Bayesian DINA Modeling Incorporating Within-Item Characteristic Dependency

Abstract

The within-item characteristic dependency (WICD) means that dependencies exist among different types of item characteristics/parameters within an item. The potential WICD has been ignored by current modeling approaches and estimation algorithms for the deterministic inputs noisy ''and'' gate (DINA) model. To explicitly model WICD, this study proposed a modified Bayesian DINA modeling approach where a bivariate normal distribution was employed as a joint prior distribution for correlated item parameters. Simulation results indicated that the model parameters were well recovered and that explicitly modeling WICD improved model parameter estimation accuracy, precision, and efficiency. In addition, when potential item blocks existed, the proposed modeling approach still demonstrated good performance and high robustness. Furthermore, the fraction subtraction data were analyzed to illustrate the application and advantage of the proposed modeling approach.

Deterministic Inputs, Noisy Mixed Modeling for Identifying Coexisting Condensation Rules

“…Figure 1 summarizes the recovery of attributes (details can be found in Table S1 in online supplements). Referencing previous studies of CDMs with unstructured LSM (e.g., Zhan, Jiao, Liao et al, 2019), the classification accuracy of the DINMix model under different conditions is good enough and in line with expectations. Furthermore, increasing the test length and item quality yielded higher classification accuracy.…”

“…Ways to incorporate attribute-level aberrant responses into the proposed model are worthy of further research, as Equation 11 in de la Torre (2011) seems to give us a reference. Second, within-item characteristic dependency (Zhan, Jiao, Liao et al, 2019), which means that the dependency exists between the guessing and slip parameters within an item, was not considered in the proposed model. It can be incorporated into the proposed model to increase the estimation accuracy of the item parameters in a future study.…”

“…These settings led the guessing and slip probabilities for all items to follow a positively skewed distribution (mean ≈ 0.1, minimum ≈ 0.01, and maximum ≈ 0.6 for higher-quality, and mean ≈ 0.2, minimum ≈ 0.05, and maximum ≈ 0.7 for lower-quality). Assuming guessing and slip parameters follow a negative correlation is more realistic (Zhan, Jiao, Liao, & Bian, 2019). In addition, (d) the type of item-level mixing proportions (TM) at two levels of uniform and skew mixing was manipulated.…”

Cognitive Diagnosis Modeling Incorporating Item-Level Missing Data Mechanism

“…In Simulation 1, three factors were manipulated, including ( a ) sample sizes ( N ) at two levels of 500 and 1,000; ( b ) test length ( I ) at two levels of 15 and 30; and ( c ) the probability of missingness for each item, high missingness (HM) and low missingness (LM). Five attributes ( K = 5) were measured and the simulated Q matrices for two test length I = 15 and I = 30 were given in Figure 1 , which were used in Zhan et al ( 2018b ). Most of the model parameters were assigned by referring to the real data analysis presented in Zhan et al ( 2018a ).…”

The Impact of Sample Attrition on Longitudinal Learning Diagnosis: A Prolog

“…In such a case, the aberrant response (i.e., guessing and slipping) probabilities are approximately equal to 0.1. In addition, the results of Zhan et al (2019b) indicate that assuming guessing and slipping parameters to follow a negative correlation is more realistic. Thus, nonanchor item parameters were generated from a bivariate normal distribution with a negative correlation coefficient as follows:…”