FCGDINA: G-DINA model for forced-choice blocks
In Pablo-Najera/cdmTools: Useful Tools for Cognitive Diagnosis Modeling

FCGDINA

R Documentation

G-DINA model for forced-choice blocks

Description

Estimation of the G-DINA model for forced-choice responses according to Nájera et al. (2024). Block polarity (i.e., statement direction), initial values for parameters, and prior distributions can be specified to determine the design of the forced-choice blocks. The GDINA package (Ma & de la Torre, 2020) is used to estimate the model via expectation maximumation (EM) algorithm if no priors are used. The code provided by Ma and Jiang (2021) is used to estimate the model via Bayes modal (BM) estimation if priors are used. The forced-choice diagnostic classification model (FC-DCM; Huang, 2023) can be efficiently estimated using Bayes modal estimation rather than Markov chain Monte Carlo. Only unidimensional statements (i.e., bidimensional blocks) are currently supported.

Usage

FCGDINA(
  dat,
  Q,
  polarity = NULL,
  polarity.initial = 1e-04,
  polarity.prior = NULL,
  att.dist = "saturated",
  att.prior = NULL,
  verbose = 1,
  higher.order = list(),
  catprob.parm = NULL,
  control = list()
)

Arguments

`dat`	A N individuals x J items (`matrix` or `data.frame`). Missing values need to be coded as `NA`. Caution is advised if missing data are present.
`Q`	A F blocks x K attributes Q-matrix (`matrix` or `data.frame`). Each q-vector must measure two attributes, reflecting the attributes measured by its statements.
`polarity`	A F blocks x 2 (`matrix` or `data.frame`). Each row reflects the direction of the first and second statement, where 1 and -1 corresponds to direct and inverse statements, respectively. Default is `NULL`, denoting that all statements are direct.
`polarity.initial`	A `numeric` value that indicates the initial value for the estimation of the probability of endorsement for the latent group whose ideal response is equal to 0. The initial value for the latent group whose ideal response is equal to 1 will be 1 - `polarity.initial`. The initial value for latent groups without a clear ideal response is always equal to 0.5. This argument is ignored if `catprob.parm != NULL`. Default is `1e-4`.
`polarity.prior`	A `list` containing three `vectors` of length 2, each containing the alpha and beta hyperparameters of the Beta distribution for the priors of the latent groups with ideal responses equal to 0, 0.5, and 1, respectively. Marginal maximum likelihood via EM algorithm is used, therefore ignoring these priors, if `polarity.prior == NULL`, while BM estimation is used if `polarity.prior != NULL`. See the examples for a case. Default is `NULL`.
`att.dist`	How is the joint attribute distribution estimated? It can be `"saturated"`, `"higher.order"`, `"fixed"`, `"independent"`, and `"loglinear"`. Only considered if EM estimation is used. Default is `"saturated"`. See the `GDINA` package documentation for more information.
`att.prior`	A `vector` of length 2^K to speficy attribute prior distribution for the latent classes. Only considered if EM estimation is used. Default is `NULL`. See the `GDINA` package documentation for more information.
`verbose`	How to print calibration information after each EM iteration? Can be 0, 1 or 2, indicating to print no information, information for current iteration, or information for all iterations.
`higher.order`	A `list` specifying the higher-order joint attribute distribution with the following components. Only considered if EM estimation is used. See the `GDINA` package documentation for more information.
`catprob.parm`	A `list` of initial values for probabilities of endorsement for each nonzero category. Default is `NULL`. See the `GDINA` package documentation for more information.
`control`	A `list` of control parameters. Only considered if EM estimation is used. See the `GDINA` package documentation for more information.

Value

FCGDINA returns an object of class FCGDINA.

GDINA.obj: Estimation output from the GDINA function of the GDINA.MJ (Ma & Jiang, 2021) function, depending on whether EM or BM estimation has been used (list).
technical: Information about the estimation method (EM or BM), initial values, and priors (list).
specifications: Function call specifications (list).

Author(s)

Pablo Nájera, Universidad Pontificia Comillas

References

Huang, H.-Y. (2023). Diagnostic Classification Model for Forced-Choice Items and Noncognitive Tests. Educational and Psychological Measurement, 83(1), 146-180. https://doi.org/10.1177/00131644211069906

Ma, W., & de la Torre, J. (2020). GDINA: An R package for cognitive diagnosis modeling. Journal of Statistical Software, 93(14). https://doi.org/10.18637/jss.v093.i14

Ma, W., & Jiang, Z. (2021). Estimating Cognitive Diagnosis Models in Small Samples: Bayes Modal Estimation and Monotonic Constraints. Applied Psychological Measurement, 45(2), 95-111. https://doi.org/10.1177/0146621620977681

Nájera, P., Kreitchmann, R. S., Escudero, S., Abad, F. J., de la Torre, J., & Sorrel, M. A. (2025). A General Diagnostic Modeling Framework for Forced-Choice Assessments. British Journal of Mathematical and Statistical Psychology.

Examples


library(GDINA)
set.seed(123)
Q.items <- do.call("rbind", replicate(5, diag(5), simplify = FALSE)) # Q-matrix for the unidimensional statements
GS <- cbind(runif(n = nrow(Q.items), min = 0.1, max = 0.3), runif(n = nrow(Q.items), min = 0.1, max = 0.3)) # Guessing and slip parameter for each statement
n.blocks <- 30 # Number of forced-choice blocks

#----------------------------------------------------------------------------------------
# Illustration with simulated data using only direct statements (i.e., homopolar blocks)
#----------------------------------------------------------------------------------------

polarity <- matrix(1, nrow = n.blocks, ncol = 2) # Block polarity (1 = direct statement; -1 = indirect statement)
sim <- simFCGDINA(N = 1000, Q.items, n.blocks = n.blocks, polarity = polarity, model = "GDINA", GDINA.args = list(GS = GS), seed = 123)
Q <- sim$Q # Generated Q-matrix of forced-choice blocks
dat <- sim$dat # Generated responses
att <- sim$att # Generated attribute profiles

fit <- FCGDINA(dat = dat, Q = Q, polarity = polarity) # Fit the G-DINA model with EM estimation
ClassRate(personparm(fit$GDINA.obj), att) # Classification accuracy

#-------------------------------------------------------------------------------------------
# Illustration with simulated data using some inverse stataments (i.e., heteropolar blocks)
#-------------------------------------------------------------------------------------------

polarity <- matrix(1, nrow = n.blocks, ncol = 2)
polarity[sample(x = 1:(2*n.blocks), size = 15, replace = FALSE)] <- -1 # Including 15 inverse statements
sim <- simFCGDINA(N = 1000, Q.items, n.blocks = n.blocks, polarity = polarity, model = "GDINA", GDINA.args = list(GS = GS), seed = 123)
Q <- sim$Q
dat <- sim$dat
att <- sim$att

fit <- FCGDINA(dat = dat, Q = Q, polarity = polarity)
ClassRate(personparm(fit$GDINA.obj), att)

#------------------------------------------------------------
# Illustration of the FC-DCM (Huang, 2023) via BM estimation
#------------------------------------------------------------

priors <- list("Minimum" = c(1, 1), # Non-informative prior, Beta(1, 1), for latent group with ideal response = 0
               "Intermediate" = c(1e8, 1e8), # Extremely informative prior, Beta(1e8, 1e8), for latent groups with ideal response = 0.5
               "Maximum" = c(1, 1)) # Non-informative prior, Beta(1, 1), for latent group with ideal response = 1
fit <- FCGDINA(dat = dat, Q = Q, polarity = polarity, polarity.prior = priors, verbose = 0)
ClassRate(fit$GDINA.obj$EAP, att)

Pablo-Najera/cdmTools documentation built on April 14, 2025, 10:49 a.m.