# Evaluation and Prediction of Higher Education System Based on AHP-TOPSIS and LSTM Neural Network
## 5 Performance Evaluation
### Comparison with Other Models  
In order to further determine the accuracy and complexity of the model, we compare the predicted results with those from existing models. In order to do so, we need to define the criteria when comparing different models. The criteria for determining the quality of a model mainly refer to two indicators: one is accuracy, and the other is complexity. They are usually contradictory. An increasing number of variables improves model accuracy but leads to a more complex model which may be in danger of over-fitting. Furthermore, less accurate models may be incapable of an adequate description of the dataset. Therefore, we attempt to find a balance between accuracy and complexity, usually with accuracy first and complexity second. From the previous investigations of existing models, we note that those studies mainly focus on a single indicator of a large higher education system, such as financial investment scale [30], population growth [31] or higher education popularization [32]. Their research methods are also one-dimensional, such as the auto-regressive integrated moving average (ARIMA) model [33] or regression model. In comparison with our comprehensive model, these existing models yield less accurate results but reduce computational complexity without considerations of multiple factors. To further illustrate accuracy and complexity, we choose China as an example again. When selecting the indicators for comparison, the existing models often use gross enrollment rate as an evaluation indicator. We determine that two models with close prediction ranges and indicators are better to be compared. In this section, our LSTM prediction model is compared with existing models, such as the rolling regression models proposed by [PERSON] et al. [34] and the logarithmic prediction model proposed by [PERSON] et al. [35]. Based on the statistics of higher education scale over the years, [PERSON] et al. [34] constructed a variety of fitting models to simultaneously predict  
Figure 12: Prediction results and corresponding RMSE values. and compare the results of various methods to reduce random errors in method selection. Finally, by comparing the coefficient of determination \(R^{2}\) of different prediction models, four rolling regression models (logarithmic, inverse, quadric and cubic) with relatively high \(R^{2}\) values are applied to predict the gross enrollment rate from 2013 to 2030. In the case of the logarithmic prediction model, [PERSON] et al. [35] proposed a model based on economic level to predict the gross enrollment rate and number of students in higher education from 2016 to 2032. They also used various regression models to reduce errors and more accurately predict the development of higher education. Combined with the judgment coefficient R2 and F value, the logarithmic model has the best-fitting degree; the prediction results are relatively close to the real data. Therefore, the logarithmic curve is finally chosen as the model for predicting the development of higher education. Combined with the prediction time range of each model, in order to ensure that the data of each model are fully utilized, we select the data from 2013 to 2032 for comparison. Then, we replace the missing data from 2013 to 2018 in our model with real data. The comparison between the predicted results of the existing model and those of our designed model is shown in Figure 13. Seen from Figure 13, the gross enrollment rates predicted by all models are apparently in rising trends. The predicted values of the four regression models designed by [PERSON] et al. [34] present little differences, which represent the standard deviations from the concentrated trend, but the average index tends to be the same. In addition, the average annual growth rates of the gross enrollment rates obtained by the models are also very similar. In addition, the predicted values of each model can be verified with one another, which shows that the results obtained by the time series method are consistent.