# Cognitive Diagnosis Method via Q-Matrix-Embedded Neural Networks
## 3 Experiments and Results
### Real Data Illustration  
#### 3.3.1 Real Datasets  
In order to better validate the effectiveness of the cognitive diagnosis method proposed in this paper, in addition to applying artificially simulated data, we also conducted experiments on real data and tested its performance. For the real dataset, we chose the \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & \multirow{2}{*}{\(\mathbf{N}\)} & \multirow{2}{*}{**DINA**} & \multirow{2}{*}{**GDINA**} & \multirow{2}{*}{**NPC**} & \multirow{2}{*}{**GNPC**} & \multirow{2}{*}{**MLP**} & \multirow{2}{*}{**ANN**} & \multicolumn{2}{c}{**Dual**} \\  & & & & & & & & & **Q-Net** \\ \hline \multirow{4}{*}{HSD1} & 100 & 0.975 & 0.965 & 0.971 & 0.971 & 0.977 & 0.983 & 0.984 \\  & 200 & 0.978 & 0.974 & 0.974 & 0.974 & 0.981 & 0.985 & 0.986 \\  & 300 & 0.974 & 0.972 & 0.972 & 0.972 & 0.972 & 0.981 & 0.983 \\  & 500 & 0.977 & 0.976 & 0.974 & 0.976 & 0.976 & 0.982 & 0.984 \\ \hline \multirow{4}{*}{ LSD1} & 100 & 0.620 & 0.545 & 0.669 & 0.627 & 0.709 & 0.720 & 0.741 \\  & 200 & 0.680 & 0.597 & 0.679 & 0.640 & 0.690 & 0.700 & 0.729 \\  & 300 & 0.682 & 0.615 & 0.674 & 0.643 & 0.681 & 0.689 & 0.707 \\  & 500 & 0.724 & 0.644 & 0.678 & 0.648 & 0.680 & 0.685 & 0.710 \\ \hline \multirow{4}{*}{HSD2} & 100 & 0.271 & 0.914 & 0.240 & 0.808 & 0.990 & 0.987 & 0.985 \\  & 200 & 0.224 & 0.935 & 0.241 & 0.870 & 0.611 & 0.983 & 0.985 \\  & 300 & 0.193 & 0.946 & 0.236 & 0.899 & 0.965 & 0.974 & 0.982 \\  & 500 & 0.206 & 0.958 & 0.239 & 0.958 & 0.968 & 0.976 & 0.982 \\ \hline \multirow{4}{*}{ LSD2} & 100 & 0.212 & 0.362 & 0.234 & 0.401 & 0.760 & 0.766 & 0.856 \\  & 200 & 0.146 & 0.421 & 0.216 & 0.434 & 0.736 & 0.775 & 0.847 \\ \cline{1-1}  & 300 & 0.164 & 0.456 & 0.224 & 0.425 & 0.664 & 0.716 & 0.802 \\ \cline{1-1}  & 500 & 0.138 & 0.499 & 0.222 & 0.423 & 0.624 & 0.677 & 0.746 \\ \hline \hline \end{tabular} Note: \(N\) denotes the sample size of the simulated dataset.  
\end{table} 
Table 3: PAR classification agreement rate between different methods on the simulated dataset. widely-used fractional subtraction dataset (FRAC [27]) and the elementary probability test theory assessment (EPTT [28]). The original fractional subtraction dataset contains 536 student responses. Its Q-matrix in this study, which consists of 20 items and 8 skills, was the same as the one used in the original in Table 8 in the study of [29]. The skill labels (\(a_{1}\)) convert a whole number to a fraction; (\(a_{2}\)) separate a whole number from a fraction; (\(a_{3}\)) simplify before subtracting; (\(a_{4}\)) find a common denominator; (\(a_{5}\)) borrow from the whole number part; (\(a_{6}\)) perform column borrowing to subtract the second numerator from the first; (\(a_{7}\)) subtract numerators; and (\(a_{8}\)) reduce answers to the simplest form. The elementary probability test theory assessment dataset consists of 12 probability items and included 504 students. This dataset examines four skills, as follows: (cp) the probability of the complement of an event; (id) two independent events; (pb) the probability of an event; and (un) the union of two disjoint events. The Q-matrix employed in this study aligned with that utilized by [PERSON] et al., as presented in Table 7 of their article [14]. For the real datasets mentioned above, it should be noted that the response data from the students and the Q-matrix can be obtained from the R _edmdata_ package 1.2.0 [30]. Since there is no ground truth for these real datasets from EPTT and FRAC, we selected the predictions of the best-fit parametric model as a benchmark by incorporating the model fit parameters AIC and BIC [31]. On the EPTT dataset, the fitting results indicated lower AIC and BIC scores for the GDINA model, while on the FRAC dataset, the DINA model demonstrated lower scores. Therefore, the benchmark for the EPTT dataset was based on the results of the GDINA model, and for the FRAC dataset, the benchmark was based on the results of the DINA model.