Ability-Residual Decoupled Modeling for Affective Cognitive Diagnosis

Boyuan Zhao; Meng Ye

cs.AISep 18, 2026

Ability-Residual Decoupled Modeling for Affective Cognitive Diagnosis

Authors: Boyuan Zhao, Meng Ye

Organizations: Key Laboratory of Modern Teaching Technology, Shaanxi Normal University, 199 Chang’an South Road, Xi’an, 710062, Shaanxi, China.

Abstract

Cognitive diagnosis infers students' concept mastery from response logs. However, students' responses are not determined by mastery alone: non-cognitive factors such as emotion, engagement, and fatigue can also affect performance. Affective cognitive diagnosis therefore extends conventional cognitive diagnosis by incorporating affective states. Existing methods often assume that the cognitive diagnosis backbone has already explained ability, item, and concept effects, so the remaining errors can be attributed mainly to affect. We argue that this assumption can be insufficient in real educational data: item calibration bias, systematic concept bias, personalized student-concept deviations, and latent student-item matching can form stable cognitive residuals. Without an explicit modeling pathway, these residuals may leak into affective representations, producing affect contamination. To address this problem, we propose an ability-residual decoupled framework for affective cognitive diagnosis. The model first captures unmodeled cognitive residuals through student, item, concept, student-concept, and low-rank student-item components, and then uses an affective module to modulate guess/slip effects. A Q-matrix-constrained concept residual attention mechanism adaptively aggregates only item-relevant concept residuals. Experiments on ASSIST2017, ASSIST2012, ASSIST2009, and Junyi with six cognitive diagnosis backbones show response-prediction gains across the reported comparisons and generally improved affect alignment when affect labels are available. Ablation studies, leakage probes, principal component analysis visualization, long-tail analysis, and case studies further indicate that ability residuals absorb stable cognitive bias, reduce cognitive contamination in the affective branch, and enhance the robustness and predictive accuracy of cognitive diagnosis models.

Figures & tables

Figure 1: Schematic illustration of affect contamination and ability-residual decoupling. Panel (a) illustrates that a student’s observed response to an exercise may reflect both cognitive ability and affective state. Panel (b) illustrates the proposed allocation of modeling roles: stable cognitive residual variation is assigned to the ability-residual pathway, reducing its leakage into the affective branch and allowing the affective representation to focus on non-cognitive modulation.

Figure 2: Overall ARACD algorithmic framework and ability residual module.

Symbol	Meaning
$s$	The student in the considered student–item pair
$i$	The item in the considered student–item pair
$k$	The $k$ -th concept
$\mathbf{q}_{i}$	Concept mask of item $i$
$\mathcal{K}_{i}$	The set of concepts involved in item $i$ , $\mathcal{K}_{i}=\{k:q_{ik}=1\}$
$b_{s}$	Stable offset indicating that student $s$ is more or less likely than the overall level to answer correctly

Table 1: Main notation used in the ability residual decomposition and concept residual attention.

Backbone	Method	ASSIST2017				ASSIST2012
Backbone	Method	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$
DINA	Base	0.6471	0.6950	0.4681	0.4383	0.7118	0.6923	0.4401	0.3654
	ACD	0.7103	0.7760	0.4374	0.4008	0.7352	0.7397	0.4234	0.3489
	ARACD	0.7390	0.8079	0.4202	0.3449	0.7494	0.7609	0.4139	0.3340
IRT	Base	0.6582	0.7224	0.4668	0.4086	0.7286	0.7242	0.4289	0.3440
	ACD	0.7152	0.7843	0.4338	0.3732	0.7401	0.7518	0.4194	0.3354

Table 5: Response prediction results on ASSIST2017 and ASSIST2012.

Backbone	Method	ASSIST2009				Junyi
Backbone	Method	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$
DINA	Base	0.7015	0.7206	0.4590	0.4473	0.7281	0.7115	0.4334	0.3866
	CACD	0.7240	0.7513	0.4344	0.3935	0.7456	0.7539	0.4100	0.3575
	ARCACD	0.7786	0.8396	0.3896	0.2799	0.7658	0.7582	0.4013	0.3298
IRT	Base	0.7175	0.7354	0.4391	0.3979	0.7335	0.7207	0.4113	0.3554
	CACD	0.7255	0.7571	0.4289	0.3581	0.7686	0.7583	0.4009	0.3284

Table 6: Response prediction results on ASSIST2009 and Junyi.

Backbone	Method	ASSIST2017		ASSIST2012
Backbone	Method	Affect RMSE $\downarrow$	Affect MAE $\downarrow$	Affect RMSE $\downarrow$	Affect MAE $\downarrow$
DINA	ACD	0.2614	0.1914	0.2184	0.1502
DINA	ARACD	0.1990	0.1489	0.1937	0.1239
IRT	ACD	0.2461	0.1785	0.2453	0.1792
IRT	ARACD	0.1925	0.1389	0.1919	0.1179
MIRT	ACD	0.2640	0.1900	0.2495	0.1814

Table 7: Affect alignment results under real affect labels.

Variant	ASSIST2017						ASSIST2012
Variant	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	Affect RMSE $\downarrow$	Affect MAE $\downarrow$	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	Affect RMSE $\downarrow$	Affect MAE $\downarrow$
Full ARACD	0.7394	0.8078	0.4203	0.3461	0.1944	0.1409	0.7487	0.7617	0.4138	0.3316	0.1922	0.1196
Only stu-item residual	0.7385	0.8051	0.4219	0.3494	0.1988	0.1456	0.7444	0.7537	0.4170	0.3328	0.1942	0.1210
Only concept residual	0.7288	0.7994	0.4286	0.3839	0.2082	0.1484	0.7457	0.7526	0.4156	0.3321	0.1973	0.1258
w/o ability residual	0.7230	0.7938	0.4296	0.4018	0.2266	0.1640	0.7421	0.7502	0.4185	0.3336	0.2422	0.1703

Table 8: Hierarchical ablation of supervised ability residual layers on ASSIST2017 and ASSIST2012.

Variant	ASSIST2009				Junyi
Variant	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	ACC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$
Full ARCACD	0.7884	0.8487	0.3823	0.2740	0.7682	0.7596	0.4007	0.3232
Only stu-item residual	0.7804	0.8388	0.3872	0.2909	0.7599	0.7517	0.4045	0.3354
Only concept residual	0.7333	0.7872	0.4116	0.3388	0.7636	0.7478	0.4032	0.3338
w/o ability residual	0.7253	0.7573	0.4332	0.3845	0.7396	0.7277	0.4289	0.3705

Table 9: Hierarchical ablation of ability residual layers on ASSIST2009 and Junyi.

Panel of Figure 3 — Figure 3: Sensitivity to the concept-attention dimension $d_{att}$ with fixed $rank=1024$ . Panels (a) and (b) report ACC/AUC and RMSE/MAE; panel (c) reports Affect RMSE/MAE.

Panel of Figure 4 — Figure 4: Sensitivity to the student-item low-rank dimension $rank$ with fixed $d_{att}=16$ . Panels (a) and (b) report ACC/AUC and RMSE/MAE; panel (c) reports Affect RMSE/MAE.

Figure 5: Ability-residual interaction maps for ASSIST2017, ASSIST2012, ASSIST2009, and Junyi.

Figure 6: Contamination leakage probe of the affective branch.

Figure 7: PCA visualization of supervised ARACD affective representations on ASSIST2017, colored by ability-residual group (left) and response label (right).

Affect dim	Abs corr. with abs residual $\downarrow$	Abs corr. with response $\uparrow$
0	0.1167	0.2114
1	0.0958	0.2081
2	0.0785	0.1933
3	0.0052	0.0011

Table 11: Absolute correlations between supervised ARACD affect dimensions and residuals/response labels.

Panel of Figure 8 — Figure 8: Student-level case study for S453. Panels (a)–(c) show probability trajectories, ARACD error reduction over ACD, and residual decomposition.

Figure 9: Student-level affect analysis for S453. Mean values of the four observed affect dimensions are compared with ACD and ARACD predictions.

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Digital learning environments record learners' responses to individual items, making it possible to study the development of specific skills rather than overall scores. Drawing conclusions about learning from these data requires a model that links responses to latent skills and tracks how mastery changes over time. When the skills measured by each item are unknown, the analyst must decide whether to estimate this structure, the Q-matrix, jointly with the learning process, or to establish it first and study learning afterwards. We show that this decision can change substantive conclusions about how learners develop. Using dynamic cognitive diagnostic models, we analyse data from two reading games measuring vocabulary and comprehension from Grade 2 to Grade 3, with item-text embeddings providing prior information for the unknown Q-matrix. A joint analysis and a bias-corrected stepwise analysis agree that most learners move toward mastering both skills, but disagree about how many remain only partially proficient at Grade 3, changing how reading progress would be reported. A simulation study identifies when the two analyses diverge and shows that joint analysis is more reliable when the item-skill structure is uncertain and the item pool changes between grades. We provide R code for both analyses.

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Abstract

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