## 3 Results
### Logistic Regression Meta-Model  
We created the final model for predicting unemployment duration using the stacking method, incorporating the predictions of individual models (CART, CHAID, and discriminant analysis). These predictions were used as input variables (prefixed with pred-) along with a confidence measure from each model (prefixed with confidence-). This approach enabled us to create a more accurate model than the individual models alone. As observed in the previous models, each model exhibited accuracy in different categories. Hence, we supposed that combining these models could lead to an improved identification of the appropriate unemployment duration category. The final meta-model was created using logistic regression and predicts not only the category of the unemployment duration for individual jobseekers but also the probabilities of all unemployment categories according to duration. Subsequently, jobseekers are assigned to the unemployment duration category with the highest probability, or predetermined criteria based on these probabilities can be made to categorise the jobseekers. The following results were obtained using the highest probability as the determinant for categorising jobseekers. Table 15 provides details on the logistic regression model and its coefficients, with the reference category being the first category, that is _up to 3 months_. This model utilises the predictions and their confidence from the abovementioned models. Their importance in the final meta-model is depicted in Figure 4.  
Figure 4: Predictor importance in the final meta-model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Unemployment Duration** & **3-6 Months** & **6-12 Months** & **More than 12 Months** \\ \hline Intercept & \(-\)2.014 & 0.475 & \(-\)0.686 \\ pred-CART\_cat1 & 0.102 & \(-\)0.738 & \(-\)1.745 \\ pred-CART\_cat2 & 0.870 & \(-\)0.390 & \(-\)2.266 \\ pred-CART\_cat3 & 0.425 & \(-\)0.023 & \(-\)1.361 \\ confidence-CART & 0.759 & \(-\)2.932 & 3.768 \\ pred-CHAID\_cat1 & \(-\)0.074 & \(-\)0.451 & \(-\)2.591 \\ pred-CHAID\_cat2 & 0.602 & \(-\)0.054 & \(-\)1.861 \\ pred-CHAID\_cat3 & 0.380 & 0.336 & \(-\)1.820 \\ confidence-CHAID & 2.379 & 2.375 & 3.087 \\ pred-discriminant\_cat1 & \(-\)0.035 & \(-\)0.158 & \(-\)0.263 \\ pred-discriminant\_cat2 & 0.144 & \(-\)0.036 & \(-\)0.453 \\ pred-discriminant\_cat3 & 0.046 & 0.196 & \(-\)0.096 \\ confidence-discriminant & 0.474 & 0.414 & 0.971 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Coefficients of the logistic regression meta-model. Finally, we evaluated the final meta-model of logistic regression using the evaluation measures. The coincidence matrix for the testing set is shown in Table 16.  
The cumulative 4-field confusion matrix for this model is presented in Table 17. The rows show real situations, and the columns are the predictions of the unemployment duration category from the model. The final model achieved an average accuracy of 77.60% (both macro- and micro-average), indicating that the predictions obtained from the model were correct in almost 78% of cases. In the category of jobseekers who were potentially unemployed for more than 12 months, the model demonstrated a high accuracy of almost 92% and more than 91% precision. This implies that our model can accurately identify problematic jobseekers at risk of long-term unemployment. When the model predicted that a jobseeker would be unemployed for more than 12 months, this prediction was correct in more than 91% of cases. Moreover, the model also achieved high accuracy for jobseekers unemployed for 3-6 months and 6-12 months. Thus, if the model predicts these unemployment durations, it is likely to be correct in most cases. The sensitivity of the overall model in correctly identifying the appropriate category of unemployment duration was over 53% (macro-average) or over 55% (micro-average).