simdata_grm: Simulate Observed Binary and Ordinal Variables Using...

In Boklauth/AUTTT: A Unified Treatment in Test Theory

Simulate Observed Binary and Ordinal Variables Using Unidimenstional and Multidimensional Graded Response Models

Description

This function simulates observed binary and ordinal variables in unidimensional and multidimensional IRT models using the graded response model (GRM) by Samejima (1969).

Usage

simdata_grm(
  model,
  theta_matrix,
  a,
  d,
  N = NULL,
  R,
  method,
  file_dir,
  file_prefix,
  seed_num
)

Arguments

model	A model as a list object (see examples).
theta_matrix	An n x m matrix of latent variables (theta), where n is the number of sample size, and m is the total number of dimensions.
a	An p x 1 vector of item discrimination parameters, where p is the total number of the observed variables. This vector must be arranged in the order of appearance in the model.
d	An p x Cj-1 matrix of the IRT intercept parameters, where Cj is the total number of category responses. A category response is represented by k, where k = 1,2,...,Cj.
N	A numeric value for the sample size
R	A numberic value for the total number of replications.
method	A name for method: "U" and "N". "U" uses a lower-tail cumulative probability , which is randomly drawn from U(0,1), a uniform distribution from 0 and 1. "N" uses a lower-tail cumulative probability from the standard normal distribution.
file_dir	A directory for storing the data sets.
file_prefix	A file prefix in characters or/and numbers but special characters.

Value

It generates data sets with the model specifications given. It also provides response probabilities for each data set and average response probabilities across the items and replications.

References

\insertRef

Samejima1969AUTTT

\insertRef

Luecht2018AUTTT

\insertRef

DeMars2012AUTTT

Examples

library(AUTTT)
# n. of dimensions = 3
mean_vec <- c(-0.1, 0, 0.1) # mean vector for each dimension
sd_vec <- c(0.95, 0.98, 1.1) # sd vector for each dimension
f_cor <- c(0.3, 0.5, 0.6) # interfactor correlation vector
# convert the cor. vector to cor.matrix
# 2-multivariate normal theta with three dimensions

theta1 <- create_theta_mvn(size = 300,
                           mean_vec = c(-0.1, 0, 0.1),
                           sd_vec = c(0.95, 0.98, 1.1),
                           ifcor_vec = c(0.3, 0.5, 0.6),
                           seed_num = 456789)

theta1$scaled.X



# CFA-OV parameters
set.seed(1234)
lambda <- runif(12, 0.8, 0.93) # loadings for 12 items
cat_prob2 <- c(0.04, 0.06, 0.11, 0.37, 0.42) # m. skewed prob.
temp <- TSK(n=300, res_prop = cat_prob2)
T2 <- temp$thresholds
# Convert to IRT parameters
# A vector of item discrimination
a_vec <- lambda/sqrt(1-lambda^2)
# a vector of item difficulty
nvar <- length(a_vec)
thresholds_m <- matrix(rep(T2, nvar),
                       nrow = nvar,
                       ncol=length(T2),
                       byrow = TRUE)
# item difficulty parameters
b_vec <- thresholds_m/lambda

# intercept parameters
d_vec <- -a_vec*b_vec

setwd("C:/Users/shh6304/Documents/My Documents/test_grm")

test1 <- simdata_grm(model = list(c(1,2,3,4), c(5,6,7,8), c(9,10,11,12)),
                     # theta_matrix = unscaled_3f_mvn300,
                     theta_matrix = theta1$scaled.X,
                     a = a_vec,
                     d = d_vec,
                     N = 300,
                     R = 50,
                     method = "U",
                     file_dir = getwd(),
                     file_prefix = "test1")

# response probabilities
test1$res_prob

# response probabilities across items and replications
test1$avg_res_prob


# One factor model

# 1 dimension of theta
scaled_1f_mvn300 <- theta1$scaled_ds[,1]

simdata_grm(model = list(seq(1,12)),
            theta_matrix = scaled_1f_mvn300,
            a = a_vec,
            d = d_vec,
            N = 300,
            R = 5,
            method = "N",
            file_dir = getwd(),
            file_prefix = "test1")

# Binary responses
# One factor model

cat_prob2 <- c(0.4, 0.6) # m. skewed prob.
temp <- TSK(n=300, res_prop = cat_prob2)
T2 <- temp$thresholds
# Convert to IRT parameters
# A vector of item discrimination
a_vec <- lambda/sqrt(1-lambda^2)
# a vector of item difficulty
nvar <- length(a_vec)
thresholds_m <- matrix(rep(T2, nvar),
                       nrow = nvar,
                       ncol=1,
                       byrow = TRUE)

b_vec <- thresholds_m/lambda
# intercept parameters

d_vec <- -a_vec*b_vec
#dir.create("C:/Users/shh6304/Documents/My Documents/test_grm")
setwd("C:/Users/shh6304/Documents/My Documents/test_grm")

simdata_grm(model = list(seq(1,12)),
            theta_matrix = unscaled_1f_mvn300,
            a = a_vec,
            d = d_vec,
            N = 300,
            R = 5,
            method = "N",
            file_dir = getwd(),
            file_prefix = "test1")

Boklauth/AUTTT documentation built on Dec. 9, 2022, 7:37 a.m.