R: Empirical Q-matrix validation

valQ {cdmTools}

R Documentation

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

[Package cdmTools version 1.0.5 Index]