DataGeneration {IRTest}

Generating an artificial item response dataset

Description

This function generates an artificial item response dataset allowing various options.

Usage

DataGeneration(
  seed = 1,
  N = 2000,
  nitem_D = 0,
  nitem_P = 0,
  nitem_C = 0,
  model_D = "2PL",
  model_P = "GPCM",
  latent_dist = "Normal",
  item_D = NULL,
  item_P = NULL,
  item_C = NULL,
  theta = NULL,
  prob = 0.5,
  d = 1.7,
  sd_ratio = 1,
  m = 0,
  s = 1,
  a_l = 0.8,
  a_u = 2.5,
  b_m = NULL,
  b_sd = NULL,
  c_l = 0,
  c_u = 0.2,
  categ = 5,
  possible_ans = seq(0.1, 0.9, length = 5)
)

Arguments

seed

A numeric value that is used for random sampling. Seed number can guarantee a replicability of the result.

N

A numeric value of the number of examinees.

nitem_D

A numeric value of the number of dichotomous items.

nitem_P

A numeric value of the number of polytomous items.

nitem_C

A numeric value of the number of continuous response items.

model_D

A vector or a character string that represents the probability model for the dichotomous items.

model_P

A character string that represents the probability model for the polytomous items.

latent_dist

A character string that determines the type of latent distribution. Currently available options are "beta" (four-parameter beta distribution; rBeta.4P), "chi" (\chi^2 distribution; rchisq), "normal", "Normal", or "N" (standard normal distribution; rnorm), and "Mixture" or "2NM" (two-component Gaussian mixture distribution; see Li (2021) for details.)

item_D

An item parameter matrix for using fixed parameter values. The number of columns should be 3: a parameter for the first, b parameter for the second, and c parameter for the third column. Default is NULL.

item_P

An item parameter matrix for using fixed parameter values. The number of columns should be 7: a parameter for the first, and b parameters for the rest of the columns. Default is NULL.

item_C

An item parameter matrix for using fixed parameter values. The number of columns should be 3: a parameter for the first, b parameter for the second, and nu parameter for the third column. Default is NULL.

theta

An ability parameter vector for using fixed parameter values. Default is NULL.

prob

A numeric value for using latent_dist = "2NM". It is the \pi = \frac{n_1}{N} parameter of two-component Gaussian mixture distribution, where n_1 is the estimated number of examinees belonging to the first Gaussian component and N is the total number of examinees (Li, 2021).

d

A numeric value for using latent_dist = "2NM". It is the \delta = \frac{\mu_2 - \mu_1}{\bar{\sigma}} parameter of two-component Gaussian mixture distribution, where \mu_1 and \mu_2 are the estimated means of the first and second Gaussian components, respectively. And \bar{\sigma} is the overall standard deviation of the latent distribution (Li, 2021). Without loss of generality, \mu_2 \ge \mu_1 is assumed, thus \delta \ge 0.

sd_ratio

A numeric value for using latent_dist = "2NM". It is the \zeta = \frac{\sigma_2}{\sigma_1} parameter of two-component Gaussian mixture distribution, where \sigma_1 and \sigma_2 are the estimated standard deviations of the first and second Gaussian components, respectively (Li, 2021).

m

A numeric value of the overall mean of the latent distribution. The default is 0.

s

A numeric value of the overall standard deviation of the latent distribution. The default is 1.

a_l

A numeric value. The lower bound of item discrimination parameters (a).

a_u

A numeric value. The upper bound of item discrimination parameters (a).

b_m

A numeric value. The mean of item difficulty parameters (b). If unspecified, m is passed on to the value.

b_sd

A numeric value. The standard deviation of item difficulty parameters (b). If unspecified, s is passed on to the value.

c_l

A numeric value. The lower bound of item guessing parameters (c).

c_u

A numeric value. The lower bound of item guessing parameters (c).

categ

A scalar or a numeric vector of length nitem_P. The default is 5. If length(categ)>1, the ith element equals the number of categories of the ith polyotomous item.

possible_ans

Possible options for continuous items (e.g., 0.1, 0.3, 0.5, 0.7, 0.9)

Value

This function returns a list of several objects:

theta

A vector of ability parameters (\theta).

item_D

A matrix of dichotomous item parameters.

initialitem_D

A matrix that contains initial item parameter values for dichotomous items.

data_D

A matrix of dichotomous item responses where rows indicate examinees and columns indicate items.

item_P

A matrix of polytomous item parameters.

initialitem_P

A matrix that contains initial item parameter values for polytomous items.

data_P

A matrix of polytomous item responses where rows indicate examinees and columns indicate items.

item_D

A matrix of continuous response item parameters.

initialitem_D

A matrix that contains initial item parameter values for continuous response items.

data_D

A matrix of continuous response item responses where rows indicate examinees and columns indicate items.

Author(s)

Seewoo Li [e-mail]

References

Li, S. (2021). Using a two-component normal mixture distribution as a latent distribution in estimating parameters of item response models. Journal of Educational Evaluation, 34(4), 759-789.

Examples

# Dichotomous item responses

Alldata <- DataGeneration(N = 500,
                          nitem_D = 10)


# Polytomous item responses

Alldata <- DataGeneration(N = 1000,
                          nitem_P = 10)


# Mixed-format items

Alldata <- DataGeneration(N = 1000,
                          nitem_D = 20,
                          nitem_P = 10)

# Continuous items

AllData <- DataGeneration(N = 1000,
                          nitem_C = 10)

# Dataset from non-normal latent density using two-component Gaussian mixture distribution

Alldata <- DataGeneration(N=1000,
                          nitem_P = 10,
                          latent_dist = "2NM",
                          d = 1.664,
                          sd_ratio = 2,
                          prob = 0.3)