This function performs a single iteration of the \(\beta\) method for A item's validation. It is designed to be used in parallel computing environments to speed up the validation process of the \(\beta\) method. The function is a utility function for validation, and it should not be called independently by the user.

parallel_iter(
  i,
  Y,
  P.alpha.Xi,
  P.alpha,
  pattern,
  ri,
  Ni,
  Q.pattern.ini,
  model,
  criter,
  search.method,
  P_GDINA,
  Q.beta,
  L,
  K,
  alpha.P,
  get.MLRlasso,
  priority
)

Arguments

i

Item number that need to be validated.

Y

Observed data matrix for validation.

P.alpha.Xi

Individual posterior

P.alpha

Attribute prior weights.

pattern

The attribute mastery pattern matrix.

ri

A vector that contains the numbers of examinees in each knowledge state who correctly answered item \(i\).

Ni

A vector that contains the total numbers of examinees in each knowledge state.

Q.pattern.ini

Initial pattern number for the model.

model

Model object used for fitting (e.g., GDINA).

criter

Fit criterion ("AIC", "BIC", "CAIC", or "SABIC").

search.method

Search method for model selection ("beta", "ESA", "SSA", or "PAA").

P_GDINA

Function to calculate probabilities for GDINA model.

Q.beta

Q-matrix for validation.

L

Number of latent pattern.

K

Number of attributes.

alpha.P

Individuals' marginal mastery probabilities matrix (Tu et al., 2022)

get.MLRlasso

Function for Lasso regression with multiple linear regression.

priority

Vector of priorities for PAA method search.

Value

An object of class validation is a list containing the following components:

fit.index.pre

The previous fit index value after applying the selected search method.

fit.index.cur

The current fit index value after applying the selected search method.

Q.pattern.cur

The pattern that corresponds to the optimal model configuration for the current iteration.

priority

The priority vector used in the PAA method, if applicable.