simFCGDINA: Forced-choice data simulation based on the G-DINA model
In cdmTools: Useful Tools for Cognitive Diagnosis Modeling

simFCGDINA

R Documentation

Forced-choice data simulation based on the G-DINA model

Description

Simulate forced-choice (FC) responses based on the G-DINA model (de la Torre, 2011) and the FC-DCM (Huang, 2023). This function accommodates FC responses to the simGDINA function from the GDINA package (Ma & de la Torre, 2020).

Usage

simFCGDINA(
  N,
  Q.items,
  n.blocks = NULL,
  polarity = NULL,
  att = NULL,
  model = "GDINA",
  GDINA.args = list(GS = NULL, GS.items = c(1/3, 1/3), AC = 0, AT = 0),
  FCDCM.args = list(d0 = c(0.2, 0.2), sd = c(0.15, 0.15), a = c(0, 0), b = 0),
  seed = NULL
)

Arguments

`N`	A `numeric` value indicating the sample size.
`Q.items`	A binary `matrix` of dimensions `J` statements x `K` attributes indicating what statements measure what attributes.
`n.blocks`	A `numeric` value indicating the number of forced-choice blocks.
`polarity`	A `matrix` of dimensions `n.blocks` x 2 indicating whether each statament in each block is direct (1) or inverse (-1). Default is a matrix full of 1 (i.e., all statements are direct).
`att`	A `matrix` of dimensions `N` individuals x `K` attributes indicating the attribute profile of each individual. Default is `NULL`, meaning that attribute profiles will be simulated based on the specifications listed on `GDINA.args` or `FCDCM.args`.
`model`	Use the G-DINA model (`"GDINA"`) or the FC-DCM (`"FCDCM"`) as the generating model. Default is `"GDINA"`.
`GDINA.args`	A `list` of arguments used if `model = "GDINA"`. `GS` A `J` statements x 2 matrix indicating the guessing and slip parameter of each statement. Default is `NULL`. `GS.items` Only used if `GDINA.args$GS = NULL`. A `vector` of length 2 indicating the minimum and maximum value for the random generation of guessing and slip parameters for each statement. Default is `c(1/3, 1/3).` `AC` A `numeric` value indicating the attribute correlations in line with the multivariate normal threshold model (Chiu et al., 2009). Default is 0. `AT` A `numeric` value indicating the attribute thresholds in line with the multivariate normal threshold model (Chiu et al., 2009). Default is 0.
`FCDCM.args`	A `list` of arguments used if `model = "FCDCM"`. `d0` A `vector` of length 2 indicating the minimum and maximum value for the baseline probability for each FC block (see Huang, 2023). Default is `c(0.2, 0.2).` `sd` A `vector` of length 2 indicating the minimum and maximum value for the statement utility parameters (see Huang, 2023). Default is `c(0.15, 0.15).` `a` A `numeric` value indicating the minimum and maximum discrimination parameter for the higher-order model. Default is `c(0, 0).` `b` A `numeric` value indicating the location parameter for the higher-order model. Default is 0.
`seed`	Random number generation seed. Default is `NULL`.

Value

simFCGDINA returns an object of class simFCGDINA.

dat: Generated FC responses (matrix).
att: Generated attribute profiles (matrix).
Q: Generated Q-matrix of FC blocks (matrix).
LCprob: Generated block response probabilities for each latent class (matrix).
item.pairs: Statements used in each FC block (matrix).
q_att: Attribute measured by each statement as used by Huang (2023) (matrix).
q_sta: Relative position of each statement as used by Huang (2023) (matrix).
simGDINA: Object of class simGDINA (list).
polarity: Polarity matrix indicating the direction of each statement in each block (matrix).
GS: Generated guessing and slip parameter for each statement (matrix).

Author(s)

Pablo Nájera, Universidad Pontificia Comillas

References

Huang, H.-Y. (2023). Diagnostic Classification Model for Forced-Choice Items and Noncognitive Tests. Educational and Psychological Measurement, 83(1), 146-180. https://doi.org/10.1177/00131644211069906

Ma, W., & de la Torre, J. (2020). GDINA: An R package for cognitive diagnosis modeling. Journal of Statistical Software, 93(14). https://doi.org/10.18637/jss.v093.i14

Examples


library(GDINA)
set.seed(123)
# Q-matrix for the unidimensional statements
Q.items <- do.call("rbind", replicate(5, diag(5), simplify = FALSE))
# Guessing and slip
GS <- cbind(runif(n = nrow(Q.items), min = 0.1, max = 0.3),
            runif(n = nrow(Q.items), min = 0.1, max = 0.3))
n.blocks <- 30 # Number of forced-choice blocks
# Block polarity (1 = direct statement; -1 = indirect statement)
polarity <- matrix(1, nrow = n.blocks, ncol = 2)
sim <- simFCGDINA(N = 1000, Q.items, n.blocks = n.blocks, polarity = polarity,
                  model = "GDINA", GDINA.args = list(GS = GS), seed = 123)

cdmTools documentation built on June 8, 2025, 12:34 p.m.