valQ: Empirical Q-matrix validation

In Pablo-Najera/cdmTools: Useful Tools for Cognitive Diagnosis Modeling

Empirical Q-matrix validation

Description

Empirical Q-matrix validation using the Hull method (Nájera, Sorrel, de la Torre, & Abad, 2020a). The procedure can be used either with the PVAF (de la Torre & Chiu, 2016) or McFadden's pseudo R-squared (McFadden, 1974). The PVAF is recommended (Nájera, Sorrel, de la Torre, & Abad, 2020a). Note that the pseudo R-squared might not be computationally feasible for highly dimensional Q-matrices, say more than 10 attributes. Different iterative implementations are available, such as the test-level implementation (see Terzi & de la Torre, 2018), attribute-test-level implementation (Nájera, Sorrel, de la Torre, & Abad, 2020a), and item-level implementation (Nájera, Sorrel, de la Torre, & Abad, 2020b). If an iterative implementation is used, the GDINA R package (Ma & de la Torre, 2020) is used for the calibration of the CDMs.

Usage

valQ(
  fit,
  index = "PVAF",
  iterative = "test.att",
  emptyatt = TRUE,
  maxitr = 100,
  CDMconv = 1e-04,
  verbose = TRUE
)

Arguments

fit	A G-DINA model fit object from the GDINA package (Ma & de la Torre, 2020).
index	What index to use. It includes "PVAF" or "R2". The default is "PVAF".
iterative	(Iterative) implementation procedure. It includes "none" (for non-iterative), "test" (for test-level iterations), "test.att" (for attribute-test-level), and "item" (for item-level iterations). The default is "test.att".
emptyatt	Is it possible for the suggested Q-matrix to have an empty attribute (i.e., an attribute not measured by any item)? Although rarely, it is possible for iterative procedures to provide a suggested Q-matrix in which one or more attributes are empty. This might indicate that the original Q-matrix had more attributes than necessary. If FALSE, then at least one item (i.e., the one that is most likely) will measure each attribute in the suggested Q-matrix. The default is TRUE.
maxitr	Maximum number of iterations if an iterative procedure has been selected. The default is 100.
CDMconv	Convergence criteria for the CDM estimations between iterations (only if an iterative procedure has been selected). The default is 0.0001.
verbose	Print information after each iteration if an iterative procedure is used. The default is TRUE.

Value

valQ returns an object of class valQ.

sug.Q

Suggested Q-matrix (matrix).

Q

Original Q-matrix (matrix).

sugQ.fit

Several fit indices from the model obtained with the suggested Q-matrix (vector).

index

PVAF or pseudo R-squared (depending on which one was used) for each item (matrix).

iter.Q

Q-matrices used in each iteration (list). Provided only if an iterative procedure has been used.

iter.index

PVAF or pseudo R-squared (depending on which one was used) for each item in each iteration (list). Provided only if an iterative procedure has been used.

n.iter

Number of iterations used (double). Provided only if an iterative procedure has been used.

convergence

Convergence information (double). It can be 1 (convergence), 2 (lack of convergence: maximum number of iterations achieved), 3 (lack of convergence: empty attribute obtained), and 4 (lack of convergence: loop Q-matrices). Provided only if an iterative procedure has been used.

time

Initial and finish time (vector).

time.used

Total computation time (difftime).

specifications

Function call specifications (list).

Author(s)

Pablo Nájera, Universidad Pontificia Comillas
Miguel A. Sorrel, Universidad Autónoma de Madrid
Francisco J. Abad, Universidad Autónoma de Madrid

References

de la Torre, J., & Chiu, C.-Y. (2016). A general method of empirical Q-matrix validation. Psychometrika, 81, 253-273. https://doi.org/10.1007/s11336-015-9467-8

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

McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in Economics (pp. 105-142). Academic Press.

Nájera, P., Sorrel, M. A., de la Torre, J., & Abad, F. J. (2020a). Balancing fit and parsimony to improve Q-matrix validation. British Journal of Mathematical and Statistical Psychology. https://doi.org/10.1111/bmsp.12228

Nájera, P., Sorrel, M. A., de la Torre, J., & Abad, F. J. (2020b). Improving robustness in Q-matrix validation using an iterative and dynamic procedure. Applied Psychological Measurement, 46, 431-446. https://doi.org/10.1177/0146621620909904

Terzi, R., & de la Torre, J. (2018). An iterative method for empirically-based Q-matrix validation. International Journal of Assessment Tools in Education, 5, 248-262. https://doi.org/10.21449/ijate.407193

Examples

library(GDINA)
dat <- sim30GDINA$simdat
Q <- sim30GDINA$simQ # Generating Q-matrix
miss.Q <- missQ(Q = Q, qjk = .30, retainJ = 5, seed = 123)$miss.Q # Misspecified Q-matrix
fit <- GDINA(dat, miss.Q) # GDINA object
sug.Q <- valQ(fit = fit, verbose = TRUE) # Hull method for Q-matrix validation
mean(sug.Q$sug.Q == Q) # Check similarity with the generating Q-matrix

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