Structural models for diagnostic classification

Structural models define how the attributes are related to one another. The currently supported options for structural models are: unconstrained, independent attributes, log-linear, hierarchical diagnostic classification model (HDCM), and, Bayesian network. See details for additional information on each model.

Usage

unconstrained()

independent()

loglinear(max_interaction = Inf)

hdcm(hierarchy = NULL)

bayesnet(hierarchy = NULL)

Arguments

max_interaction: For the log-linear structural model, the highest structural-level interaction to include in the model.
hierarchy: Optional. If present, the quoted attribute hierarchy. See vignette("dagitty4semusers", package = "dagitty") for a tutorial on how to draw the attribute hierarchy.

Value

A structural model object.

Details

The unconstrained structural model places no constraints on how the attributes relate to each other. This is equivalent to a saturated model described by Hu & Templin (2020) and in Chapter 8 of Rupp et al. (2010).

The independent attributes model assumes that the presence of the attributes are unrelated to each other. That is, there is no relationship between the presence of one attribute and the presence of any other. For an example of independent attributes model, see Lee (2016).

The loglinear structural model assumes that class membership proportions can be estimated using a loglinear model that includes main and interaction effects (see Xu & von Davier, 2008). A saturated loglinear structural model includes interaction effects for all attributes measured in the model, and is equivalent to the unconstrained structural model and the saturated model described by Hu & Templin (2020) and in Chapter 8 of Rupp et al. (2010). A reduced form of the loglinear structural model containing only main effects is equivalent to an independent attributes model (e.g. Lee, 2016).

The hierarchical attributes model assumes some attributes must be mastered before other attributes can be mastered. For an example of the hierarchical attributes model, see Leighton et al. (2004) and Templin & Bradshaw (2014).

The Bayesian network model defines the statistical relationships between the attributes using a directed acyclic graph and a joint probability distribution. Attribute hierarchies are explicitly defined by decomposing the joint distribution for the latent attribute space into a series of marginal and conditional probability distributions. The unconstrained structural model described in Chapter 8 of Rupp et al. (2010) can be parameterized as a saturated Bayesian network (Hu & Templin, 2020). Further, structural models implying an attribute hierarchy are viewed as nested models within a saturated Bayesian network (Martinez & Templin, 2023).

References

Hu, B., & Templin, J. (2020). Using diagnostic classification models to validate attribute hierarchies and evaluate model fit in Bayesian Networks. Multivariate Behavioral Research, 55(2), 300-311. doi:10.1080/00273171.2019.1632165

Lee, S. Y. (2016). Cognitive diagnosis model: DINA model with independent attributes. https://mc-stan.org/documentation/case-studies/dina_independent.html

Leighton, J. P., Gierl, M. J., & Hunka, S. M. (2004). The attribute hierarchy method for cognitive assessment: A variation on Tatsuoka's rule-space approach. Journal of Educational Measurement, 41(3), 205-237. doi:10.1111/j.1745-3984.2004.tb01163.x

Martinez, A. J., & Templin, J. (2023). Approximate Invariance Testing in Diagnostic Classification Models in the Presence of Attribute Hierarchies: A Bayesian Network Approach. Psych, 5(3), 688-714. doi:10.3390/psych5030045

Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic measurement: Theory, methods, and applications. Guilford Press.

Templin, J. L., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79(2), 317-339 doi:10.1007/s11336-013-9362-0

Xu, X., & von Davier, M. (2008). Fitting the structured general diagnostic model to NAEP data (RR-08-27). Princeton, NJ: Educational Testing Service.

Examples

unconstrained()
#> <dcmstan::UNCONSTRAINED>
#>  @ model     : chr "unconstrained"
#>  @ model_args: list()

independent()
#> <dcmstan::INDEPENDENT>
#>  @ model     : chr "independent"
#>  @ model_args: list()

loglinear()
#> <dcmstan::LOGLINEAR>
#>  @ model     : chr "loglinear"
#>  @ model_args:List of 1
#>  .. $ max_interaction: num Inf

loglinear(max_interaction = 1)
#> <dcmstan::LOGLINEAR>
#>  @ model     : chr "loglinear"
#>  @ model_args:List of 1
#>  .. $ max_interaction: num 1

hdcm(hierarchy = "att1 -> att2 -> att3")
#> <dcmstan::HDCM>
#>  @ model     : chr "hdcm"
#>  @ model_args:List of 1
#>  .. $ hierarchy: chr "att1 -> att2 -> att3"

bayesnet(hierarchy = "att1 -> att2 -> att3")
#> <dcmstan::BAYESNET>
#>  @ model     : chr "bayesnet"
#>  @ model_args:List of 1
#>  .. $ hierarchy: chr "att1 -> att2 -> att3"