- 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; betafunctions::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)