# Cognitive Diagnosis Method via Q-Matrix-Embedded Neural Networks
## 3 Experiments and Results
### Real Data Illustration
#### 3.3.2 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Data** & \(N\) & **Metrics** & **DINA** & **GDINA** & **NPC** & **GNPC** & **MLP** & **ANN** &
\begin{tabular}{c} **Dual** \\ **Q-Net** \\ \end{tabular} \\ \hline \multirow{8}{*}{EPTT} & \multirow{3}{*}{100} & AAR & 0.953 & 0.960 & 0.940 & 0.938 & 0.977 & 0.978 & 0.987 \\  & & PAR(\(K_{e}\)) & 0.840 & 0.862 & 0.809 & 0.773 & 0.914 & 0.915 & 0.953 \\  & & PAR(\(K_{e}-1\)) & 0.972 & 0.981 & 0.957 & 0.981 & 0.996 & 0.995 & 0.996 \\ \cline{2-10}  & \multirow{3}{*}{200} & AAR & 0.961 & 0.972 & 0.944 & 0.946 & 0.968 & 0.974 & 0.983 \\  & & PAR(\(K_{e}\)) & 0.861 & 0.903 & 0.818 & 0.800 & 0.881 & 0.903 & 0.937 \\  & & PAR(\(K_{e}-1\)) & 0.985 & 0.986 & 0.961 & 0.987 & 0.991 & 0.993 & 0.994 \\ \cline{2-10}  & \multirow{3}{*}{300} & AAR & 0.962 & 0.983 & 0.940 & 0.942 & 0.969 & 0.973 & 0.985 \\  & & PAR(\(K_{e}\)) & 0.865 & 0.937 & 0.808 & 0.781 & 0.887 & 0.899 & 0.943 \\  & & PAR(\(K_{e}-1\)) & 0.982 & 0.994 & 0.956 & 0.986 & 0.991 & 0.992 & 0.997 \\ \hline \multirow{8}{*}{FRAC} & \multirow{3}{*}{100} & AAR & 0.935 & 0.882 & 0.850 & 0.857 & 0.956 & 0.955 & 0.979 \\  & & PAR(\(K_{f}\)) & 0.606 & 0.416 & 0.388 & 0.351 & 0.699 & 0.687 & 0.837 \\  & & PAR(\(K_{f}-1\)) & 0.895 & 0.725 & 0.686 & 0.663 & 0.951 & 0.958 & 0.993 \\ \cline{2-10}  & \multirow{3}{*}{200} & AAR & 0.956 & 0.886 & 0.850 & 0.829 & 0.962 & 0.963 & 0.973 \\  & & PAR(\(K_{f}\)) & 0.733 & 0.430 & 0.397 & 0.300 & 0.739 & 0.741 & 0.806 \\  & & PAR(\(K_{f}-1\)) & 0.932 & 0.753 & 0.688 & 0.601 & 0.965 & 0.967 & 0.977 \\ \cline{2-10}  & \multirow{3}{*}{300} & AAR & 0.969 & 0.873 & 0.845 & 0.831 & 0.969 & 0.970 & 0.976 \\ \cline{2-10}  & & PAR(\(K_{f}\)) & 0.787 & 0.363 & 0.392 & 0.317 & 0.779 & 0.786 & 0.826 \\ \cline{2-10}  & & PAR(\(K_{f}-1\)) & 0.967 & 0.700 & 0.684 & 0.594 & 0.978 & 0.980 & 0.981 \\ \hline \hline \end{tabular} Note: \(N\) denotes the sample size of the subdataset. The symbols \(K_{e}\) and \(K_{f}\) denote the number of skills examined in the datasets EPTT and FRAC, respectively, where \(K_{e}=4\) and \(K_{f}=8\). PAR(\(k\)) represents the agreement rate for two vectors of length \(K\) that have \(k\) identical elements in them.  
\end{table} 
Table 4: Performance statistics of different methods on various real datasets. In terms of PAR, the trends in the scores of the individual models were generally consistent with those for AAR. For PAR(\(K\)), the models overall scored higher on the EPTT dataset. For PAR(\(K-1\)), the classical models maintained higher scores on the EPTT dataset. However, the neural-network-based methods did not strictly follow this pattern. On the same dataset, models usually scored lower for PAR (\(K\)) than for AAR. The models' scores for PAR(\(K-1\)) did not follow this pattern strictly, which suggests that classification errors are inevitable in real-world practice and that relaxing assessment conditions appropriately may be a more pragmatic method of evaluation. In addition, the scores of the classical methods for PAR(\(K-1\)) did not strictly follow the increase in scores with increasing sample size.