_cov is "continuous" or "binary", a single value should be provided.
item_cov	Either NULL (no covariate), "continuous" to generate a uniform random covariate, "binary" to generate a binary (0/1) covariate, or a numeric matrix with num_items rows where each column is a covariate.
item_discrim_cov_effect	A numeric vector of regression coefficients for the effect of item covariates on item discrimination parameters (gamma). Length must match the number of columns in item_cov matrix.
item_miss_cov	Either NULL (no covariate), "continuous" to generate a uniform random covariate, "binary" to generate a binary (0/1) covariate, or a numeric matrix with num_items rows where each column is a covariate. Used for missingness model parameters.
item_miss_discrim_cov_effect	A numeric vector of regression coefficients for the effect of item missing covariates on absence discrimination parameters (nu). Length must match the number of columns in item_miss_cov matrix.
model_type	One of 'binary', 'ordinal_rating', 'ordinal_grm', 'poisson' 'normal', or 'lognormal'
latent_space	Whether to use the latent space formulation of the ideal point model FALSE by default. NOTE: currently, the package only has estimation for a binary response with the latent space formulation.
absence_discrim_sd	The SD of the discrimination parameters for the inflated model
absence_diff_mean	The mean intercept for the inflated model; increasing it will lower the total number of missing data
discrim_reg_upb	The upper bound of the generalized Beta distribution for the observed discrimination parameters (gamma)
discrim_reg_lb	The lower bound of the generalized Beta distribution for the observed discrimination parameters (gamma)
discrim_miss_upb	The upper bound of the generalized Beta distribution for the missingness discrimination parameters (nu)
discrim_miss_lb	The lower bound of the generalized Beta distribution for the missingness discrimination parameters (nu)
discrim_reg_scale	The scale parameter for the generalized Beta distribution for the observed discrimination parameters (gamma)
discrim_reg_shape	The shape parameter for the generalized Beta distribution for the observed discrimination parameters (gamma)
discrim_miss_scale	The scale parameter for the generalized Beta distribution for the missingness discrimination parameters (nu)
discrim_miss_shape	The shape parameter for the generalized Beta distribution for the missingness discrimination parameters (nu)
diff_sd	The SD of the difficulty parameters (bill/item intercepts) for both missing and observed parameters (beta and omega)
time_points	The number of time points for time-varying legislator/person parameters
time_process	The process used to generate the ideal points: either 'random' for a random walk, 'AR' for an AR1 process, 'GP' for a Gaussian process, or 'splines' for a spline (see parameters spline_knots and spline_degree).
time_sd	The standard deviation of the change in ideal points over time (should be low relative to ideal_pts_sd)
ideal_pts_sd	The SD for the person/person ideal points
prior_type	The statistical distribution that generates the data for ideal point parameters (alpha) and difficulty intercepts (beta and omega). Currently only 'gaussian' is supported.
ordinal_outcomes	If model is 'ordinal', an integer giving the total number of categories
inflate	If TRUE, an missing-data-inflated dataset is produced.
sigma_sd	If a normal or log-normal distribution is being fitted, this parameter gives the standard
spline_knots	Number of knots (essentially, number of points at which to calculate time-varying ideal points given T time points). Default is NULL, which means that the spline is equivalent to polynomial time trend of degree spline_degree. Note that the spline number (if not null) must be equal or less than the number of time points.
spline_degree	The degree of the spline polynomial. The default is 2 which is a quadratic polynomial. A value of 1 will result in independent knots (essentially pooled across time points T). A higher value will result in wigglier time series.
spline_intercept_sd	The SD of the Normal distribution (centered on 0) used to draw the intercept for the basis spline function
spline_basis_sd	The SD of the Normal distribution (centered on 0) for the coefficients used to create the simulated ideal points from the spline function
phi	The phi (dispersion) parameter for the ordered beta distribution deviation of the outcome (i.e. the square root of the variance).
gp_rho	The rho parameter to the squared exponential kernel function for the GP model
gp_alpha	The alpha parameter to the squared exponential kernel function for the GP model
gp_nugget	The nugget of the squared-exponential kernel (equals additional variance of the GP-distributed ideal points)

Details

This function produces simulated data that matches (as closely as possible) the models used in the underlying Stan code. Currently the simulation can produce inflated and non-inflated models with binary, ordinal (GRM and rating-scale), Poisson, Normal and Log-Normal responses.

Value

The results is a idealdata object that can be used in the id_estimate function to run a model. It can also be used in the simulation plotting functions.

See Also

id_show_trues() for plotting fitted models versus true values.

Examples

# Simulate binary (non-inflated) data for 20 persons and 50 items
sim <- id_sim_gen(num_person=20, num_items=50, inflate=FALSE)
head(sim@score_matrix)

# Simulate an ordinal graded-response model with missing-data inflation
sim_ord <- id_sim_gen(model='ordinal_grm', inflate=TRUE, num_person=10, num_items=20)

idealstan documentation built on May 13, 2026, 1:08 a.m.