sim.data: generate response

In Qval: The Q-Matrix Validation Methods Framework

generate response

Description

randomly generate response matrix according to certain conditions, including attributes distribution, item quality, sample size, Q-matrix and cognitive diagnosis models (CDMs).

Usage

sim.data(
  Q = NULL,
  N = NULL,
  IQ = list(P0 = NULL, P1 = NULL),
  model = "GDINA",
  distribute = "uniform",
  control = NULL,
  verbose = TRUE
)

Arguments

Q	The Q-matrix. A random 30 × 5 Q-matrix (sim.Q) will be used if Q = NULL.
N	Sample size. Default = 500.
IQ	A list containing two I-length vectors: P0 and P1. P0 represents the probability of examinees who have not mastered any attributes ([00...0]) correctly answering the item, while P1 represents the probability of examinees who have mastered all attributes ([11...1]) correctly answering the item.
model	Type of model to be fitted; can be "GDINA", "LCDM", "DINA", "DINO", "ACDM", "LLM", or "rRUM".
distribute	Attribute distributions; can be "uniform" for the uniform distribution, "mvnorm" for the multivariate normal distribution (Chiu, Douglas, & Li, 2009) and "horder" for the higher-order distribution (Tu et al., 2022).
control	A list of control parameters with elements: sigma A positive-definite symmetric matrix specifying the variance-covariance matrix when distribute = "mvnorm". Default = 0.5 (Chiu, Douglas, & Li, 2009). cutoffs A vector giving the cutoff for each attribute when distribute = "mvnorm". Default = k/(1+K) (Chiu, Douglas, & Li, 2009). theta A vector of length N representing the higher-order ability for each examinee. By default, generate randomly from the standard normal distribution (Tu et al, 2022). a The slopes for the higher-order model when distribute = "horder". Default = 1.5 (Tu et al, 2022). b The intercepts when distribute = "horder". By default, select equally spaced values between -1.5 and 1.5 according to the number of attributes (Tu et al, 2022).
verbose	Logical indicating to print information or not. Default is TRUE

Value

Object of class sim.data. An sim.data object initially gained by simGDINA function form GDINA package. Elements that can be extracted using method extract include:

dat

An N × I simulated item response matrix.

Q

The Q-matrix.

attribute

An N × K matrix for inviduals' attribute patterns.

catprob.parm

A list of non-zero success probabilities for each attribute mastery pattern.

delta.parm

A list of delta parameters.

higher.order.parm

Higher-order parameters.

mvnorm.parm

Multivariate normal distribution parameters.

LCprob.parm

A matrix of success probabilities for each attribute mastery pattern.

Author(s)

Haijiang Qin <[e-mail]>

References

Chiu, C.-Y., Douglas, J. A., & Li, X. (2009). Cluster Analysis for Cognitive Diagnosis: Theory and Applications. Psychometrika, 74(4), 633-665. DOI: 10.1007/s11336-009-9125-0.

Tu, D., Chiu, J., Ma, W., Wang, D., Cai, Y., & Ouyang, X. (2022). A multiple logistic regression-based (MLR-B) Q-matrix validation method for cognitive diagnosis models:A confirmatory approach. Behavior Research Methods. DOI: 10.3758/s13428-022-01880-x.

Examples

################################################################
#                           Example 1                          #
#          generate data follow the uniform distrbution        #
################################################################
library(Qval)

set.seed(123)

K <- 5
I <- 10
Q <- sim.Q(K, I)

IQ <- list(
  P0 = runif(I, 0.0, 0.2),
  P1 = runif(I, 0.8, 1.0)
)

data <- sim.data(Q = Q, N = 10, IQ=IQ, model = "GDINA", distribute = "uniform")

print(data$dat)

################################################################
#                           Example 2                          #
#          generate data follow the mvnorm distrbution         #
################################################################
set.seed(123)
K <- 5
I <- 10
Q <- sim.Q(K, I)

IQ <- list(
  P0 = runif(I, 0.0, 0.2),
  P1 = runif(I, 0.8, 1.0)
)

example_cutoffs <- sample(qnorm(c(1:K)/(K+1)), ncol(Q))
data <- sim.data(Q = Q, N = 10, IQ=IQ, model = "GDINA", distribute = "mvnorm",
                 control = list(sigma = 0.5, cutoffs = example_cutoffs))

print(data$dat)

#################################################################
#                            Example 3                          #
#           generate data follow the horder distrbution         #
#################################################################
set.seed(123)
K <- 5
I <- 10
Q <- sim.Q(K, I)

IQ <- list(
  P0 = runif(I, 0.0, 0.2),
  P1 = runif(I, 0.8, 1.0)
)

example_theta <- rnorm(10, 0, 1)
example_b <- seq(-1.5,1.5,length.out=K)
data <- sim.data(Q = Q, N = 10, IQ=IQ, model = "GDINA", distribute = "horder",
                 control = list(theta = example_theta, a = 1.5, b = example_b))

print(data$dat)

Qval documentation built on April 3, 2025, 6:20 p.m.